Add a solution to climbing-stairs problem.

Author: KyrieJ95

climbing-stairs/joon.py

@@ -0,0 +1,24 @@
+from typing import Dict
+
+
+class Solution:
+    # Time: O(n)
+    # Space: O(n)
+    # ---
+    # 1. Prepare a table for caching. Initially put trivial answers for n = 1, 2.
+    # Space: O(n)
+    cacheTableOfAnswerByN: Dict[int, int] = {1: 1, 2: 2}
+
+    def climbStairs(self, n: int) -> int:
+        # 2. Use caching.
+        # Time: O(1)
+        try: return self.cacheTableOfAnswerByN[n]
+        except KeyError:
+            # 3. Simply, the answers follow Fibonacci sequence. Use recursion.
+            # O(n)
+            answerBeforeTwoSteps = self.climbStairs(n - 2)
+            # 4. Cache the answer during recursion.
+            self.cacheTableOfAnswerByN[n - 2] = answerBeforeTwoSteps
+            answerBeforeOneStep = self.climbStairs(n - 1)
+            self.cacheTableOfAnswerByN[n - 1] = answerBeforeOneStep
+            return answerBeforeTwoSteps + answerBeforeOneStep