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64. Minimum Path Sum

Medium

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]

Output: 7

Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]

Output: 12

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 100

Solution

object Solution {
    def minPathSum(grid: Array[Array[Int]]): Int = {
        val numRows = grid.length
        val numCols = grid(0).length
        val dp = Array.ofDim[Int](numRows, numCols)

        for (r <- numRows - 1 to 0 by -1) {
            for (c <- numCols - 1 to 0 by -1) {
                if (r == numRows - 1 && c == numCols - 1) {
                    dp(r)(c) = grid(r)(c)
                } else if (r == numRows - 1) {
                    dp(r)(c) = grid(r)(c) + dp(r)(c + 1)
                } else if (c == numCols - 1) {
                    dp(r)(c) = grid(r)(c) + dp(r + 1)(c)
                } else {
                    dp(r)(c) = grid(r)(c) + Math.min(dp(r + 1)(c), dp(r)(c + 1))
                }
            }
        }
        dp(0)(0)
    }
}

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