Maximize sum of an Array by flipping sign of all elements of a single subarray
Last Updated :
15 Jul, 2025
Given an array arr[] of N integers, the task is to find the maximum sum of the array that can be obtained by flipping signs of any subarray of the given array at most once.
Examples:
Input: arr[] = {-2, 3, -1, -4, -2}
Output: 8
Explanation:
Flipping the signs of subarray {-1, -4, -2} modifies the array to {-2, 3, 1, 4, 2}. Therefore, the sum of the array = -2 + 3 + 1 + 4 + 2 = 8, which is the maximum possible.
Input: arr[] = {1, 2, -10, 2, -20}
Output: 31
Explanation:
Flipping the signs of subarray {-10, 2, -20} modifies the array to {1, 2, 10, -2, 20}. Therefore, the sum of the array = 1 + 2 + 10 - 2 + 20 = 31, which is the maximum possible.
Naive Approach: The simplest approach is to calculate the total sum of the array and then generate all possible subarrays. Now, for each subarray {A[i], ... A[j]}, subtract its sum, sum(A[i], ..., A[j]), from the total sum and flip the signs of the subarray elements. After flipping the subarray, add the sum of the flipped subarray, i.e. (-1 * sum(A[i], ..., A[j])), to the total sum. Below are the steps:
- Find the total sum of the original array (say total_sum) and store it.
- Now, for all possible subarrays find the maximum of total_sum - 2 * sum(i, j).
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the maximum sum
// after flipping a subarray
int maxSumFlip(int a[], int n)
{
// Stores the total sum of array
int total_sum = 0;
for (int i = 0; i < n; i++)
total_sum += a[i];
// Initialize the maximum sum
int max_sum = INT_MIN;
// Iterate over all possible subarrays
for (int i = 0; i < n; i++)
{
// Initialize sum of the subarray
// before flipping sign
int sum = 0;
for (int j = i; j < n; j++)
{
// Calculate the sum of
// original subarray
sum += a[j];
// Subtract the original
// subarray sum and add
// the flipped subarray
// sum to the total sum
max_sum = max(max_sum, total_sum - 2 * sum);
}
}
// Return the max_sum
return max(max_sum, total_sum);
}
// Driver Code
int main()
{
int arr[] = { -2, 3, -1, -4, -2 };
int N = sizeof(arr) / sizeof(int);
cout << maxSumFlip(arr, N);
}
// This code is contributed by sanjoy_62
// Java program for the above approach
import java.io.*;
public class GFG
{
// Function to find the maximum sum
// after flipping a subarray
public static int maxSumFlip(int a[], int n)
{
// Stores the total sum of array
int total_sum = 0;
for (int i = 0; i < n; i++)
total_sum += a[i];
// Initialize the maximum sum
int max_sum = Integer.MIN_VALUE;
// Iterate over all possible subarrays
for (int i = 0; i < n; i++)
{
// Initialize sum of the subarray
// before flipping sign
int sum = 0;
for (int j = i; j < n; j++)
{
// Calculate the sum of
// original subarray
sum += a[j];
// Subtract the original
// subarray sum and add
// the flipped subarray
// sum to the total sum
max_sum = Math.max(max_sum,
total_sum - 2 * sum);
}
}
// Return the max_sum
return Math.max(max_sum, total_sum);
}
// Driver Code
public static void main(String args[])
{
int arr[] = { -2, 3, -1, -4, -2 };
int N = arr.length;
// Function call
System.out.println(maxSumFlip(arr, N));
}
}
# Python3 program for the above approach
import sys
# Function to find the maximum sum
# after flipping a subarray
def maxSumFlip(a, n):
# Stores the total sum of array
total_sum = 0
for i in range(n):
total_sum += a[i]
# Initialize the maximum sum
max_sum = -sys.maxsize - 1
# Iterate over all possible subarrays
for i in range(n):
# Initialize sum of the subarray
# before flipping sign
sum = 0
for j in range(i, n):
# Calculate the sum of
# original subarray
sum += a[j]
# Subtract the original
# subarray sum and add
# the flipped subarray
# sum to the total sum
max_sum = max(max_sum,
total_sum - 2 * sum)
# Return the max_sum
return max(max_sum, total_sum)
# Driver Code
arr = [-2, 3, -1, -4, -2]
N = len(arr)
print(maxSumFlip(arr, N))
# This code is contributed by sanjoy_62
// C# program for the above approach
using System;
class GFG {
// Function to find the maximum sum
// after flipping a subarray
public static int maxSumFlip(int[] a, int n)
{
// Stores the total sum of array
int total_sum = 0;
for (int i = 0; i < n; i++)
total_sum += a[i];
// Initialize the maximum sum
int max_sum = int.MinValue;
// Iterate over all possible subarrays
for (int i = 0; i < n; i++)
{
// Initialize sum of the subarray
// before flipping sign
int sum = 0;
for (int j = i; j < n; j++)
{
// Calculate the sum of
// original subarray
sum += a[j];
// Subtract the original
// subarray sum and add
// the flipped subarray
// sum to the total sum
max_sum = Math.Max(max_sum,
total_sum - 2 * sum);
}
}
// Return the max_sum
return Math.Max(max_sum, total_sum);
}
// Driver Code
public static void Main(String[] args)
{
int[] arr = { -2, 3, -1, -4, -2 };
int N = arr.Length;
// Function call
Console.WriteLine(maxSumFlip(arr, N));
}
}
// This code is contributed by 29AjayKumar
<script>
// Javascript program to implement
// the above approach
// Function to find the maximum sum
// after flipping a subarray
function maxSumFlip(a, n)
{
// Find the total sum of array
let total_sum = 0;
for (let i = 0; i < n; i++)
total_sum += a[i];
// Using Kadane's Algorithm
let max_ending_here = -a[0] - a[0];
let curr_sum = -a[0] - a[0];
for (let i = 1; i < n; i++)
{
// Either extend previous
// sub_array or start
// new subarray
curr_sum = Math.max(curr_sum + (-a[i] - a[i]),
(-a[i] - a[i]));
// Keep track of max_sum array
max_ending_here
= Math.max(max_ending_here, curr_sum);
}
// Add the sum to the total_sum
let max_sum = total_sum + max_ending_here;
// Check max_sum was maximum
// with flip or without flip
max_sum = Math.max(max_sum, total_sum);
// Return max_sum
return max_sum;
}
// Driver Code
let arr = [ -2, 3, -1, -4, -2 ];
let N = arr.length;
// Function Call
document.write(maxSumFlip(arr, N));
</script>
Time Complexity: O(N2)
Auxiliary Space: O(1)
Efficient Approach: From the above approach, it can be observed that, to obtain maximum array sum, (2 * subarray sum) needs to be maximized for all subarrays. This can be done by using Dynamic Programming. Below are the steps:
- Find the minimum sum subarray from l[] using Kadane's Algorithm
- This maximizes the contribution of (2 * sum) over all subarrays.
