leetcode 062 —— 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.
思路：动态规划

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