Unique Paths [LeetCode]

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.

Solution: Pretty easy, use dynamic programming, from bottom line to top line, caculate every the path num of every cell.

 1 class Solution {

 2 public:

 3     int uniquePaths(int m, int n) {

 4         if(m <= 0 || n <= 0)

 5             return 0;

 6         vector<int> nums;

 7         for(int i = 0; i < m; i ++) {

 8             if(i == 0) {

 9                 for(int j = 0; j < n; j++)

10                     nums.push_back(1);

11             } else {

12                 for(int j = 1; j < n; j ++) {

13                     nums[j] += nums[j - 1];

14                 }

15             }

16         }

17         return nums[n - 1];

18     }

19 };