# Leetcode: 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.

Version 1. Initialize first row and first column separately

```    public int uniquePaths(int m, int n) {
if (m <= 0 || n <= 0) {
return 0;
}
int[][] f = new int[m][n];
//initialize the first column
for (int i = 0; i < m; i++) {
f[i] = 1;
}
//initialize the first row
for (int j = 0; j < n; j++) {
f[j] = 1;
}
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];
}
}
return f[m - 1][n - 1];
}```

Version 2. Put initialization in the 2 for loop.

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