【LeetCode】62. Unique Paths

Unique Paths

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.

 

采用動態規划。

對於格點(i,j)。由於只能從上格點(i-1,j)或左格點(i,j-1)到達，並且兩者路徑是不重復的

因此path[i][j] = path[i-1][j]+path[i][j-1]

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int> > path(m, vector<int>(n, 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];
    }
};