70 Climbing Stairs

70. Climbing Stairs

1. Question

You are climbing a stair case. It takesnsteps 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

2. Implementation

(1) DP

public class Solution {
    public int climbStairs(int n) {
        if (n <= 2) {
            return n;
        }

        int[] step = new int[n + 1];

        step[0] = 0;
        step[1] = 1;
        step[2] = 2;

        for (int i = 3; i <= n; i++) {
            step[i] = step[i - 1] + step[i - 2];
        }
        return step[n];
    }
}

3. Time & Space Complexity

时间复杂度O(n), 空间复杂度O(n)