Leetcode Climbing Stairs

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

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解题思路：

这道题就是经典的讲解最简单的DP问题的问题。。

假设梯子有n层，那么如何爬到第n层呢，因为每次只能怕1或2步，那么爬到第n层的方法要么是从第n-1层一步上来的，要不就是从n-2层2步上来的，所以递推公式非常容易的就得出了：

dp[n] = dp[n-1] + dp[n-2]

如果梯子有1层或者2层，dp[1] = 1, dp[2] = 2，如果梯子有0层，自然dp[0] = 0 

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 Java code:

 public int climbStairs(int n) {
        if(n == 0 || n==1 || n==2) {
            return n;
        }
        int[] dp = new int[n+1];
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 2;
        
        for(int i = 3; i< n+1; i++){
            dp[i] = dp[i-1] + dp[i-2];
        }
        return dp[n];
    }

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Reference:

1. http://www.cnblogs.com/springfor/p/3886576.html