Leetcode 70. Climbing Stairs

题目

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?

思路

到达当前节点的走法，只取决于上一次是走了 one step 或者 two steps，所以比较容易求得递归方程。

countOfWays(n) = countOfWays(n-1) + countOfWays(n-2)

代码

有了递归方程就非常容易写出代码了。

int climbStairs(int n) {
    if(n == 1)  return 1;
    if(n == 2)  return 2;
    
    int a = 1, b = 2, curr;
    for(int i = 3; i <= n; i++) {
        curr = a + b;
        a = b;
        b = curr;
    }
        
    return curr;
}

时间复杂度 O（n）