From 72fbed2bc3dce280eb6b39f6a2ec64eb369280d6 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 29 Jan 2026 21:19:59 +0300 Subject: [PATCH 01/25] feat(datastructures, binary-trees): sum nodes in range --- .../trees/binary/search_tree/__init__.py | 871 +---------------- .../binary/search_tree/binary_search_tree.py | 889 ++++++++++++++++++ .../trees/binary/tree/binary_tree.py | 17 + 3 files changed, 911 insertions(+), 866 deletions(-) create mode 100755 datastructures/trees/binary/search_tree/binary_search_tree.py diff --git a/datastructures/trees/binary/search_tree/__init__.py b/datastructures/trees/binary/search_tree/__init__.py index 64714baf..c8342547 100755 --- a/datastructures/trees/binary/search_tree/__init__.py +++ b/datastructures/trees/binary/search_tree/__init__.py @@ -1,867 +1,6 @@ -from typing import List, Any, Optional -from datastructures.trees.binary.node import BinaryTreeNode +from datastructures.trees.binary.search_tree.binary_search_tree import BinarySearchTree +from datastructures.trees.binary.search_tree.bst_iterator import ( + BinarySearchTreeIterator, +) -from datastructures.queues.fifo import FifoQueue -from datastructures.stacks.dynamic import DynamicSizeStack -from datastructures.trees import T -from datastructures.trees.binary.tree import BinaryTree - - -class BinarySearchTree(BinaryTree): - def __init__(self, root: Optional[BinaryTreeNode] = None): - super().__init__(root) - self.stack = DynamicSizeStack() - - def __len__(self) -> int: - if not self.root: - return 0 - - counter = 1 - stack = DynamicSizeStack() - stack.push(self.root) - - while not stack.is_empty(): - node = stack.pop() - - if node.left: - counter += 1 - stack.push(node.left) - - if node.right: - counter += 1 - stack.push(node.right) - - return counter - - @staticmethod - def construct_bst(items: List[T]) -> Optional["BinarySearchTree"]: - """ - Constructs a binary search tree from a sorted list of items. - - This method works by recursively finding the middle element of the list and assigning it to the root of the tree. - The left and right subtrees are then constructed by recursively calling the method on the left and right halves - of the list. - - @param items: A sorted list of items to construct the tree from. - @return: A binary search tree constructed from the items. - """ - if not items: - return None - - def construct_bst_helper(left: int, right: int) -> Optional[BinaryTreeNode]: - # base case for the method if the left is greater than the right - if left > right: - return None - - # Find the middle index - this element becomes the root - # Using (left + right) // 2 ensures we get the left-middle for even-length arrays - mid = (left + right) // 2 - root = BinaryTreeNode(items[mid]) - root.left = construct_bst_helper(left, mid - 1) - root.right = construct_bst_helper(mid + 1, right) - return root - - return BinarySearchTree(root=construct_bst_helper(0, len(items) - 1)) - - def insert_node(self, data: Optional[T]): - """ - Inserts a node in a BST given an element - If there is no root, then create a new root node with the data and return it - - If there is a root, then check the data against the root node's data and determine if it should go left or right - If the data is greater than the root node's data, then go right, if the data is less than the root node's data, - then go left. Repeat this operation, until we can insert the node in the right place. - """ - if not self.root: - self.root = BinaryTreeNode(data) - return - - def insert_helper(value: T, node: BinaryTreeNode) -> BinaryTreeNode: - if not node: - return BinaryTreeNode(data) - if value < node.data: - node.left = insert_helper(value, node.left) - else: - node.right = insert_helper(value, node.right) - return node - - if data: - insert_helper(data, self.root) - - def delete_node(self, key: T) -> Optional[BinaryTreeNode]: - """Deletes a node from the Binary Search Tree. If the node is found, it is deleted and the tree re-ordered to - remain a valid binary search tree. - - This will be typically an O(log(n) operation because deletion requires a search plus a few extra steps to deal - with any hanging children. - - Args: - key (T): Value to delete from binary search tree - - Return: - BinaryTreeNode: New root of binary search tree - """ - # nothing to delete here as root is none - if self.root is None: - return self.root - - def delete_helper( - value: T, node: Optional[BinaryTreeNode] - ) -> Optional[BinaryTreeNode]: - # base case when we have hit the bottom of the tree, and the parent node has no children - if node is None: - return None - # if the value to delete is less than or greater than the current node, we set the left or right child - # respectively to be the return value of a recursive call of this very method on the current node's left or - # right subtree - elif value < node.data: - node.left = delete_helper(value, node.left) - - # we return the current node (and its subtree if existent) to be used as the new value of its parent's - # left or right child - return node - elif value > node.data: - node.right = delete_helper(value, node.right) - return node - # if the current node is the one we want to delete - elif value == node.data: - # if the current node has no left child, we delete it by returning it's right child (and it's subtree if - # existent) to be its parent's new subtree - if node.left is None: - return node.right - # if the node has no left nor right child, this ends up being None as per the first line of code in this - # function - elif node.right is None: - return node.left - # if the current node has 2 children, we delete the current node by calling the lift function, which - # changes the current node's value to the value of it's successor node - else: - node.right = lift(node.right, node) - return node - return None - - def lift( - node: BinaryTreeNode, node_to_delete: BinaryTreeNode - ) -> BinaryTreeNode: - # if the current node of this function has a left child, we recursively call this function to continue down - # the left subtree to find the successor node - if node.left is not None: - node.left = lift(node.left, node_to_delete) - return node - # if the current node has no left child, that means the current node of this function is the successor node - # and we take its value and make it the new value of the node that we are deleting. - else: - node_to_delete.data = node.data - # we return the successor node's right child to be now used as its parent's left child - return node.right - - return delete_helper(key, self.root) - - @property - def height(self) -> int: - if self.root is None: - return 0 - - # if we don't have either left and right nodes from the root, we return 1 - if not self.root.left and not self.root.right: - return 1 - - height = 0 - queue = FifoQueue() - queue.enqueue(self.root) - - while True: - current_level_nodes = queue.size - - if current_level_nodes == 0: - return height - - height += 1 - - while current_level_nodes > 0: - node = queue.dequeue() - - if node.left is not None: - queue.enqueue(node.left) - - if node.right is not None: - queue.enqueue(node.right) - current_level_nodes -= 1 - - def next(self) -> int: - """ - Returns the next smallest number in a BST. - This involves two major operations. One is where we pop an element from the stack which becomes the next smallest element to return. This is a O(1) operation. - However, we then make a call to our helper function _leftmost_inorder which iterates over a bunch of nodes. This is clearly a linear time operation i.e. O(N) in the worst case. - However, the important thing to note here is that we only make such a call for nodes which have a right child. Otherwise, we simply return. - Also, even if we end up calling the helper function, it won't always process N nodes. They will be much lesser. Only if we have a skewed tree would there be N nodes for the root. - But that is the only node for which we would call the helper function. - - Thus, the amortized (average) time complexity for this function would still be O(1). We don't need to have a solution which gives constant time operations for every call. - We need that complexity on average and that is what we get. - """ - - # this is the smallest element in the BST - topmost_node = self.stack.pop() - - # if the node has a right child, call the helper function for the right child to - # get the next smallest item - # We don't need to check for the left child because of the way we have added nodes onto the stack. - # The topmost node either won't have a left child or would already have the left subtree processed. - # If it has a right child, then we call our helper function on the node's right child. - # This would comparatively be a costly operation depending upon the structure of the tree - if topmost_node.right: - self.