LeetCode Climbing Stairs DP

思想：

斐波那契数列。

c++:

方法一：迭代。

class Solution {
public:
    int climbStairs(int n) {
        if(n == 0 || n == 1 || n == 2) return n;
        int *sum = new int[n];
<span style="white-space:pre">	</span>sum[0] = 1;
<span style="white-space:pre">	</span>sum[1] = 2;
        for(int i=2;i<n;i++) {
            sum[i] = sum[i-1] + sum[i-2];
        }
        return sum[n - 1];
    }
};

方法二：通项公式。

class Solution {
public:
    int climbStairs(int n) {
        const double s = sqrt(5);
        return floor(((pow((1+s)/2, n+1))-(pow((1-s)/2, n+1)))/s + 0.5);
    }
};

java:

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