Climbing Stairs

Description

You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Example 1:

Input: n = 2 Output: 2 Explanation: There are two ways to climb to the top.

1. 1 step + 1 step
2. 2 steps

Example 2:

Input: n = 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

Constraints:

• 1 <= n <= 45

Code

其實就是 Fibonacci Number。

Time Complexity: $O(n)$, Space Complexity: $O(n)$

class Solution {
public:
    int climbStairs(int n) {
        if (n <= 2) return n;
        int n1 = 1;
        int n2 = 2;
        int ways;
        for(int i = 3; i <= n; i++) {
            ways = n1 + n2;
            n1 = n2;
            n2 = ways;
        }
        return ways;
    }
};

Fibonacci computing hack: a = (b += a) - a;

class Solution {
public:
    int climbStairs(int n) {
        int a = 1, b = 1;
        while (n--)
            a = (b += a) - a;
        return a;
    }
};

Link

• 70. Climbing Stairs