__leftmost_inorder(topmost_node.right) - - return topmost_node.data - - def has_next(self) -> bool: - """ - Checks if the BST has items left. Since this uses a stack, then we simply check if the stack still has items. - This is used in an iterator approach to getting items from the BST. This returns True if there are items & False - otherwise, the Time Complexity here is O(1) - """ - return self.stack.is_empty() - - def __leftmost_inorder(self, root: BinaryTreeNode) -> None: - # Add all the nodes of the left most branch to the stack - while root: - self.stack.push(root) - root = root.left - - def find_largest(self, node: BinaryTreeNode) -> BinaryTreeNode: - """ - Simply finds the largest node in a BST. We walk rightward down the BST until the current node has no right child - and return it. This assumes that the Tree is a valid BST - :param node: root node, or current node - :return: Value of the largest node - :rtype: object - """ - current = node - while current: - if not current.right: - return current - current = current.right - - return current - - def find_second_largest(self) -> BinaryTreeNode: - """ - Finds the second largest node in the Binary Search Tree given a root node - :return: Value of the second largest Node - :rtype: object - """ - if not self.root or (not self.root.left and not self.root.right): - raise Exception("Tree must have at least 2 nodes") - - current = self.root - - while current: - # case: current is largest and has a left subtree - # 2nd largest is the largest in that subtree - if current.left and not current.right: - return self.find_largest(current.left) - - # case: current is parent of largest, and - # largest has no children, so - # current is 2nd largest - if current.right and not current.right.left and not current.right.right: - return current - - current = current.right - - return current - - def find_kth_largest(self, k: int) -> Optional[BinaryTreeNode]: - """ - Finds the kth largest value in a binary search tree. This uses a reverse in order traversal moving from right - to root to left until the kth largest node can be found. We don't have to traverse the whole tree since binary - search trees are already ordered following the property of the right subtree has nodes which have the left - sub-tree always less than their parent and the right subtree has nodes with values that are either equal to or - greater than the parent. With this property in mind, we perform a reverse in order traversal to be able to move - from right to root to left to find the kth largest node in the tree. - - Complexity: - Time: O(h + k): where h is the height of the tree and k is the input - Space: O(h): where h is the height of the tree. - - Args: - k (int): The kth largest value to find - Returns: - Optional[BinaryTreeNode]: The kth largest node - """ - - # This is a helper class that helps to track the algorithm's progress of traversing the tree - class TreeInfo: - def __init__(self): - self.number_of_nodes_visited: int = 0 - self.latest_visited_node: Optional[BinaryTreeNode] = None - - def reverse_in_order_traverse(node: BinaryTreeNode, tree_information: TreeInfo): - """ - Helper function to traverse the tree in reverse in order - Args: - node (BinaryTreeNode): The node to traverse - tree_information (TreeInfo): The tree information - """ - # base case: if node is None or we've already found the kth largest - if not node or tree_information.number_of_nodes_visited >= k: - return - - # traverse right subtree first for larger values - reverse_in_order_traverse(node.right, tree_information) - - # Visit the current node if we haven't found k nodes yet - if tree_information.number_of_nodes_visited < k: - tree_information.number_of_nodes_visited += 1 - tree_information.latest_visited_node = node - - # traverse the left subtree for smaller values if needed - reverse_in_order_traverse(node.left, tree_information) - - tree_info = TreeInfo() - reverse_in_order_traverse(self.root, tree_info) - return tree_info.latest_visited_node - - def find_closest_value_in_bst(self, target: T) -> Optional[BinaryTreeNode]: - """ - Finds the closest value in the binary search tree to the given target value. - - Args: - target T: Value to search for - Returns: - Node with the closest value to the target - """ - # edge case for empty nodes, if none is provided, we can't find a value that is close to the target - if not self.root: - return None - - # if the node's data is the target, exit early by returning it - if self.root.data == target: - return self.root - - # this keeps track of the minimum on both the left and the right - closest_node = self.root - min_diff = abs(target - self.root.data) - current = self.root - - # while the queue is not empty, we pop off nodes from the queue and check for their values - while current: - current_diff = abs(target - self.root.data) - - if current_diff < min_diff: - min_diff = current_diff - closest_node = current - - if current.data == target: - return current - - if target < current.data: - current = current.left - else: - current = current.right - - return closest_node - - def range_sum(self, low: int, high: int): - """ - returns the sum of datas of all nodes with a data in the range [low, high]. - - Example: - Input: root = [10,5,15,3,7,null,18], low = 7, high = 15 - Output: 32 - - Uses an iterative approach to solving the problem with Breadth First Search Traversal - - Complexity Analysis: - - Time Complexity: O(N), where N is the number of nodes in the tree - - Space Complexity: O(N) - - The stack will contain no more than 2 levels of the nodes. The maximal number of nodes in a binary tree is - N/2. Therefore, the maximal space needed for the stack is O(N) - """ - - ans = 0 - - stack = [self.root] - - while stack: - node = stack.pop() - - if node: - if low <= node.data <= high: - ans += node.data - - if low < node.data: - if node.left: - stack.append(node.left) - - if node.data < high: - if node.right: - stack.append(node.right) - - return ans - - def breadth_first_search(self) -> List[Any]: - """ - Performs a breadth first search through a Binary Tree - This will traverse the tree level by level and depth by depth. Using a Queue to put elements into the queue - """ - queue = FifoQueue() - - # start off by adding the root node - queue.enqueue(self.root) - - # while the queue is not empty, we want to traverse the tree and add elements to the queue, - while not queue.is_empty(): - current_node = queue.dequeue() - - if current_node.left: - queue.enqueue(current_node.left) - - if current_node.right: - queue.enqueue(current_node.right) - - def pre_order(self) -> List[Any]: - """ - Type of Depth First Traversal (DFS) for binary trees which will start at root node and proceed to the left - data and print it until it reaches the leaf(node with no more children) and then backtrack to the node and - check if the current node has a right child and print it. This will continue until all nodes have been - tracked and printed. - """ - result = [] - stack = DynamicSizeStack() - - if not self.root: - return result - - current = self.root - - while current or not stack.is_empty(): - while current: - result.append(current.data) - stack.push(current) - current = current.left - - current = stack.pop() - - current = current.right - - return result - - def increasing_order_traversal(self) -> Optional[BinaryTreeNode]: - if not self.root: - return None - - def inorder(node: BinaryTreeNode): - if node: - yield from inorder(node.left) - yield node.data - yield from inorder(node.right) - - result = current = BinaryTreeNode(None) - for data in inorder(self.root): - current.right = BinaryTreeNode(data) - current = current.right - - return result.right - - def in_order_recurse(self, node: BinaryTreeNode) -> List[T]: - """ - Another type of Depth First Search (DFS) that traverses the tree from the left to middle to right of the tree. - This type of search will begin at the left node and check if that node has a left child and continually check - until that left node is a leaf(has no children) and will then print its data and "bubble up" back to the - current node and execute that (in this case print it) and then print the right node. The same procedure is - executed for the right side of the tree. - """ - result = [] - if self.root: - if self.root.left: - self.in_order_recurse(self.root.left) - - result.append(self.root.data) - - if self.root.right: - self.in_order_recurse(self.root.right) - return result - - def in_order_iterate(self) -> List[T]: - """ - Iterative approach using a stack - """ - result = [] - stack = DynamicSizeStack() - current = self.root - - while current or not stack.is_empty(): - while current: - stack.push(current) - current = current.left - - current = stack.pop() - result.append(current.data) - current = current.right - - return result - - def in_order_morris_traversal(self) -> List[Any]: - result = [] - current = self.root - pre = None - - while current: - if not current.left: - # add the current data of the node - result.append(current.data) - # Move to next right node - current = current.right - else: - # we have a left subtree - pre = current.left - - # find rightmost - while pre.right: - pre = pre.right - - # put current after the pre node - pre.right = current - # store current node - temp = current - # move current to top of new tree - current = current.left - # original current left be None, avoid infinite loops - temp.left = None - - return result - - def post_order(self) -> List[Any]: - """ - 1. Push root to first stack. - 2. Loop while first stack is not empty - 2.1 Pop a node from first