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?

Solution:DP

Ways to destination point is equal to ways to up neighbor of destination point and left neighbor of destination point

then we can generalize

ways[m][n]=ways[m-1][n] + ways[m][n-1]