LeetCode 576. Out of Boundary Paths

最新推荐文章于 2025-09-12 17:31:31 发布

转载最新推荐文章于 2025-09-12 17:31:31 发布 · 47 阅读

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原文链接：http://www.cnblogs.com/A-Little-Nut/p/10074022.html

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#数据结构与算法

本文探讨了在一个m*n的网格中，从指定起点出发，球可以向四个方向移动并可能跨出边界的问题。通过动态规划算法，计算出在限定步数内，球能跨出网格边界的路径数量。考虑到答案可能非常大，最终结果会取模10^9+7。

There is an m by n grid with a ball. Given the start coordinate (i,j) of the ball, you can move the ball to adjacent cell or cross the grid boundary in four directions (up, down, left, right). However, you can at most move N times. Find out the number of paths to move the ball out of grid boundary. The answer may be very large, return it after mod 109 + 7.

Example 1:

Input:m = 2, n = 2, N = 2, i = 0, j = 0
Output: 6
Explanation:

Example 2:

Input:m = 1, n = 3, N = 3, i = 0, j = 1
Output: 12
Explanation:

Note:

Once you move the ball out of boundary, you cannot move it back.
The length and height of the grid is in range [1,50].
N is in range [0,50].

分析

动态规划

class Solution {
public:
    int findPaths(int m, int n, int N, int i, int j) {
        if(N==0) return 0;
        uint t=pow(10,9);
        vector<vector<uint>> dp(m,vector<uint>(n,0));
        for(int step=1;step<=N;step++){
            vector<vector<uint>> temp(m,vector<uint>(n,0));
            for(int p=0;p<m;p++)
                for(int q=0;q<n;q++){
                    if(p!=0)
                       temp[p][q]+=dp[p-1][q];
                    else
                       temp[p][q]++;
                    if(p!=m-1)
                       temp[p][q]+=dp[p+1][q];
                    else
                       temp[p][q]++;
                    if(q!=0)
                       temp[p][q]+=dp[p][q-1];
                    else
                       temp[p][q]++;
                    if(q!=n-1)
                       temp[p][q]+=dp[p][q+1];
                    else
                       temp[p][q]++;
                    temp[p][q]=temp[p][q]%(1000000007);
                }
          dp=temp;
        }
        return dp[i][j];
    }
};

转载于:https://www.cnblogs.com/A-Little-Nut/p/10074022.html