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Author: assassint2017

Climbing Stairs/Climbing_Stairs.py

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+# 第一种思路，使用组合计算公式
+# 36ms 78.71%
+class Solution:
+    def climbStairs(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        def c(n, m):
+            def factorial(num):
+                if num is 0:
+                    return 1
+                else:
+                    return num * factorial(num - 1)
+            return factorial(n) / (factorial(m) * factorial(n - m))
+
+        res = 1
+        index = 1
+        
+        while index * 2 <= n:
+            res += c(n - index * 2 + index, index)
+            index += 1
+        
+        return int(res)
+
+# 第二种思路，使用动态规划，但是超时了
+class Solution:
+    def climbStairs(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        if n is 1:
+            return 1
+        elif n is 2:
+            return 2
+        else:
+            return self.climbStairs(n - 1) + self.climbStairs(n - 2)
+
+# 第三种思路，使用基于备忘录的动态规划
+# 32ms 99.97%
+class Solution:
+    def climbStairs(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        memo = {}
+        def dp(n):
+            if n in memo:
+                return memo[n]
+            else:
+                if n is 1:
+                    ans = 1
+                elif n is 2:
+                    ans = 2
+                else:
+                    ans = dp(n - 1) + dp(n - 2)
+                memo[n] = ans
+                return memo[n]
+        return dp(n)