stack and push it to second stack - 2.2 Push left and right children of the popped node to first stack - 3. Print contents of second stack - """ - if not self.root: - return [] - - # create 2 stacks - stack_one = DynamicSizeStack() - stack_two = DynamicSizeStack() - data = [] - - # push root to stack one - stack_one.push(self.root) - - # while stack 1 is not empty - while stack_one: - # pop a node from stack 1 and add it to stack 2 - node = stack_one.pop() - stack_two.push(node) - - # push left & right children of removed item to stack one - if node.left: - stack_one.push(node.left) - - if node.right: - stack_one.push(node.right) - - while stack_two: - node = stack_two.pop() - data.append(node.data) - - return data - - def get_depth(self) -> int: - pass - - def level_order_traversal(self) -> List[Any]: - pass - - def pre_order_traversal(self) -> List[Any]: - data = [] - if not self.root: - return data - - def pre_order_helper(root: BinaryTreeNode): - if not root: - return - data.append(root.data) - pre_order_helper(root.left) - pre_order_helper(root.right) - - pre_order_helper(self.root) - return data - - def is_binary_search_tree(self): - """ - Checks if a binary search tree is valid. A data of None is a valid Binary Search Tree - Complexity Analysis: - Space Complexity: O(n) as we are using a stack to keep track of the nodes, where n is the height of the tree - Time Complexity: O(n), worst case we travers all the nodes of the tree(left sub tree and right sub tree) to - check if the tree is a valid BST - :rtype: bool - :return: Boolean True if valid, False otherwise - """ - - # Tree with no root is still valid - if not self.root: - return True - - # start with the root with an arbitrarily low lower bound and an arbitrarily higher bound - stack = [(float("-inf"), self.root, float("inf"))] - - # depth first traversal - while stack: - lower_bound, node, upper_bound = stack.pop() - - if not node: - continue - - # if this node is invalid, return false immediately - if node.data <= lower_bound or node.data >= upper_bound: - return False - - if node.left: - # this node must be less than the current node - stack.append((lower_bound, node.left, node.data)) - - if node.right: - # this node must be greater than the current node - stack.append((node.data, node.right, upper_bound)) - - # if none of the nodes are invalid, return true - # at this point we have checked all the nodes - return True - - def is_binary_search_tree_recursive( - self, root: BinaryTreeNode, lower_bound=-float("inf"), upper_bound=float("inf") - ): - """ - This uses the call stack to check if the binary search tree node is valid. - This will work, but is vulnerable to stack overflow error - Possible :exception: OverflowError - :param root: Binary search tree node to check for - :param lower_bound: the lower bound set arbitrarily - :param upper_bound: upper bound set arbitrarily - :return: True/False if the root is a valid binary search tree - :rtype: bool - """ - - if not root: - return True - - # if the data is out of bounds - if root.data > upper_bound or root.data < lower_bound: - return False - - return not ( - not self.is_binary_search_tree_recursive(root.left, lower_bound, root.data) - or not self.is_binary_search_tree_recursive( - root.right, root.data, upper_bound - ) - ) - - def search_node(self, data: T) -> bool: - """ - Searches for the given data in a binary search tree. If the data exists in the tree, then True is returned, - else false - Arguments: - data: data to search for - """ - - def search_helper(current: Optional[BinaryTreeNode], value: T) -> bool: - """ - Search helper that is used to search the binary search tree for the given value - Arguments: - current: the current binary search tree node, could be a missing value - value: the value to search for - """ - if current: - if current.data == value: - return True - elif current.data < value: - return search_helper(current.right, value) - else: - return search_helper(current.left, value) - return False - - return search_helper(self.root, data) - - def merge_trees(self, other_node: BinaryTreeNode) -> BinaryTreeNode: - """ - Merges this tree with another tree given another node - :param other_node Other Root node, may be None, therefore we return the root node if availables - :type BinaryTreeNode - :returns Binary Tree Node - """ - if not other_node: - return self.root - - if not self.root: - return other_node - - self.root.data += other_node.data - - self.root.left = self.merge_trees(other_node.left) - self.root.right = self.merge_trees(other_node.right) - - return self.root - - def is_balanced(self) -> bool: - """ - Checks if a binary tree is balanced - :return: True/False, if a binary tree is balanced - :rtype: bool - """ - if self.root is None: - return True - - tree_root = self.root - - # short circuit as soon as we find more than 2 - depths = [] - - # treat this list as a stack, that will store tuples of (node, depth) - # give the stack a maximum size of the length of the tree root - # alternatively, we could use a list - # nodes = [] - nodes = DynamicSizeStack() - - # nodes.append((tree_root, 0)) - nodes.push((tree_root, 0)) - - while len(nodes): - # pop a node and its depth from the top of a stack - node, depth = nodes.pop() - - # case, we found a leaf - if not node.left and not node.right: - # we only care if it is a new depth - if depth not in depths: - depths.append(depth) - - # two ways we might now have an unbalanced tree: - # 1) more than 2 different leaf depths - # 2) 2 leaf depths that are more than 1 apart - if len(depths) > 2 or ( - len(depths) == 2 and abs(depths[0] - depths[1]) > 1 - ): - return False - - # case, this is not a leaf, keep stepping down - else: - if node.left: - nodes.push((node.left, depth + 1)) - if node.right: - nodes.push((node.right, depth + 1)) - - return True - - def lowest_common_ancestor( - self, node_one: BinaryTreeNode, node_two: BinaryTreeNode - ) -> BinaryTreeNode: - """ - Considering it is a BST, we can assume that this tree is a valid BST, we could also check for this - If both of the datas in the 2 nodes provided are greater than the root node, then we move to the right. - if the nodes are less than the root node, we move to the left. - If there is no root node, then we exit and return None, as no common ancestor could exist in such a case with - no root node. - - Assumptions: - - assumes that the node itself can also be an ancestor/descendant of itself - - Complexity Analysis: - - Time Complexity: O(h). - The Time Complexity of the above solution is O(h), where h is the height of the tree. - - Space Complexity: O(1). - The space complexity of the above solution is constant. - """ - - if not self.root: - return None - - # if any of the node datas matches the data data for the root node, return the root node - if self.root.data == node_one.data or self.root.data == node_two.data: - return self.root - - while self.root: - # if both node_one and node_two are smaller than root, then LCA lies in the left - if self.root.data > node_one.data and self.root.data > node_two.data: - self.root = self.root.left - - # if both node_one and node_two are greater than root, then LCA lies in the right - elif self.root.data < node_one.data and self.root.data < node_two.data: - self.root = self.root.right - else: - break - - return self.root - - @property - def paths(self) -> list: - """ - Gets all the paths of this tree from root node to leaf nodes - """ - if not self.root: - return [] - - stack = DynamicSizeStack() - stack.push((self.root, "")) - res = [] - - while stack: - node, path = stack.pop() - - if not (node.left or node.right): - res.append(path + str(node.data)) - - if node.left: - stack.push((node.left, path + str(node.data) + "->")) - - if node.right: - stack.push((node.right, path + str(node.data) + "->")) - - return [list(map(int, x.split("->"))) for x in res] - - def inorder_successor(self, node: BinaryTreeNode) -> Optional[BinaryTreeNode]: - """ - Returns the inorder successor of the node. If there is no node, None is returned. The inorder successor of the - node is the node with the smallest value greater than node.data in the binary search tree. - - This assumes that the node is in the tree already. - - Complexity: - - Time Complexity: The time complexity of this solution is O(n) in the worst-case scenario where the given tree - is skewed. However, for a balanced binary search tree, it will be O(logn). - - Space Complexity: O(1) because we don't use any additional space. - - Args: - node (BinaryTreeNode): node to search for inorder successor - Returns: - Optional[BinaryTreeNode]: returns inorder successor of node if available, else None - """ - if not self.root: - return None - - successor = None - current = self.root - - # current is the best candidate so far - while current: - # when current.data is greater than the node.data, we have found a valid successor, so, we save it in the - # successor variable - if current.data > node.data: - successor = current - # Move left to find a better(smaller) candidate. By moving to current.left, we are exploring values that - # are smaller than current.data. Since we want the smallest possible successor, we must check the left - # side of current to see if there is a node that is still greater than node.data, but close to node.data - current = current.left - else: - # this node is too small, so we must go right to find a larger value - current = current.right - - return successor +__all__ = ["BinarySearchTree", "BinarySearchTreeIterator"] diff --git a/datastructures/trees/binary/search_tree/binary_search_tree.py b/datastructures/trees/binary/search_tree/binary_search_tree.py new file mode 100755 index 00000000..3b02d614 --- /dev/null +++ b/datastructures/trees/binary/search_tree/binary_search_tree.py @@ -0,0 +1,889 @@ +from typing import List, Any, Optional +from datastructures.trees.binary.node import BinaryTreeNode + +from datastructures.queues.fifo import FifoQueue +from datastructures.stacks.dynamic import DynamicSizeStack +from datastructures.trees import T +from datastructures.trees.binary.tree import BinaryTree + + +class BinarySearchTree(BinaryTree): + def __init__(self, root: Optional[BinaryTreeNode] = None): + super().