Problems / Unique Paths
Medium

Unique Paths

Medium 0 submissions 25 coins +100 XP
Dynamic Programming Math
Problem Description
There is a robot on an `m x n` grid. The robot is initially located at the **top-left corner** (i.e., `grid[0][0]`). The robot tries to move to the **bottom-right corner** (i.e., `grid[m - 1][n - 1]`). The robot can only move either **down** or **right** at any point in time. Given the two integers `m` and `n`, return the number of possible unique paths that the robot can take to reach the bottom-right corner. The test cases are generated so that the answer will be less than or equal to `2 * 10^9`. **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 = 1, n = 1 Output: 1 **Hint:** Use dynamic programming where `dp[i][j]` = number of paths to cell (i, j) = `dp[i-1][j] + dp[i][j-1]`.
Constraints
- 1 <= m, n <= 100

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