Minimum Path Sum Program in Go (Golang)

Overview

There is an m*n matrix that contains non-negative integers. The objective is to find a minimum sum path moving from Top-Left to Bottom-Right. You can only move right or down.

For example, let’s say we have below matrix

Then minimum sum path is below the path. It has a sum of 1+1+2+2+1 = 7

[{0,0}, {1,0}, {1,1}, {2,1}, {2,2}

It is a dynamic programming question as it has an optimal substructure. Let’s say the name of the matrix is input

• minPath[0][0] = input[0][0]

• minPath[i][j] = ming(minPath[i-1][j], minPath[i][j-1])) + input[i][j]

where minPath[i][j] represents the minimum sum from {0,0} to {i,j}

Program

Here is the program for the same.

package main

import "fmt"

func minPathSum(grid [][]int) int {
	rows := len(grid)
	columns := len(grid[0])
	sums := make([][]int, rows)

	for i := 0; i < rows; i++ {
		sums[i] = make([]int, columns)
	}

	sums[0][0] = grid[0][0]

	for i := 1; i < rows; i++ {
		sums[i][0] = grid[i][0] + sums[i-1][0]
	}

	for i := 1; i < columns; i++ {
		sums[0][i] = grid[0][i] + sums[0][i-1]
	}

	for i := 1; i < rows; i++ {
		for j := 1; j < columns; j++ {
			if sums[i-1][j] < sums[i][j-1] {
				sums[i][j] = grid[i][j] + sums[i-1][j]
			} else {
				sums[i][j] = grid[i][j] + sums[i][j-1]
			}
		}
	}

	return sums[rows-1][columns-1]

}

func main() {
	input := [][]int{{1, 4, 2}, {1, 3, 2}, {2, 2, 1}}
	output := minPathSum(input)
	fmt.Println(output)
}

Output

7

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