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Maximize array sum after K negations | Set 1
  • Difficulty Level : Easy
  • Last Updated : 16 Apr, 2021

Given an array of size n and a number k. We must modify array K number of times. Here modify array means in each operation we can replace any array element arr[i] by -arr[i]. We need to perform this operation in such a way that after K operations, sum of array must be maximum?

Examples : 

Input : arr[] = {-2, 0, 5, -1, 2} 
        K = 4
Output: 10
Explanation:
1. Replace (-2) by -(-2), array becomes {2, 0, 5, -1, 2}
2. Replace (-1) by -(-1), array becomes {2, 0, 5, 1, 2}
3. Replace (0) by -(0), array becomes {2, 0, 5, 1, 2}
4. Replace (0) by -(0), array becomes {2, 0, 5, 1, 2}

Input : arr[] = {9, 8, 8, 5} 
        K = 3
Output: 20

This problem has very simple solution, we just have to replace the minimum element arr[i] in array by -arr[i] for current operation. In this way we can make sum of array maximum after K operations. One interesting case is, once the minimum element becomes 0, we don’t need to make any more changes. 

C++




// C++ program to maximize array sum after
// k operations.
#include <bits/stdc++.h>
using namespace std;
 
// This function does k operations on array
// in a way that maximize the array sum.
// index --> stores the index of current minimum
// element for j'th operation
int maximumSum(int arr[], int n, int k)
{
    // Modify array K number of times
    for (int i = 1; i <= k; i++)
    {
        int min = INT_MAX;
        int index = -1;
 
        // Find minimum element in array for
        // current operation and modify it
        // i.e; arr[j] --> -arr[j]
        for (int j = 0; j < n; j++)
        {
            if (arr[j] < min) {
                min = arr[j];
                index = j;
            }
        }
 
        // this the condition if we find 0 as
        // minimum element, so it will useless to
        // replace 0 by -(0) for remaining operations
        if (min == 0)
            break;
 
        // Modify element of array
        arr[index] = -arr[index];
    }
 
    // Calculate sum of array
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += arr[i];
    return sum;
}
 
// Driver code
int main()
{
    int arr[] = { -2, 0, 5, -1, 2 };
    int k = 4;
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << maximumSum(arr, n, k);
    return 0;
}

Java




// Java program to maximize array
// sum after k operations.
 
class GFG {
    // This function does k operations
    // on array in a way that maximize
    // the array sum. index --> stores
    // the index of current minimum
    // element for j'th operation
    static int maximumSum(int arr[], int n, int k)
    {
        // Modify array K number of times
        for (int i = 1; i <= k; i++)
        {
            int min = +2147483647;
            int index = -1;
 
            // Find minimum element in array for
            // current operation and modify it
            // i.e; arr[j] --> -arr[j]
            for (int j = 0; j < n; j++)
            {
                if (arr[j] < min)
                {
                    min = arr[j];
                    index = j;
                }
            }
 
            // this the condition if we find 0 as
            // minimum element, so it will useless to
            // replace 0 by -(0) for remaining operations
            if (min == 0)
                break;
 
            // Modify element of array
            arr[index] = -arr[index];
        }
 
        // Calculate sum of array
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += arr[i];
        return sum;
    }
 
    // Driver code
    public static void main(String arg[])
    {
        int arr[] = { -2, 0, 5, -1, 2 };
        int k = 4;
        int n = arr.length;
        System.out.print(maximumSum(arr, n, k));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python3 program to maximize
# array sum after k operations.
 
# This function does k operations on array
# in a way that maximize the array sum.
# index --> stores the index of current
# minimum element for j'th operation
 
 
def maximumSum(arr, n, k):
 
    # Modify array K number of times
    for i in range(1, k + 1):
 
        min = +2147483647
        index = -1
 
        # Find minimum element in array for
        # current operation and modify it
        # i.e; arr[j] --> -arr[j]
        for j in range(n):
 
            if (arr[j] < min):
 
                min = arr[j]
                index = j
 
        # this the condition if we find 0 as
        # minimum element, so it will useless to
        # replace 0 by -(0) for remaining operations
        if (min == 0):
            break
 