- Add the maximum contribution to the total sum of the array.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// Function to find the maximum sum
// after flipping a subarray
int maxSumFlip(int a[], int n)
{
// Stores the total sum of array
int total_sum = 0;
for (int i = 0; i < n; i++)
total_sum += a[i];
// Kadane's algorithm to find the minimum subarray sum
int b=0,temp=2e9;
for (int i = 0; i < n; i++)
{
b+=a[i];
if(temp>b)
temp=b;
if(b>0)
b=0;
}
// Return the max_sum
return max(total_sum,total_sum-2*temp);
}
// Driver Code
int main()
{
int arr[] = { -2, 3, -1, -4, -2 };
int N = sizeof(arr) / sizeof(int);
cout << maxSumFlip(arr, N);
}
import java.util.*;
import java.io.*;
// Java program for the above approach
class GFG{
// Function to find the maximum sum
// after flipping a subarray
static int maxSumFlip(int ar[], int n)
{
// Stores the total sum of array
int total_sum = 0;
for (int i = 0 ; i < n ; i++){
total_sum += ar[i];
}
// Kadane's algorithm to find the minimum subarray sum
int b = 0;
int a = 2000000000;
for (int i = 0 ; i < n ; i++)
{
b += ar[i];
if(a > b){
a = b;
}
if(b > 0){
b = 0;
}
}
// Return the max_sum
return Math.max(total_sum, total_sum - 2*a);
}
// Driver Code
public static void main(String args[])
{
int arr[] = new int[]{ -2, 3, -1, -4, -2 };
int N = arr.length;
System.out.println(maxSumFlip(arr, N));
}
}
// This code is contributed by entertain2022.
def maxsum(l,n):
total_sum=sum(l)
#kadane's algorithm to find the minimum subarray sum
current_sum=0
minimum_sum=0
for i in l:
current_sum+=i
minimum_sum=min(minimum_sum,current_sum)
current_sum=min(current_sum,0)
return max(total_sum,total_sum-2*minimum_sum)
l=[-2,3,-1,-4,-2]
n=len(l)
print(maxsum(l,n))
// Include namespace system
using System;
// C# program for the above approach
public class GFG
{
// Function to find the maximum sum
// after flipping a subarray
public static int maxSumFlip(int[] ar, int n)
{
// Stores the total sum of array
var total_sum = 0;
for (int i = 0; i < n; i++)
{
total_sum += ar[i];
}
// Kadane's algorithm to find the minimum subarray sum
var b = 0;
var a = 2000000000;
for (int i = 0; i < n; i++)
{
b += ar[i];
if (a > b)
{
a = b;
}
if (b > 0)
{
b = 0;
}
}
// Return the max_sum
return Math.Max(total_sum,total_sum - 2 * a);
}
// Driver Code
public static void Main(String[] args)
{
int[] arr = new int[]{-2, 3, -1, -4, -2};
var N = arr.Length;
Console.WriteLine(GFG.maxSumFlip(arr, N));
}
}
// This code is contributed by sourabhdalal0001.
<script>
function maxsum(l,n){
let total_sum = 0;
for (let i = 0; i < n; i++)
total_sum += l[i];
// kadane's algorithm to find the minimum subarray sum
let current_sum=0
let minimum_sum=0
for(let i of l){
current_sum += i
minimum_sum = Math.min(minimum_sum,current_sum)
current_sum = Math.min(current_sum,0)
}
return Math.max(total_sum, total_sum-2*minimum_sum)
}
// driver code
let l = [-2, 3, -1, -4, -2]
let n = l.length
document.write(maxsum(l,n))
// This code is contributed by shinjanpatra
</script>
Time Complexity: O(N)
Auxiliary Space: O(1)
Note: Can also be done by finding minimum subarray sum and print max(TotalSum, TotalSum-2*(minsubarraysum))
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem