【LeetCode】 062. 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?



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) {
Integer[][] path = new Integer[m]
;
for (int i = 0; i < m; i++) {
path[i][0] = 1;
}
for (int i = 0; i < n; i++) {
path[0][i] = 1;
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
path[i][j] = path[i - 1][j] + path[i][j - 1];
}
}
return path[m - 1][n - 1];
}
}

public class Solution {
public int uniquePaths(int m, int n) {
int N = n + m - 2, k = m - 1;
double res = 1;
for (int i = 1; i <= k; i++)
res = res * (N - k + i) / i;
return (int)res;
}
}