[LeetCode]Unique Paths

题目

Number: 62

Difficulty: Medium

Tags: Array, Dynamic Programming

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?

题解

经典的动态规划问题。

m*n

的矩阵，从

(0, 0)

到

(m-1, n-1)

有多少种路径。

代码

[code]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][j - 1] + path[i - 1][j];
        }
    }
    return path[m - 1][n - 1];
}