[LeetCode] Problem 62 - Unique Paths

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A robot is located at the top-left corner of a m x n grid.

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.

How many possible unique paths are there?

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Note

m and n will be at most 100.

Example

No.1

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 -> Right -> Down
  2. Right -> Down -> Right
  3. Down -> Right -> Right

No.2

Input: m = 7, n = 3

Output: 28

Code

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// O(mn) runtime, O(mn) space – Bottom-up dynamic programming
public int uniquePaths(int m, int n) {
    int[][] dp = new int[m][n];

    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            if (i == 0 || j == 0)
                dp[i][j] = 1;
            else
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
        }
    }

    return dp[m-1][n-1];
}