        # Modify element of array
        arr[index] = -arr[index]
 
    # Calculate sum of array
    sum = 0
    for i in range(n):
        sum += arr[i]
    return sum
 
 
# Driver code
arr = [-2, 0, 5, -1, 2]
k = 4
n = len(arr)
print(maximumSum(arr, n, k))
 
# This code is contributed by Anant Agarwal.

C#




// C# program to maximize array
// sum after k operations.
using System;
 
class GFG {
 
    // This function does k operations
    // on array in a way that maximize
    // the array sum. index --> stores
    // the index of current minimum
    // element for j'th operation
    static int maximumSum(int[] arr, int n, int k)
    {
 
        // Modify array K number of times
        for (int i = 1; i <= k; i++)
        {
            int min = +2147483647;
            int index = -1;
 
            // Find minimum element in array for
            // current operation and modify it
            // i.e; arr[j] --> -arr[j]
            for (int j = 0; j < n; j++)
            {
                if (arr[j] < min)
                {
                    min = arr[j];
                    index = j;
                }
            }
 
            // this the condition if we find
            // 0 as minimum element, so it
            // will useless to replace 0 by -(0)
            // for remaining operations
            if (min == 0)
                break;
 
            // Modify element of array
            arr[index] = -arr[index];
        }
 
        // Calculate sum of array
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += arr[i];
        return sum;
    }
 
    // Driver code
    public static void Main()
    {
        int[] arr = { -2, 0, 5, -1, 2 };
        int k = 4;
        int n = arr.Length;
        Console.Write(maximumSum(arr, n, k));
    }
}
 
// This code is contributed by Nitin Mittal.

PHP




<?php
// PHP program to maximize
// array sum after k operations.
 
// This function does k operations
// on array in a way that maximize
// the array sum. index --> stores
// the index of current minimum
// element for j'th operation
function maximumSum($arr, $n, $k)
{
    $INT_MAX = 0;
    // Modify array K
    // number of times
    for ($i = 1; $i <= $k; $i++)
    {
        $min = $INT_MAX;
        $index = -1;
 
        // Find minimum element in
        // array for current operation
        // and modify it i.e;
        // arr[j] --> -arr[j]
        for ($j = 0; $j < $n; $j++)
        {
            if ($arr[$j] < $min)
            {
                $min = $arr[$j];
                $index = $j;
            }
        }
 
        // this the condition if we
        // find 0 as minimum element, so
        // it will useless to replace 0
        // by -(0) for remaining operations
        if ($min == 0)
            break;
 
        // Modify element of array
        $arr[$index] = -$arr[$index];
    }
 
    // Calculate sum of array
    $sum = 0;
    for ($i = 0; $i < $n; $i++)
        $sum += $arr[$i];
    return $sum;
}
 
// Driver Code
$arr = array(-2, 0, 5, -1, 2);
$k = 4;
$n = sizeof($arr) / sizeof($arr[0]);
echo maximumSum($arr, $n, $k);
     
// This code is contributed
// by nitin mittal.
?>

Javascript




<script>
     
// Javascript program to maximize array
// sum after k operations.
 
// This function does k operations
// on array in a way that maximize
// the array sum. index --> stores
// the index of current minimum
// element for j'th operation
function maximumSum(arr, n, k)
{
     
    // Modify array K number of times
    for(let i = 1; i <= k; i++)
    {
        let min = +2147483647;
        let index = -1;
 
        // Find minimum element in array for
        // current operation and modify it
        // i.e; arr[j] --> -arr[j]
        for(let j = 0; j < n; j++)
        {
            if (arr[j] < min)
            {
                min = arr[j];
                index = j;
            }
        }
 
        // This the condition if we find 0 as
        // minimum element, so it will useless to
        // replace 0 by -(0) for remaining operations
        if (min == 0)
            break;
 
        // Modify element of array
        arr[index] = -arr[index];
    }
 
    // Calculate sum of array
    let sum = 0;
    for(let i = 0; i < n; i++)
        sum += arr[i];
         
    return sum;
}
     
// Driver code
let arr = [ -2, 0, 5, -1, 2 ];
let k = 4;
let n = arr.length;
 
document.write(maximumSum(arr, n, k));
 
// This code is contributed by code_hunt
 
</script>
Output
10

Time Complexity: O(k*n) 
Auxiliary Space: O(1)



  1. Approach 2 (Using Sort): 
    This approach is somewhat better than the above-discussed method. In this method, we will first sort the given array using the java in-built sort function which has the worst running time complexity of O(nlogn).
  2. Then for a given value of k we will continue to iterate through the array till k remains greater than 0, If the value of the array at any index is less than 0 we will change its sign and decrement k by 1.
  3. If we find a 0 in the array we will immediately set k equal to 0 to maximize our result.
  4. In some cases, if we have all the values in an array greater than 0 we will change the sign of positive values, as our array is already sorted we will be changing signs of lower values present in the array which will eventually maximize our sum.

