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UniquePaths.java
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UniquePaths.java
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package Leetcode;
/**
* @author kalpak
*
* 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.
*/
public class UniquePaths {
public static int uniquePaths(int m, int n) {
int[][] dp = new int[m][n];
// first column
for(int i = 0; i < m; i++)
dp[i][0] = 1;
// first row
for (int j = 0; j < n; j++)
dp[0][j] = 1;
for(int i = 1; i < m; i++)
{
for(int j = 1; j < n; j++)
{
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
}
return dp[m - 1][n - 1];
}
public static void main(String[] args) {
System.out.println(uniquePaths(7, 3));
}
}