__init__(root) + self.stack = DynamicSizeStack() + + def __len__(self) -> int: + if not self.root: + return 0 + + counter = 1 + stack = DynamicSizeStack() + stack.push(self.root) + + while not stack.is_empty(): + node = stack.pop() + + if node.left: + counter += 1 + stack.push(node.left) + + if node.right: + counter += 1 + stack.push(node.right) + + return counter + + @staticmethod + def construct_bst(items: List[T]) -> Optional["BinarySearchTree"]: + """ + Constructs a binary search tree from a sorted list of items. + + This method works by recursively finding the middle element of the list and assigning it to the root of the tree. + The left and right subtrees are then constructed by recursively calling the method on the left and right halves + of the list. + + @param items: A sorted list of items to construct the tree from. + @return: A binary search tree constructed from the items. + """ + if not items: + return None + + def construct_bst_helper(left: int, right: int) -> Optional[BinaryTreeNode]: + # base case for the method if the left is greater than the right + if left > right: + return None + + # Find the middle index - this element becomes the root + # Using (left + right) // 2 ensures we get the left-middle for even-length arrays + mid = (left + right) // 2 + root = BinaryTreeNode(items[mid]) + root.left = construct_bst_helper(left, mid - 1) + root.right = construct_bst_helper(mid + 1, right) + return root + + return BinarySearchTree(root=construct_bst_helper(0, len(items) - 1)) + + def insert_node(self, data: Optional[T]): + """ + Inserts a node in a BST given an element + If there is no root, then create a new root node with the data and return it + + If there is a root, then check the data against the root node's data and determine if it should go left or right + If the data is greater than the root node's data, then go right, if the data is less than the root node's data, + then go left. Repeat this operation, until we can insert the node in the right place. + """ + if not self.root: + self.root = BinaryTreeNode(data) + return + + def insert_helper(value: T, node: BinaryTreeNode) -> BinaryTreeNode: + if not node: + return BinaryTreeNode(data) + if value < node.data: + node.left = insert_helper(value, node.left) + else: + node.right = insert_helper(value, node.right) + return node + + if data: + insert_helper(data, self.root) + + def delete_node(self, key: T) -> Optional[BinaryTreeNode]: + """Deletes a node from the Binary Search Tree. If the node is found, it is deleted and the tree re-ordered to + remain a valid binary search tree. + + This will be typically an O(log(n) operation because deletion requires a search plus a few extra steps to deal + with any hanging children. + + Args: + key (T): Value to delete from binary search tree + + Return: + BinaryTreeNode: New root of binary search tree + """ + # nothing to delete here as root is none + if self.root is None: + return self.root + + def delete_helper( + value: T, node: Optional[BinaryTreeNode] + ) -> Optional[BinaryTreeNode]: + # base case when we have hit the bottom of the tree, and the parent node has no children + if node is None: + return None + # if the value to delete is less than or greater than the current node, we set the left or right child + # respectively to be the return value of a recursive call of this very method on the current node's left or + # right subtree + elif value < node.data: + node.left = delete_helper(value, node.left) + + # we return the current node (and its subtree if existent) to be used as the new value of its parent's + # left or right child + return node + elif value > node.data: + node.right = delete_helper(value, node.right) + return node + # if the current node is the one we want to delete + elif value == node.data: + # if the current node has no left child, we delete it by returning it's right child (and it's subtree if + # existent) to be its parent's new subtree + if node.left is None: + return node.right + # if the node has no left nor right child, this ends up being None as per the first line of code in this + # function + elif node.right is None: + return node.left + # if the current node has 2 children, we delete the current node by calling the lift function, which + # changes the current node's value to the value of it's successor node + else: + node.right = lift(node.right, node) + return node + return None + + def lift( + node: BinaryTreeNode, node_to_delete: BinaryTreeNode + ) -> BinaryTreeNode: + # if the current node of this function has a left child, we recursively call this function to continue down + # the left subtree to find the successor node + if node.left is not None: + node.left = lift(node.left, node_to_delete) + return node + # if the current node has no left child, that means the current node of this function is the successor node + # and we take its value and make it the new value of the node that we are deleting. + else: + node_to_delete.data = node.data + # we return the successor node's right child to be now used as its parent's left child + return node.right + + return delete_helper(key, self.root) + + @property + def height(self) -> int: + if self.root is None: + return 0 + + # if we don't have either left and right nodes from the root, we return 1 + if not self.root.left and not self.root.right: + return 1 + + height = 0 + queue = FifoQueue() + queue.enqueue(self.root) + + while True: + current_level_nodes = queue.size + + if current_level_nodes == 0: + return height + + height += 1 + + while current_level_nodes > 0: + node = queue.dequeue() + + if node.left is not None: + queue.enqueue(node.left) + + if node.right is not None: + queue.enqueue(node.right) + current_level_nodes -= 1 + + def next(self) -> int: + """ + Returns the next smallest number in a BST. + This involves two major operations. One is where we pop an element from the stack which becomes the next smallest element to return. This is a O(1) operation. + However, we then make a call to our helper function _leftmost_inorder which iterates over a bunch of nodes. This is clearly a linear time operation i.e. O(N) in the worst case. + However, the important thing to note here is that we only make such a call for nodes which have a right child. Otherwise, we simply return. + Also, even if we end up calling the helper function, it won't always process N nodes. They will be much lesser. Only if we have a skewed tree would there be N nodes for the root. + But that is the only node for which we would call the helper function. + + Thus, the amortized (average) time complexity for this function would still be O(1). We don't need to have a solution which gives constant time operations for every call. + We need that complexity on average and that is what we get. + """ + + # this is the smallest element in the BST + topmost_node = self.stack.pop() + + # if the node has a right child, call the helper function for the right child to + # get the next smallest item + # We don't need to check for the left child because of the way we have added nodes onto the stack. + # The topmost node either won't have a left child or would already have the left subtree processed. + # If it has a right child, then we call our helper function on the node's right child. + # This would comparatively be a costly operation depending upon the structure of the tree + if topmost_node.right: + self.