[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 step + 1 step
- 2 steps
Example 2:
Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
- 1 step + 1 step + 1 step
- 1 step + 2 steps
- 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];
}
};