70. Climbing Stairs

题目分析

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

代码一

时间复杂度为O(2^n)，Time Limit Exceeded。

class Solution {
    public int climbStairs(int n) {
        if(n <= 2) {
            return n;
        }
        return climbStairs(n - 2) + climbStairs(n - 1);
    }
}

代码二

动态规划的解法

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

代码三

class Solution {
    public int climbStairs(int n) {
        if (n == 1) return 1;
        int t1 = 1, t2 = 1, res = 0;
        for(int i = 2; i <= n; i++) {
            res = t1 + t2;
            t2 = t1;
            t1 = res;
        }
        return res;
    }
}