Dynamic Programming
Medium
Unique Paths
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. Find the number of unique paths to the bottom-right corner.
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Solve on LeetCodeProblem Understanding
We need to count how many ways to reach (m-1, n-1) from (0, 0) moving only Right or Down.
Example: m = 3, n = 2
- Right -> Down -> Down
- Down -> Down -> Right
- Down -> Right -> Down
- Output: 3
Algorithm Strategy
This is a classic DP problem on a grid.
Key Insight:
To reach cell (i, j), you must have come from either:
- Top:
(i-1, j) - Left:
(i, j-1)
Recurrence: dp[i][j] = dp[i-1][j] + dp[i][j-1]
Base Cases: dp[i][0] = 1 and dp[0][j] = 1 (only 1 way to reach cells in first row/col - go straight).
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