Below is the implementation of the above approach:

C++




// C++ program to find maximum array sum
// after at most k negations.
#include <bits/stdc++.h>
 
using namespace std;
 
int sol(int arr[], int n, int k)
{
    int sum = 0;
    int i = 0;
   
    // Sorting given array using in-built
    // sort function
    sort(arr, arr + n);
    while (k > 0)
    {
        // If we find a 0 in our
        // sorted array, we stop
        if (arr[i] >= 0)
            k = 0;
        else
        {
            arr[i] = (-1) * arr[i];
            k = k - 1;
        }
        i++;
        
    }
 
    // Calculating sum
    for(int j = 0; j < n; j++)
    {
        sum += arr[j];
    }
    return sum;
}
 
// Driver code
int main()
{
    int arr[] = { -2, 0, 5, -1, 2 };
 
    int n = sizeof(arr) / sizeof(arr[0]);
     
    cout << sol(arr, n, 4) << endl;
 
    return 0;
}
 
// This code is contributed by pratham76

Java




// Java program to find maximum array sum
// after at most k negations.
import java.util.Arrays;
 
public class GFG {
 
    static int sol(int arr[], int k)
    {
        // Sorting given array using in-built
        // java sort function
        Arrays.sort(arr);
        int sum = 0;
 
        int i = 0;
        while (k > 0)
        {
            // If we find a 0 in our
            // sorted array, we stop
            if (arr[i] >= 0)
                k = 0;
 
            else
            {
                arr[i] = (-1) * arr[i];
                k = k - 1;
            }
 
            i++;
        }
 
        // Calculating sum
        for (int j = 0; j < arr.length; j++)
        {
            sum += arr[j];
        }
        return sum;
    }
   
    // Driver Code
    public static void main(String[] args)
    {
        int arr[] = { -2, 0, 5, -1, 2 };
        System.out.println(sol(arr, 4));
    }
}

Python3




# Python3 program to find maximum array
# sum after at most k negations
 
 
def sol(arr, k):
 
    # Sorting given array using
    # in-built java sort function
    arr.sort()
 
    Sum = 0
    i = 0
 
    while (k > 0):
 
        # If we find a 0 in our
        # sorted array, we stop
        if (arr[i] >= 0):
            k = 0
        else:
            arr[i] = (-1) * arr[i]
            k = k - 1
 
        i += 1
 
    # Calculating sum
    for j in range(len(arr)):
        Sum += arr[j]
 
    return Sum
 
 
# Driver code
arr = [-2, 0, 5, -1, 2]
 
print(sol(arr, 4))
 
# This code is contributed by avanitrachhadiya2155

C#




// C# program to find maximum array sum
// after at most k negations.
using System;
  
class GFG{
  
static int sol(int []arr, int k)
{
     
    // Sorting given array using
    // in-built java sort function
    Array.Sort(arr);
     
    int sum = 0;
    int i = 0;
     
    while (k > 0)
    {
         
        // If we find a 0 in our
        // sorted array, we stop
        if (arr[i] >= 0)
            k = 0;
 
        else
        {
            arr[i] = (-1) * arr[i];
            k = k - 1;
        }
        i++;
    }
     
    // Calculating sum
    for(int j = 0; j < arr.Length; j++)
    {
        sum += arr[j];
    }
    return sum;
}
 
// Driver code
public static void Main(string[] args)
{
    int []arr = { -2, 0, 5, -1, 2 };
     
    Console.Write(sol(arr, 4));
}
}
 
// This code is contributed by rutvik_56

Javascript




<script>
 
// JavaScript program to find maximum array sum
// after at most k negations.
 
    function sol(arr, k)
    {
     
        // Sorting given array using in-built
        // java sort function
        arr.sort();
        let sum = 0;
  
        let i = 0;
        while (k > 0)
        {
         
            // If we find a 0 in our
            // sorted array, we stop
            if (arr[i] >= 0)
                k = 0;
  
            else
            {
                arr[i] = (-1) * arr[i];
                k = k - 1;
            }
  
            i++;
        }
  
        // Calculating sum
        for (let j = 0; j < arr.length; j++)
        {
            sum += arr[j];
        }
        return sum;
    }
 
