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?

Notice: m and n will be at most 100.

Notes:

1. Coordinate DP

    public int uniquePaths(int m, int n) {
        if (m <= 0 || n <= 0) {
            return 0;
        }

        // state
        int[][] f = new int[m][n];

        // initialize
        for (int i = 0; i < m; ++i) {
            f[i][0] = 1;
        }
        for (int i = 0; i < n; ++i) {
            f[0][i] = 1;
        }

        // function
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                f[i][j] = f[i-1][j] + f[i][j-1];
            }
        }

        // answer
        return f[m-1][n-1];
    }