Climbing Stairs

最新推荐文章于 2024-01-18 13:59:59 发布

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本文探讨了经典的爬楼梯问题，给出了两种不同的解决方案：递归方法和动态规划方法。通过对比，强调了动态规划方法在解决此类问题时的高效性和实用性。

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?

public class Solution {
    public int climbStairs(int n) {
        if (n == 0 || n == 1) return 1;
        if (n < 0) return 0;
        return climbStairs(n - 1) + climbStairs(n - 2);      
    }
}

From the code above, it is not hard to observe that this problem is almost identical to the Fibonacci Problem, if n is large, it takes a long time to find out the result. Therefore, we need to use DP to solve this problem.

public class Solution {
    public int climbStairs(int n) {
        if (n == 0 || n == 1) return 1;
        int prev = 1;
        int current = 1;
        for (int i = 2; i <= n; i++) {
            int temp = current + prev;
            prev = current;
            current = temp;
        }
        return current;      
    }
}