Minimum Path Sum Program in Go (Golang) - Welcome To Golang By Example

Table of Contents

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

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