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dynamic_programming/climbing_stairs.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+'''
+You are climbing a staircase. It takes n steps to reach the top.
+Each time you can either climb 1 or 2 steps. 
+In how many distinct ways can you climb to the top?
+'''
+ 
+
+def climb_stairs_o2n(n: int) -> int:
+        if n == 0 or n == 1:
+            return 1
+        return climb_stairs_o2n(n-1) + climb_stairs_o2n(n-2)
+
+
+
+def helper(n: int, memo: dict[int, int]) -> int:
+        if n == 0 or n == 1:
+            return 1
+        if n not in memo:
+            memo[n] = helper(n-1, memo) + helper(n-2, memo)
+        return memo[n]
+
+def climb_stairs_memoization(n: int) -> int:
+        memo = {}    
+        return helper(n, memo)
+    
+
+    
+def climb_stairs_optimized(n: int) -> int:
+        if n == 0 or n == 1:
+            return 1
+        prev, curr = 1, 1
+        for i in range(2, n+1):
+            temp = curr
+            curr = prev + curr
+            prev = temp
+        return curr
+
+
+
+def climb_stairs_tabulation(n: int) -> int:
+        if n == 0 or n == 1:
+            return 1
+
+        dp = [0] * (n+1)
+        dp[0] = dp[1] = 1
+        
+        for i in range(2, n+1):
+            dp[i] = dp[i-1] + dp[i-2]
+        return dp[n]
+
+
+if __name__ == "__main__":
+    print(climb_stairs_o2n(4))
+    print(climb_stairs_memoization(4))
+    print(climb_stairs_optimized(4))
+    print(climb_stairs_tabulation(4))