[LeetCode] 70. Climbing Stairs

[LeetCode] 70. Climbing Stairs

题目描述

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

分析

状态转移方程为dp[i] = dp[i-1] + dp[i-2] (i >= 3), dp[i] = i (i < 3);
即当楼梯数量大于3时，它可以从上一级一步到达，也可以从上两级一步到达。

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