LeetCode-in-All
62. Unique Paths
Medium
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?
Example 1:
Input: m = 3, n = 7
Output: 28
Example 2:
Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down
Example 3:
Input: m = 7, n = 3
Output: 28
Example 4:
Input: m = 3, n = 3
Output: 6
Constraints:
1 <= m, n <= 100- It’s guaranteed that the answer will be less than or equal to
2 * 109.
Solution
class Solution {
/**
* @param Integer $m
* @param Integer $n
* @return Integer
*/
public function uniquePaths($m, $n) {
$dp = array_fill(0, $m, array_fill(0, $n, 0));
for ($i = 0; $i < $m; $i++) {
$dp[$i][0] = 1;
}
for ($j = 0; $j < $n; $j++) {
$dp[0][$j] = 1;
}
for ($i = 1; $i < $m; $i++) {
for ($j = 1; $j < $n; $j++) {
$dp[$i][$j] = $dp[$i - 1][$j] + $dp[$i][$j - 1];
}
}
return $dp[$m - 1][$n - 1];
}
}