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20. Unique Paths

Pattern: 2D DP

Problem

Robot on m×n grid, starts top-left, can only move right or down. How many unique paths to bottom-right?

Solution

func uniquePaths(m int, n int) int {
    dp := make([][]int, m)
    for i := 0; i < m; i++ {
        dp[i] = make([]int, n)
        dp[i][0] = 1
    }
    for j := 0; j < n; j++ {
        dp[0][j] = 1
    }

    for i := 1; i < m; i++ {
        for j := 1; j < n; j++ {
            dp[i][j] = dp[i-1][j] + dp[i][j-1]
        }
    }

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

dp[i][j] = dp[i-1][j] + dp[i][j-1]. First row and column are all 1s (only one way to reach them).