LeetCode: Unique Paths

最新推荐文章于 2019-04-14 18:52:56 发布

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本文介绍了一个经典的动态规划问题——计算机器人从网格左上角到右下角的不同路径数量。通过使用二维数组记录到达每个格子的不同路径数，最终求得目标格子的路径总数。

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A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

DP。

class Solution {
public:
    int uniquePaths(int m, int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if (m == 0 || n == 0)
            return 0;
            
        vector< vector<int> > path(m, vector<int>(n));
        for (int i = 0; i < m; ++i)
            path[i][0] = 1;
        for (int j = 0; j < n; ++j)
            path[0][j] = 1;
        
        for (int i = 1; i < m; ++i)
        {
            for (int j = 1; j < n; ++j)
            {
                path[i][j] = path[i-1][j] + path[i][j-1];
            }
        }
        return path[m-1][n-1];
    }
};