__leftmost_inorder(topmost_node.right) + + return topmost_node.data + + def has_next(self) -> bool: + """ + Checks if the BST has items left. Since this uses a stack, then we simply check if the stack still has items. + This is used in an iterator approach to getting items from the BST. This returns True if there are items & False + otherwise, the Time Complexity here is O(1) + """ + return self.stack.is_empty() + + def __leftmost_inorder(self, root: BinaryTreeNode) -> None: + # Add all the nodes of the left most branch to the stack + while root: + self.stack.push(root) + root = root.left + + def find_largest(self, node: BinaryTreeNode) -> BinaryTreeNode: + """ + Simply finds the largest node in a BST. We walk rightward down the BST until the current node has no right child + and return it. This assumes that the Tree is a valid BST + :param node: root node, or current node + :return: Value of the largest node + :rtype: object + """ + current = node + while current: + if not current.right: + return current + current = current.right + + return current + + def find_second_largest(self) -> BinaryTreeNode: + """ + Finds the second largest node in the Binary Search Tree given a root node + :return: Value of the second largest Node + :rtype: object + """ + if not self.root or (not self.root.left and not self.root.right): + raise Exception("Tree must have at least 2 nodes") + + current = self.root + + while current: + # case: current is largest and has a left subtree + # 2nd largest is the largest in that subtree + if current.left and not current.right: + return self.find_largest(current.left) + + # case: current is parent of largest, and + # largest has no children, so + # current is 2nd largest + if current.right and not current.right.left and not current.right.right: + return current + + current = current.right + + return current + + def find_kth_largest(self, k: int) -> Optional[BinaryTreeNode]: + """ + Finds the kth largest value in a binary search tree. This uses a reverse in order traversal moving from right + to root to left until the kth largest node can be found. We don't have to traverse the whole tree since binary + search trees are already ordered following the property of the right subtree has nodes which have the left + sub-tree always less than their parent and the right subtree has nodes with values that are either equal to or + greater than the parent. With this property in mind, we perform a reverse in order traversal to be able to move + from right to root to left to find the kth largest node in the tree. + + Complexity: + Time: O(h + k): where h is the height of the tree and k is the input + Space: O(h): where h is the height of the tree. + + Args: + k (int): The kth largest value to find + Returns: + Optional[BinaryTreeNode]: The kth largest node + """ + + # This is a helper class that helps to track the algorithm's progress of traversing the tree + class TreeInfo: + def __init__(self): + self.number_of_nodes_visited: int = 0 + self.latest_visited_node: Optional[BinaryTreeNode] = None + + def reverse_in_order_traverse(node: BinaryTreeNode, tree_information: TreeInfo): + """ + Helper function to traverse the tree in reverse in order + Args: + node (BinaryTreeNode): The node to traverse + tree_information (TreeInfo): The tree information + """ + # base case: if node is None or we've already found the kth largest + if not node or tree_information.number_of_nodes_visited >= k: + return + + # traverse right subtree first for larger values + reverse_in_order_traverse(node.right, tree_information) + + # Visit the current node if we haven't found k nodes yet + if tree_information.number_of_nodes_visited < k: + tree_information.number_of_nodes_visited += 1 + tree_information.latest_visited_node = node + + # traverse the left subtree for smaller values if needed + reverse_in_order_traverse(node.left, tree_information) + + tree_info = TreeInfo() + reverse_in_order_traverse(self.root, tree_info) + return tree_info.latest_visited_node + + def find_closest_value_in_bst(self, target: T) -> Optional[BinaryTreeNode]: + """ + Finds the closest value in the binary search tree to the given target value. + + Args: + target T: Value to search for + Returns: + Node with the closest value to the target + """ + # edge case for empty nodes, if none is provided, we can't find a value that is close to the target + if not self.root: + return None + + # if the node's data is the target, exit early by returning it + if self.root.data == target: + return self.root + + # this keeps track of the minimum on both the left and the right + closest_node = self.root + min_diff = abs(target - self.root.data) + current = self.root + + # while the queue is not empty, we pop off nodes from the queue and check for their values + while current: + current_diff = abs(target - self.root.data) + + if current_diff < min_diff: + min_diff = current_diff + closest_node = current + + if current.data == target: + return current + + if target < current.data: + current = current.left + else: + current = current.right + + return closest_node + + def range_sum(self, low: int, high: int): + """ + returns the sum of datas of all nodes with a data in the range [low, high]. + + Example: + Input: root = [10,5,15,3,7,null,18], low = 7, high = 15 + Output: 32 + + Uses an iterative approach to solving the problem with Breadth First Search Traversal + + Complexity Analysis: + - Time Complexity: O(N), where N is the number of nodes in the tree + - Space Complexity: O(N) + - The stack will contain no more than 2 levels of the nodes. The maximal number of nodes in a binary tree is + N/2. Therefore, the maximal space needed for the stack is O(N) + """ + + ans = 0 + + stack = [self.root] + + while stack: + node = stack.pop() + + if node: + if low <= node.data <= high: + ans += node.data + + if low < node.data: + if node.left: + stack.append(node.left) + + if node.data < high: + if node.right: + stack.append(node.right) + + return ans + + def breadth_first_search(self) -> List[Any]: + """ + Performs a breadth first search through a Binary Tree + This will traverse the tree level by level and depth by depth. Using a Queue to put elements into the queue + """ + queue = FifoQueue() + + # start off by adding the root node + queue.enqueue(self.root) + + # while the queue is not empty, we want to traverse the tree and add elements to the queue, + while not queue.is_empty(): + current_node = queue.dequeue() + + if current_node.left: + queue.enqueue(current_node.left) + + if current_node.right: + queue.enqueue(current_node.right) + + def pre_order(self) -> List[Any]: + """ + Type of Depth First Traversal (DFS) for binary trees which will start at root node and proceed to the left + data and print it until it reaches the leaf(node with no more children) and then backtrack to the node and + check if the current node has a right child and print it. This will continue until all nodes have been + tracked and printed. + """ + result = [] + stack = DynamicSizeStack() + + if not self.root: + return result + + current = self.root + + while current or not stack.is_empty(): + while current: + result.append(current.data) + stack.push(current) + current = current.left + + current = stack.pop() + + current = current.right + + return result + + def increasing_order_traversal(self) -> Optional[BinaryTreeNode]: + if not self.root: + return None + + def inorder(node: BinaryTreeNode): + if node: + yield from inorder(node.left) + yield node.data + yield from inorder(node.right) + + result = current = BinaryTreeNode(None) + for data in inorder(self.root): + current.right = BinaryTreeNode(data) + current = current.right + + return result.right + + def in_order_recurse(self, node: BinaryTreeNode) -> List[T]: + """ + Another type of Depth First Search (DFS) that traverses the tree from the left to middle to right of the tree. + This type of search will begin at the left node and check if that node has a left child and continually check + until that left node is a leaf(has no children) and will then print its data and "bubble up" back to the + current node and execute that (in this case print it) and then print the right node. The same procedure is + executed for the right side of the tree. + """ + result = [] + if self.root: + if self.root.left: + self.in_order_recurse(self.root.left) + + result.append(self.root.data) + + if self.root.right: + self.in_order_recurse(self.root.right) + return result + + def in_order_iterate(self) -> List[T]: + """ + Iterative approach using a stack + """ + result = [] + stack = DynamicSizeStack() + current = self.root + + while current or not stack.is_empty(): + while current: + stack.push(current) + current = current.left + + current = stack.pop() + result.append(current.data) + current = current.right + + return result + + def in_order_morris_traversal(self) -> List[Any]: + result = [] + current = self.root + pre = None + + while current: + if not current.left: + # add the current data of the node + result.append(current.data) + # Move to next right node + current = current.right + else: + # we have a left subtree + pre = current.left + + # find rightmost + while pre.right: + pre = pre.right + + # put current after the pre node + pre.right = current + # store current node + temp = current + # move current to top of new tree + current = current.left + # original current left be None, avoid infinite loops + temp.left = None + + return result + + def post_order(self) -> List[Any]: + """ + 1. Push root to first stack. + 2. Loop while first stack is not empty + 2.1 Pop a node from first stack and push it to second stack + 2.2 Push left and right children of the popped node to first stack + 3. Print contents of second stack + """ + if not self.root: + return [] + + # create 2 stacks + stack_one = DynamicSizeStack() + stack_two = DynamicSizeStack() + data = [] + + # push root to stack one + stack_one.push(self.root) + + # while stack 1 is not empty + while stack_one: + # pop a node from stack 1 and add it to stack 2 + node = stack_one.pop() + stack_two.push(node) + + # push left & right children of removed item to stack one + if node.left: + stack_one.push(node.left) + + if node.right: + stack_one.push(node.right) + + while stack_two: + node = stack_two.pop() + data.append(node.data) + + return data + + def get_depth(self) -> int: + pass + + def level_order_traversal(self) -> List[Any]: + pass + + def pre_order_traversal(self) -> List[Any]: + data = [] + if not self.root: + return data + + def pre_order_helper(root: BinaryTreeNode): + if not root: + return + data.append(root.data) + pre_order_helper(root.left) + pre_order_helper(root.right) + + pre_order_helper(self.root) + return data + + def is_binary_search_tree(self): + """ + Checks if a binary search tree is valid. A data of None is a valid Binary Search Tree + Complexity Analysis: + Space Complexity: O(n) as we are using a stack to keep track of the nodes, where n is the height of the tree + Time Complexity: O(n), worst case we travers all the nodes of the tree(left sub tree and right sub tree) to + check if the tree is a valid BST + :rtype: bool + :return: Boolean True if valid, False otherwise + """ + + # Tree with no root is still valid + if not self.root: + return True + + # start with the root with an arbitrarily low lower bound and an arbitrarily higher bound + stack = [(float("-inf"), self.root, float("inf"))] + + # depth first traversal + while stack: + lower_bound, node, upper_bound = stack.pop() + + if not node: + continue + + # if this node is invalid, return false immediately + if node.data <= lower_bound or node.data >= upper_bound: + return False + + if node.left: + # this node must be less than the current node + stack.append((lower_bound, node.left, node.data)) + + if node.right: + # this node must be greater than the current node + stack.append((node.data, node.right, upper_bound)) + + # if none of the nodes are invalid, return true + # at this point we have checked all the nodes + return True + + def is_binary_search_tree_recursive( + self, root: BinaryTreeNode, lower_bound=-float("inf"), upper_bound=float("inf") + ): + """ + This uses the call stack to check if the binary search tree node is valid. + This will work, but is vulnerable to stack overflow error + Possible :exception: OverflowError + :param root: Binary search tree node to check for + :param lower_bound: the lower bound set arbitrarily + :param upper_bound: upper bound set arbitrarily + :return: True/False if the root is a valid binary search tree + :rtype: bool + """ + + if not root: + return True + + # if the data is out of bounds + if root.data > upper_bound or root.data < lower_bound: + return False + + return not ( + not self.is_binary_search_tree_recursive(root.left, lower_bound, root.data) + or not self.is_binary_search_tree_recursive( + root.right, root.data, upper_bound + ) + ) + + def search_node(self, data: T) -> bool: + """ + Searches for the given data in a binary search tree. If the data exists in the tree, then True is returned, + else false + Arguments: + data: data to search for + """ + + def search_helper(current: Optional[BinaryTreeNode], value: T) -> bool: + """ + Search helper that is used to search the binary search tree for the given value + Arguments: + current: the current binary search tree node, could be a missing value + value: the value to search for + """ + if current: + if current.data == value: + return True + elif current.data < value: + return search_helper(current.right, value) + else: + return search_helper(current.left, value) + return False + + return search_helper(self.root, data) + + def merge_trees(self, other_node: BinaryTreeNode) -> BinaryTreeNode: + """ + Merges this tree with another tree given another node + :param other_node Other Root node, may be None, therefore we return the root node if availables + :type BinaryTreeNode + :returns Binary Tree Node + """ + if not other_node: + return self.root + + if not self.root: + return other_node + + self.root.data += other_node.data + + self.root.left = self.merge_trees(other_node.left) + self.root.right = self.merge_trees(other_node.right) + + return self.root + + def is_balanced(self) -> bool: + """ + Checks if a binary tree is balanced + :return: True/False, if a binary tree is balanced + :rtype: bool + """ + if self.root is None: + return True + + tree_root = self.root + + # short circuit as soon as we find more than 2 + depths = [] + + # treat this list as a stack, that will store tuples of (node, depth) + # give the stack a maximum size of the length of the tree root + # alternatively, we could use a list + # nodes = [] + nodes = DynamicSizeStack() + + # nodes.append((tree_root, 0)) + nodes.push((tree_root, 0)) + + while len(nodes): + # pop a node and its depth from the top of a stack + node, depth = nodes.pop() + + # case, we found a leaf + if not node.left and not node.right: + # we only care if it is a new depth + if depth not in depths: + depths.append(depth) + + # two ways we might now have an unbalanced tree: + # 1) more than 2 different leaf depths + # 2) 2 leaf depths that are more than 1 apart + if len(depths) > 2 or ( + len(depths) == 2 and abs(depths[0] - depths[1]) > 1 + ): + return False + + # case, this is not a leaf, keep stepping down + else: + if node.left: + nodes.push((node.left, depth + 1)) + if node.right: + nodes.push((node.right, depth + 1)) + + return True + + def lowest_common_ancestor( + self, node_one: BinaryTreeNode, node_two: BinaryTreeNode + ) -> BinaryTreeNode: + """ + Considering it is a BST, we can assume that this tree is a valid BST, we could also check for this + If both of the datas in the 2 nodes provided are greater than the root node, then we move to the right. + if the nodes are less than the root node, we move to the left. + If there is no root node, then we exit and return None, as no common ancestor could exist in such a case with + no root node. + + Assumptions: + - assumes that the node itself can also be an ancestor/descendant of itself + + Complexity Analysis: + + Time Complexity: O(h). + The Time Complexity of the above solution is O(h), where h is the height of the tree. + + Space Complexity: O(1). + The space complexity of the above solution is constant. + """ + + if not self.root: + return None + + # if any of the node datas matches the data data for the root node, return the root node + if self.root.data == node_one.data or self.root.data == node_two.data: + return self.root + + while self.root: + # if both node_one and node_two are smaller than root, then LCA lies in the left + if self.root.data > node_one.data and self.root.data > node_two.data: + self.root = self.root.left + + # if both node_one and node_two are greater than root, then LCA lies in the right + elif self.root.data < node_one.data and self.root.data < node_two.data: + self.root = self.root.right + else: + break + + return self.root + + @property + def paths(self) -> list: + """ + Gets all the paths of this tree from root node to leaf nodes + """ + if not self.root: + return [] + + stack = DynamicSizeStack() + stack.push((self.root, "")) + res = [] + + while stack: + node, path = stack.pop() + + if not (node.left or node.right): + res.append(path + str(node.data)) + + if node.left: + stack.push((node.left, path + str(node.data) + "->")) + + if node.right: + stack.push((node.right, path + str(node.data) + "->")) + + return [list(map(int, x.split("->"))) for x in res] + + def inorder_successor(self, node: BinaryTreeNode) -> Optional[BinaryTreeNode]: + """ + Returns the inorder successor of the node. If there is no node, None is returned. The inorder successor of the + node is the node with the smallest value greater than node.data in the binary search tree. + + This assumes that the node is in the tree already. + + Complexity: + + Time Complexity: The time complexity of this solution is O(n) in the worst-case scenario where the given tree + is skewed. However, for a balanced binary search tree, it will be O(logn). + + Space Complexity: O(1) because we don't use any additional space. + + Args: + node (BinaryTreeNode): node to search for inorder successor + Returns: + Optional[BinaryTreeNode]: returns inorder successor of node if available, else None + """ + if not self.root: + return None + + successor = None + current = self.root + + # current is the best candidate so far + while current: + # when current.data is greater than the node.data, we have found a valid successor, so, we save it in the + # successor variable + if current.data > node.data: + successor = current + # Move left to find a better(smaller) candidate. By moving to current.left, we are exploring values that + # are smaller than current.data. Since we want the smallest possible successor, we must check the left + # side of current to see if there is a node that is still greater than node.data, but close to node.data + current = current.left + else: + # this node is too small, so we must go right to find a larger value + current = current.right + + return successor + + def sum_nodes_in_range(self, low: int, high: int) -> int: + """ + Finds and sums all the nodes in the range [low, high]. Utilizes pruning to avoid checking subtrees whose values + fall outside the range [low, high]. + Args: + low (int): Lower bound. + high (int): Upper bound. + Returns: + int: Total sum of nodes within the range [low, high]. + """ + + def dfs(node: Optional[BinaryTreeNode]): + if not node: + return 0 + if node.data < low: + return dfs(node.right) + if node.data > high: + return dfs(node.left) + return node.data + dfs(node.left) + dfs(node.right) + + return dfs(self.root) diff --git a/datastructures/trees/binary/tree/binary_tree.py b/datastructures/trees/binary/tree/binary_tree.py index b4e7562f..c4767435 100644 --- a/datastructures/trees/binary/tree/binary_tree.py +++ b/datastructures/trees/binary/tree/binary_tree.py @@ -933,3 +933,20 @@ def invert_tree_helper( return node return invert_tree_helper(self.root) + + def sum_nodes_in_range(self, low: int, high: int) -> int: + """ + Finds and sums all the nodes in the range [low, high]. + Args: + low (int): Lower bound. + high (int): Upper bound. + Returns: + int: Total sum of nodes within the range [low, high]. + """ + + def dfs(node: Optional[BinaryTreeNode]): + if not node or node.data < low or node.data > high: + return 0 + return node.data + dfs(node.left) + dfs(node.right) + + return dfs(self.root) From 7075c1b76fec57dad348ac32c00f0beaa024e34f Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Thu, 29 Jan 2026 18:20:18 +0000 Subject: [PATCH 02/25] updating DIRECTORY.md --- DIRECTORY.md | 27 ++++++++++++++++++--------- 1 file changed, 18 insertions(+), 9 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 491f4d62..9bf3d6ce 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -79,6 +79,9 @@ * [Test Longest Common Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/longest_common_subsequence/test_longest_common_subsequence.py) * Longest Increasing Subsequence * [Test Longest Increasing Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/longest_increasing_subsequence/test_longest_increasing_subsequence.py) + * Max Subarray + * [Sub Array Maxsum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/max_subarray/sub_array_maxsum.py) + * [Test Max Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/max_subarray/test_max_subarray.py) * Maximal Square * [Test Maximal Square](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/maximal_square/test_maximal_square.py) * Min Distance @@ -147,6 +150,8 @@ * [Test Assign Cookies](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/assign_cookies/test_assign_cookies.py) * Boats * [Test Boats To Save People](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/boats/test_boats_to_save_people.py) + * Create Maximum Number + * [Test Create Maximum Number](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/create_maximum_number/test_create_maximum_number.py) * Gas Stations * [Test Gas Stations](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/gas_stations/test_gas_stations.py) * Jump Game @@ -220,6 +225,8 @@ * [Test Min Meeting Rooms](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/meeting_rooms/test_min_meeting_rooms.py) * Merge Intervals * [Test Merge Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/merge_intervals/test_merge_intervals.py) + * Non Overlapping Intervals + * [Test Non Overlapping Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/non_overlapping_intervals/test_non_overlapping_intervals.py) * Remove Intervals * [Test Remove Covered Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/remove_intervals/test_remove_covered_intervals.py) * Task Scheduler @@ -250,12 +257,13 @@ * Search Suggestions * [Test Search Suggestions](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/trie/search_suggestions/test_search_suggestions.py) * Sliding Window + * Length Of Longest Substring + * [Test Length Of Longest Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/length_of_longest_substring/test_length_of_longest_substring.py) + * [Test Longest Substring Without Repeating Characters](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/length_of_longest_substring/test_longest_substring_without_repeating_characters.py) * Longest Repeating Char Replacement * [Test Longest Repeating Character Replacement](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/longest_repeating_char_replacement/test_longest_repeating_character_replacement.py) * Longest Substring With K Repeating Chars * [Test Longest Substring K Repeating Chars](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/longest_substring_with_k_repeating_chars/test_longest_substring_k_repeating_chars.py) - * Longest Substring Without Repeating Characters - * [Test Longest Substring Without Repeating Characters](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/longest_substring_without_repeating_characters/test_longest_substring_without_repeating_characters.py) * Max Points From Cards * [Test Max Points From Cards](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/max_points_from_cards/test_max_points_from_cards.py) * Max Sum Of Subarray @@ -288,6 +296,8 @@ * Two Pointers * Array 3 Pointers * [Test Array 3 Pointers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/array_3_pointers/test_array_3_pointers.py) + * Container With Most Water + * [Test Container With Most Water](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/container_with_most_water/test_container_with_most_water.py) * Count Pairs * [Test Count Pairs](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/count_pairs/test_count_pairs.py) * Find Sum Of Three @@ -327,6 +337,8 @@ * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/two_sum/test_two_sum.py) * Two Sum Less K * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/two_sum_less_k/test_two_sum.py) + * Valid Word Abbreviation + * [Test Valid Word Abbreviation](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/valid_word_abbreviation/test_valid_word_abbreviation.py) * Unique Bsts * [Unique Bsts](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/unique_bsts/unique_bsts.py) * Word Count @@ -394,12 +406,8 @@ * Matrix * Settozero * [Test Set Matrix Zero](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/arrays/matrix/settozero/test_set_matrix_zero.py) - * Max Subarray - * [Sub Array Maxsum](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/arrays/max_subarray/sub_array_maxsum.py) * Minincrementsforunique * [Min Increment For Unique](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/arrays/minincrementsforunique/min_increment_for_unique.py) - * Non Overlapping Intervals - * [Test Non Overlapping Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/arrays/non_overlapping_intervals/test_non_overlapping_intervals.py) * Sub Array With Sum * [Test Sub Array With Sum](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/arrays/sub_array_with_sum/test_sub_array_with_sum.py) * Subarrays With Fixed Bounds @@ -446,6 +454,7 @@ * [Test Singly Linked List Remove Duplicates](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_list_remove_duplicates.py) * [Test Singly Linked List Remove Nth Last Node](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_list_remove_nth_last_node.py) * [Test Singly Linked List Reorder List](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_list_reorder_list.py) + * [Test Singly Linked List Reverse K Group](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_list_reverse_k_group.py) * [Test Singly Linked List Rotate](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_list_rotate.py) * [Test Singly Linked Merge And Weave](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_merge_and_weave.py) * [Test Singly Linked Move Tail To Head](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/singly_linked_list/test_singly_linked_move_tail_to_head.py) @@ -506,6 +515,7 @@ * Search Tree * Avl * [Node](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/trees/binary/search_tree/avl/node.py) + * [Binary Search Tree](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/trees/binary/search_tree/binary_search_tree.py) * [Bst Iterator](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/trees/binary/search_tree/bst_iterator.py) * [Test Binary Search Tree Delete Node](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/trees/binary/search_tree/test_binary_search_tree_delete_node.py) * [Test Binary Search Tree Inorder Successor](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/trees/binary/search_tree/test_binary_search_tree_inorder_successor.py) @@ -695,8 +705,6 @@ * [Test Can Place Flowers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/can_place_flowers/test_can_place_flowers.py) * Candy * [Test Candy](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/candy/test_candy.py) - * Container With Most Water - * [Test Container With Most Water](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/container_with_most_water/test_container_with_most_water.py) * H Index * [Test H Index](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/h_index/test_h_index.py) * Increasing Triplet Subsequence @@ -874,6 +882,8 @@ * [Test Perfect Squares](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/perfect_square/test_perfect_squares.py) * Rectangle Area * [Test Compute