62. Unique Paths

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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.

public class Solution {    public int uniquePaths(int m, int n) {        if (m == 0 || n == 0) {            return 0;        }                int[][] sum = new int[m][n];        for (int i = 0; i < m; i++) {            sum[i][0] = 1;        }        for (int i = 0; i < n; i++) {            sum[0][i] = 1;        }        for (int i = 1; i < m; i++) {            for (int j = 1; j < n; j++) {                sum[i][j] = sum[i - 1][j] + sum[i][j - 1];            }        }        return sum[m - 1][n - 1];    }}

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