Add week 12 solutions: longestCommonSubsequence, maximumSubarray

Author: yolophg

longest-common-subsequence/yolophg.js

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+// Time Complexity: O(m * n) m : the length of text1, n : the length of text2
+// Space Complexity: O(m * n)
+
+var longestCommonSubsequence = function (text1, text2) {
+  // a memoization array to store results
+  const memo = Array(text1.length)
+    .fill(null)
+    .map(() => Array(text2.length).fill(null));
+
+  // helper function that uses recursion and memoization
+  function lcsHelper(i, j) {
+    // if either string is exhausted, return 0
+    if (i === text1.length || j === text2.length) {
+      return 0;
+    }
+
+    // if characters match, move diagonally and add 1 to the result
+    if (text1[i] === text2[j]) {
+      memo[i][j] = 1 + lcsHelper(i + 1, j + 1);
+    } else {
+      // if characters don't match, take the maximum result from moving right or down
+      memo[i][j] = Math.max(lcsHelper(i + 1, j), lcsHelper(i, j + 1));
+    }
+
+    return memo[i][j];
+  }
+
+  // start the recursion from the beginning of both strings
+  return lcsHelper(0, 0);
+};

maximum-subarray/yolophg.js

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+// Time Complexity: O(n)
+// Space Complexity: O(1)
+
+var maxSubArray = function (nums) {
+  let maxSum = nums[0];
+  let currentSum = 0;
+
+  // iterate through the array
+  for (let i = 0; i < nums.length; i++) {
+    // if currentSum is negative, reset it to 0
+    if (currentSum < 0) {
+      currentSum = 0;
+    }
+
+    // add the current element to currentSum
+    currentSum += nums[i];
+
+    // update maxSum if currentSum is greater
+    if (currentSum > maxSum) {
+      maxSum = currentSum;
+    }
+  }
+
+  // return the maximum subarray sum
+  return maxSum;
+};