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?

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
= 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

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
;
}

Reference:

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