Unique Paths | Problems

A robot is on an m×n grid starting top-left. It can only move right or down. How many unique paths to bottom-right?

Example: m = 3, n = 7 → Output: 28

Sample Input

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Sample Output

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Constraints

1 <= m, n <= 100

Test Cases

Case 1

Args: [3,7] Expected: 28

Case 2

Args: [3,2] Expected: 3

Topics

Dynamic Programming Memoization

DP

function uniquePaths(m, n) {
  const dp = Array(n).fill(1);
  for (let i = 1; i < m; i++)
    for (let j = 1; j < n; j++)
      dp[j] += dp[j-1];
  return dp[n-1];
}

Time: O(mn) | Space: O(n)

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