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