leetcode-62-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?

思路：

很朴素，除了最上边一行和最左边一列，路径数跟左边和上边的路径数有关系。于是不难写出：

grid[i][j] = grid[i - 1][j] + grid[i][j-1];

int uniquePaths(int m, int n)
    {
        if (m <= 0 || n <= 0)return 0;
        vector<vector<int>>grid(m,vector<int>(n));
        grid[0][0] = 1;
        for (int i = 0; i < m;i++)
        {
            for (int j = 0; j < n;j++)
            {
                if (i ==0 && j != 0)
                {
                    grid[i][j] = 1;
                }
                if (i != 0 && j == 0)
                {
                    grid[i][j] = 1;
                }
                if (i != 0 && j != 0)
                {
                    grid[i][j] = grid[i - 1][j] + grid[i][j-1];
                }
            }
        }
        return grid[m-1][n-1];
    }