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? Note: Given n will be a positive integer. Example 1: Input: 2 Output: 2 Explanation: There are two ways to climb to the top. 1. 1 step + 1 step 2. 2 steps Example 2: Input: 3 Output: 3 Explanation: There are three ways to climb to the top. 1. 1 step + 1 step + 1 step 2. 1 step + 2 steps 3. 2 steps + 1 step
动态规划解法:
class Solution{ public: int climbStairs(int n){ if(n == 1) return 1; if(n == 2) return 2; vector<int> memo(n+1,-1); memo[1] = 1; memo[2] = 2; for(int i = 3; i <= n; i++){ memo[i] = memo[i-1] + memo[i-2]; } return memo[n]; } };
参考:
怕什么真理无穷,进一寸有一寸的欢喜。---胡适