Area](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/rectangle_area/test_compute_area.py) + * Reverse Integer + * [Test Reverse Integer](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/reverse_integer/test_reverse_integer.py) * Super Size * [Test Super Size](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/super_size/test_super_size.py) * Triangles @@ -1039,7 +1049,6 @@ * [Test Highest Rank](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/arrays/test_highest_rank.py) * [Test Lonely Integer](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/arrays/test_lonely_integer.py) * [Test Longest Consecutive Sequence](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/arrays/test_longest_consecutive_sequence.py) - * [Test Max Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/arrays/test_max_subarray.py) * [Test Zig Zag Sequence](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/arrays/test_zig_zag_sequence.py) * [Test Build One 2 3](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/test_build_one_2_3.py) * [Test Consecutive](https://github.com/BrianLusina/PythonSnips/blob/master/tests/datastructures/test_consecutive.py) From 7d19b5f9cd37fc3f71515b4c244d9d5962ef6dae Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 2 Feb 2026 14:10:31 +0300 Subject: [PATCH 03/25] feat(algorithms, dynamic-proramming): frog jumps --- .../dynamic_programming/frog_jump/README.md | 84 ++ .../dynamic_programming/frog_jump/__init__.py | 38 + .../images/solutions/frog_jump_solution_1.png | Bin 0 -> 53187 bytes .../solutions/frog_jump_solution_10.png | Bin 0 -> 94939 bytes 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dynamic_programming}/frog_jumps/__init__.py (100%) rename algorithms/{ => dynamic_programming}/frog_river_one/README.md (100%) rename algorithms/{ => dynamic_programming}/frog_river_one/__init__.py (100%) create mode 100644 algorithms/dynamic_programming/maximal_rectangle/README.md create mode 100644 algorithms/dynamic_programming/maximal_rectangle/__init__.py create mode 100644 algorithms/dynamic_programming/maximal_rectangle/images/examples/maximal_rectangle_example_1.png create mode 100644 algorithms/dynamic_programming/maximal_rectangle/images/examples/maximal_rectangle_example_2.png create mode 100644 algorithms/dynamic_programming/maximal_rectangle/images/examples/maximal_rectangle_example_3.png create mode 100644 algorithms/dynamic_programming/maximal_rectangle/images/examples/maximal_rectangle_example_4.png create mode 100644 algorithms/dynamic_programming/maximal_rectangle/images/examples/maximal_rectangle_example_5.png create mode 100644 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b/algorithms/dynamic_programming/frog_jump/README.md @@ -0,0 +1,84 @@ +# Frog Jump + +A frog is trying to cross a river by jumping on stones placed at various positions along the river. The river is divided +into units, and some units contain stones while others do not. The frog can only land on a stone, but it must not jump +into the water. + +You are given an array, stones, that represents the positions of the stones in ascending order (in units). The frog +starts on the first stone, and its first jump must be exactly 1 unit. + +If the frog’s last jump was of length k units, its next jump must be either k−1, k, or k+1 units. The frog can only move +forward. + +Your task is to determine whether the frog can successfully reach the last stone. + +## Constraints + +- 2 ≤ `stones.length` ≤ 1000 +- 0 ≤ `stones[i]` ≤ 2^20 − 1 +- stones[0] == 0 +- The stones array is sorted in a strictly increasing order. + +## Topics + +- Array +- Dynamic Programming + +## Solution + +The solution’s essence lies in leveraging dynamic programming to track all the jump lengths that can reach each stone. +The frog begins on the first stone with a jump length of zero, and from every reachable stone, it tries jumps of the +same size, one unit longer, or one unit shorter. Each valid move updates the DP table to record new reachable states. +The algorithm stores each stone’s position along with its index in a map, allowing for quick checks to determine if a +stone exists at a given position. Finally, if any jump length reaches the last stone, the frog can successfully cross +the river. + +Using the intuition above, we implement the algorithm as follows: +- Store the number of stones in a variable n. +- Create an unordered map, `mapper`, to store each stone’s position as the key and its index as the value for fast + lookups. +- Populate the `mapper` by mapping every stone position, `stones[i]`, to its index, `i`. +- Initialize a 2D array, `dp`, of size `1001 x 1001` with zeros to track reachable states. + > Note that this is highly dependable on the constraints, larger sizes of stones will cause an Index out of bounds + > error. So, ensure to initialize the size correctly +- Set `dp[0][0]` to `1` to indicate that the frog starts on the first stone with a previous jump of 0. +- Iterate over each stone index `i`: + - For each stone, iterate over all possible previous jump lengths `prevJump`. + - Check if `dp[i][prevJump]` is 1 to confirm that the frog can reach stone `i` with jump size `prevJump`: + - If reachable, store the current position as `currPos = stones[i]`. + - Check if a stone exists at `currPos + prevJump`; if yes, mark `dp[mapper[currPos + prevJump]][prevJump]` as `1`. + - Check if a stone exists at `currPos + prevJump + 1`; if yes, mark `dp[mapper[currPos + prevJump + 1]][prevJump + 1]` as `1` + - If `prevJump > 1` and a stone exists at `currPos + prevJump - 1`, mark `dp[mapper[currPos + prevJump - 1]][prevJump - 1]` as `1`. +- After filling the DP table, iterate over all possible jump sizes `jump` for the last stone. + - If any `dp[n - 1][jump]` equals `1`, return TRUE to indicate that the frog can cross the river. +- If no valid jump leads to the last stone, return FALSE. + +![Solution 1](./images/solutions/frog_jump_solution_1.png) +![Solution 2](./images/solutions/frog_jump_solution_2.png) +![Solution 3](./images/solutions/frog_jump_solution_3.png) +![Solution 4](./images/solutions/frog_jump_solution_4.png) +![Solution 5](./images/solutions/frog_jump_solution_5.png) +![Solution 6](./images/solutions/frog_jump_solution_6.png) +![Solution 7](./images/solutions/frog_jump_solution_7.png) +![Solution 8](./images/solutions/frog_jump_solution_8.png) +![Solution 9](./images/solutions/frog_jump_solution_9.png) +![Solution 10](./images/solutions/frog_jump_solution_10.png) +![Solution 11](./images/solutions/frog_jump_solution_11.png) +![Solution 12](./images/solutions/frog_jump_solution_12.png) +![Solution 13](./images/solutions/frog_jump_solution_13.png) +![Solution 14](./images/solutions/frog_jump_solution_14.png) +![Solution 15](./images/solutions/frog_jump_solution_15.png) +![Solution 16](./images/solutions/frog_jump_solution_16.png) +![Solution 17](./images/solutions/frog_jump_solution_17.png) +![Solution 18](./images/solutions/frog_jump_solution_18.png) +![Solution 19](./images/solutions/frog_jump_solution_19.png) +![Solution 20](./images/solutions/frog_jump_solution_20.png) + +### Time Complexity + +The algorithm’s time complexity is O(n^2), where n is the number of stones. For each stone, it may check all possible +previous jump lengths, and for each valid state, it performs constant-time lookups in the map. + +### Space Complexity + +The algorithm’s space complexity is `O(n)` occupied by the mapper map. diff --git a/algorithms/dynamic_programming/frog_jump/__init__.py b/algorithms/dynamic_programming/frog_jump/__init__.py new file mode 100644 index 00000000..5dad925f --- /dev/null +++ b/algorithms/dynamic_programming/frog_jump/__init__.py @@ -0,0 +1,38 @@ +from typing import List + + +def can_cross(stones: List[int]) -> bool: + n = len(stones) + + # Map each stone's position to its index for O(1) lookups + mapper = {stones[i]: i for i in range(n)} + + # dp[i][k] = 1 if the frog can reach stone i with a jump of length k + dp = [[0] * 2001 for _ in range(2001)] + dp[0][0] = 1 # Starting point: frog at first stone with jump size 0 + + # Try to reach every stone using all possible previous jump sizes + for i in range(n): + for prev_jump in range(n + 1): + if dp[i][prev_jump]: + curr_pos = stones[i] + + # Jump of the same length + if curr_pos + prev_jump in mapper: + dp[mapper[curr_pos + prev_jump]][prev_jump] = 1 + + # Jump one unit longer + if curr_pos + prev_jump + 1 in mapper: + dp[mapper[curr_pos + prev_jump + 1]][prev_jump + 1] = 1 + + # Jump one unit shorter (if valid) + if prev_jump > 1 and curr_pos + prev_jump - 1 in mapper: + dp[mapper[curr_pos + prev_jump - 1]][prev_jump - 1] = 1 + + # Check if the last stone is reachable with any jump size + for jump in range(n + 1): + if dp[n - 1][jump]: + return True + + # If no valid path reaches the last stone + return False diff --git a/algorithms/dynamic_programming/frog_jump/images/solutions/frog_jump_solution_1.png b/algorithms/dynamic_programming/frog_jump/images/solutions/frog_jump_solution_1.png new file mode 100644 index 0000000000000000000000000000000000000000..555bedf54a1cdac47ce762118b4560b84750595f GIT binary patch literal 53187 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