[LeetCode] Unique Paths

最新推荐文章于 2020-05-24 11:10:04 发布

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本文探讨了在给定大小的网格中，机器人从左上角到达右下角的所有可能路径数量。通过使用动态规划方法，解决了网格路径计数问题。

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.

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int> > f(m, vector<int>(n));
        for(int i = 0; i < n; i++)
            f[0][i] = 1;
        for(int j = 0; j < m; j++)
            f[j][0] = 1;
        
        for(int i = 1; i < m; i++)
            for(int j = 1; j < n; j++)
                f[i][j] = f[i-1][j] + f[i][j-1];
        
        return f[m-1][n-1];
    }
};