Climbing Stairs 解答

Question

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?

Solution

Classic DP problem. When we climb n steps, we have two choices for last step, either one step or two steps. To save space, we can further improve the solution using O(1) space.

public class Solution {
    public int climbStairs(int n) {
        if (n < 1)
            return 0;
        int[] dp = new int[3];
        dp[0] = 1;
        dp[1] = 1;
        for (int i = 2; i <= n; i++) {
            dp[2] = dp[0] + dp[1];
            dp[0] = dp[1];
            dp[1] = dp[2];
        }
        return dp[1];
    }
}