// Driver code
    let arr = [ -2, 0, 5, -1, 2 ];
    document.write(sol(arr, 4));
 
// This code is contributed by souravghosh0416.                            
</script>
Output
10

Time Complexity: O(n*logn) 
Auxiliary Space: O(1)

Approach 3(Using Sort):

The above approach 2 is optimal when there is a need to negate at most k elements. To solve when there are exactly k negations the algorithm is given below.

  1. Sort the array in ascending order. Initialize i = 0.
  2. Increment i and multiply all negative elements by -1 till k becomes or a positive element is reached.
  3. Check if the end of the array has occurred. If true then go to (n-1)th element.
  4. If k ==0 or k is even, return the sum of all elements. Else multiply the absolute of minimum of ith or (i-1) th element by -1.
  5. Return sum of the array.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <algorithm>
#include <iostream>
using namespace std;
 
// Function to calculate sum of the array
long long int sumArray(long long int* arr, int n)
{
    long long int sum = 0;
   
    // Iterate from 0 to n - 1
    for (int i = 0; i < n; i++) {
        sum += arr[i];
    }
    return sum;
}
 
// Function to maximize sum
long long int maximizeSum(long long int arr[], int n, int k)
{
    sort(arr, arr + n);
    int i = 0;
   
    // Iterate from 0 to n - 1
    for (i = 0; i < n; i++) {
        if (k && arr[i] < 0) {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
 
    if (k == 0 || k % 2 == 0) {
        return sumArray(arr, n);
    }
 
    if (abs(arr[i]) >= abs(arr[i - 1])) {
        i--;
    }
 
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
int main()
{
    int n = 5;
    int k = 4;
    long long int arr[5] = { -3, -2, -1, 5, 6 };
   
    // Function Call
    cout << maximizeSum(arr, n, k) << endl;
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to calculate sum of the array
static int sumArray( int[] arr, int n)
{
    int sum = 0;
    
    // Iterate from 0 to n - 1
    for(int i = 0; i < n; i++)
    {
        sum += arr[i];
    }
    return sum;
}
  
// Function to maximize sum
static int maximizeSum(int arr[], int n, int k)
{
    Arrays.sort(arr);
    int i = 0;
    
    // Iterate from 0 to n - 1
    for(i = 0; i < n; i++)
    {
        if (k != 0 && arr[i] < 0)
        {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
  
    if (k == 0 || k % 2 == 0)
    {
        return sumArray(arr, n);
    }
  
    if (Math.abs(arr[i]) >=
        Math.abs(arr[i - 1]))
    {
        i--;
    }
  
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
public static void main(String args[])
{
    int n = 5;
    int k = 4;
    int arr[] = { -3, -2, -1, 5, 6 };
    
    // Function Call
    System.out.print(maximizeSum(arr, n, k));
}
}
 
// This code is contributed by sanjoy_62

Python3




# Python3 program for the above approach
 
# Function to calculate sum of the array
def sumArray(arr, n):
    sum = 0
     
    # Iterate from 0 to n - 1
    for i in range(n):
        sum += arr[i]
         
    return sum
 
# Function to maximize sum
def maximizeSum(arr, n, k):
     
    arr.sort()
    i = 0
   
    # Iterate from 0 to n - 1
    for i in range(n):
        if (k and arr[i] < 0):
            arr[i] *= -1
            k -= 1
            continue
         
        break
     
    if (i == n):
        i -= 1
 
    if (k == 0 or k % 2 == 0):
        return sumArray(arr, n)
 
    if (abs(arr[i]) >= abs(arr[i - 1])):
        i -= 1
 
    arr[i] *= -1
    return sumArray(arr, n)
 
# Driver Code
n = 5
k = 4
arr = [ -3, -2, -1, 5, 6 ]
   
# Function Call
print(maximizeSum(arr, n, k))
 
# This code is contributed by rohitsingh07052
Output
15

Time Complexity: O(n*logn)  

Auxiliary Space: O(1)

Maximize array sum after K negations | Set 2 

This article is contributed by Shashank Mishra ( Gullu ). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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