Golang Program to Implement Kaden's Algorithm

There is a famous maximum sum subarray problem, in which we have a 1 Dimensional array and must find the maximum sum in that subarray. To solve this problem, the most naive approach will be to find all the sub − arrays, sum their elements, and return the maximum, but the time complexity will be O(N*N). To reduce this there is an algorithm that will reduce the time complexity from O(N*N) to O(N) named as Kadens Algorithm.

In programming, there are algorithms based on the Dynamic programming concept in which the problem is broken into sub − problems and the result is saved that is used for similar sub − problem. Kaden’s algorithm is also one of the Dynamic programming algorithms which will store the maximum subarray sum till the current index using the previous index.

Algorithm

Step 1: Import the required packages at the top using the import keyword.

Step 2: Then the main function will get run first.

• First, we declare and initialize the array.

• Now we are calling the maxSumSubArray() function in which we are implementing Kaden’s algorithm.

Step 3: maxSumSubArray() function implementation

• Initialize the variables named sum and maxSum and initialize with the values 0 and INT_MIN respectively.

• Running for loop for every element of the array. On each iteration

• Adding current index value to variable sum.

• If the condition is to check whether the sum is greater than maxSum or not if yes then we will dp maxSum = sum.

• Another if condition is to check whether the sum is less than zero or not if yes then make sum = 0.

• Return the maxSum value.

Step 4: Print the max sum subarray in the given array that is returned by the maxSumSubArray() function.

Example

Let us find the maximum subarray sum of the array {3, −3, 4, 2, −1, 5}

Sum = 0

maxSum = INT_MIN

Iteration 1

At i = 0 array[i] = 3
Sum = 0 + 3
    = 3
maxSum < sum
maxSum = 3  

Iteration 2

At i = 1 array[i] = −3
Sum = 3 + (−3)
    = 0
maxSum > sum
maxSum = 3

Iteration 3

At i = 2 array[i] = 4
Sum = 0 + 4
    = 4
maxSum < sum
maxSum = 4

Iteration 4

At i = 3 array[i] = 2
Sum = 4 + 2
    = 6
maxSum < sum
maxSum = 6

Iteration 5

At i = 4 array[i] = −1
Sum = 6 + (−1)
    = 5
maxSum > sum
maxSum = 6

Iteration 6

At i = 5 array[i] = 5
Sum = 5 + (5)
   = 10
maxSum < sum
maxSum = 10

Example

In the following example, we will demonstrate how to develop a Golang program that will implement Kaden's algorithm

package main

import (
    "fmt"
    "math"
)

// function to print the array with array and
// size of the array as argument
func printArray(array []int, size int) {
    for i := 0; i < size; i++ {
        fmt.Print(array[i], " ")
    }
    fmt.Println()
}

func maxSumSubArray(array []int, size int) int {
    // declaring variable sum of int type
    // and an iterator i
    var sum, maxSum, i int

    // initializing the variables declared above
    sum = 0
    maxSum = math.MinInt
    i = 0

    // running for loop from o to the size of the array
    for i < size {
        sum = sum + array[i]
        if sum > maxSum {
            maxSum = sum
        }
        if sum < 0 {
            sum = 0
        }
        i++
    }
    return maxSum
}

func main() {
    // declaring and initializing the
    // array of size 6 using the shorthand method
    array := []int{-2, -3, 4, -1, -2, 1, 5, -3}

    fmt.Println("Golang program to find the maximum sum subarray in the given array using Kaden's algorithm.")
    fmt.Print("array: ")
    printArray(array, len(array))

    // calling maxSumSubArray() function by passing array and length as a parameter
    sum := maxSumSubArray(array, len(array))

    fmt.Println("The maximum sum is", sum)
}

Output

Golang program to find the maximum sum subarray in the given array using Kaden's algorithm.
array: -2 -3 4 -1 -2 1 5 -3
The maximum sum is 7

Conclusion

This is the implementation of Kaden’s algorithm which is one of the dynamic programming algorithms to find the max sum subarray. To solve such a problem in the interviews in the least time everyone uses Kaden’s algorithm. To learn more about Golang you can explore these tutorials.