Climbing Stairs

Author: Shikha-code36

Dynamic-Programming/70-Climbing-Stairs.py

@@ -0,0 +1,67 @@
+'''Leetcode- https://leetcode.com/problems/climbing-stairs/ '''
+'''
+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?
+
+ 
+
+Example 1:
+
+Input: n = 2
+Output: 2
+Explanation: There are two ways to climb to the top.
+1. 1 step + 1 step
+2. 2 steps
+'''
+#Top down TLE #T:O(2^n)
+def climbStairs(n):
+    if n==1:
+        return 1
+    if n==2:
+        return 2
+
+    return climbStairs(n-1)+climbStairs(n-1)
+
+#Top down + memorization (list)
+def climbStairs(self,n):
+    if n == 1:
+        return 1
+    arr = [-1 for i in range(n)]
+    arr[0], arr[1] = 1, 2
+    return self.helper(n-1, arr)
+
+def helper(self, n, arr):
+    if arr[n] < 0:
+        arr[n] = self.helper(n-1, arr)+self.helper(n-2, arr)
+    return arr[n]
+
+# Top down + memorization (dictionary/hashmap) #TLE
+def climbStairs(n):
+    dic = {1:1,2:2}
+    if n not in dic:
+        dic[n] = climbStairs(n-1)+climbStairs(n-2)
+    return dic[n]
+
+# Bottom up, O(n) space
+def climbStairs(n):
+    if n==1:
+        return 1
+    res = [0 for i in range(n)]
+    res[0],res[1] = 1,2
+
+    for i in range(2,n):
+        res[i] = res[i-1] + res [i-2]
+    return res[-1]
+
+# Bottom up, constant space
+def climbStairs(n):
+    one,two = 1,1
+
+    for i in range(n-1):
+        temp = one
+        one = one+two
+        two = temp
+    return one
+
+#T:O(n)

README.md

@@ -16,4 +16,6 @@ Check the notes for the explaination - [Notes](https://stingy-shallot-4ea.notion
 - [x] [Matrix](Matrix)
     - [x] [Word Search](Matrix/79-Word-Search.py)
 - [x] [Dynamic Programming](Dynamic-Programming)
-    - [x] [Combination Sum](Dynamic-Programming/39-Combination-Sum.py)
+    - [x] [Combination Sum](Dynamic-Programming/39-Combination-Sum.py)
+    - [x] [Climbing Stairs](Dynamic-Programming/70-Climbing-Stairs.py)
+