From 1b702cb5ad0e02179bb7a6b500725ef33f1bc0cc Mon Sep 17 00:00:00 2001
From: hiteshskp <51043123+hiteshskp@users.noreply.github.com>
Date: Sat, 5 Apr 2025 20:34:24 +0530
Subject: [PATCH] Solution 3 to Climbing Stairs Problem
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As 1 <= n <= 45 we can use Binet’s Formula (Fibonacci closed form) PS: this won't work for n>70 or 100
The "climb stairs" problem is equivalent to computing the nth Fibonacci number (with a slight index shift), where:
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2)
The number of ways to climb n stairs is the (n + 1)th Fibonacci number.
---
 Python/climbing-stairs.py | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/Python/climbing-stairs.py b/Python/climbing-stairs.py
index f1dcdfaec5..7ff54b51b5 100644
--- a/Python/climbing-stairs.py
+++ b/Python/climbing-stairs.py
@@ -42,3 +42,17 @@ def climbStairs(self, n):
         for i in xrange(n):
             prev, current = current, prev + current,
         return current
+        
+# Time:  O(1)
+# Space: O(1)
+"""
+As 1 <= n <= 45 we can use Binet’s Formula (Fibonacci closed form) PS: this won't work for n>70 or 100
+The "climb stairs" problem is equivalent to computing the nth Fibonacci number (with a slight index shift), where:
+F(0) = 0
+F(1) = 1
+F(n) = F(n-1) + F(n-2)
+The number of ways to climb n stairs is the (n + 1)th Fibonacci number.
+"""
+class Solution3:
+    def climbStairs(self, n: int) -> int:
+        return round((((1 + 5**0.5)/2) ** (n + 1)) / 5**0.5)