Find a pair with maximum product in array of Integers
Last Updated :
23 Jul, 2025
Given an array with both +ive and -ive integers, return a pair with the highest product.
Examples :
Input: arr[] = {1, 4, 3, 6, 7, 0}
Output: {6,7}
Input: arr[] = {-1, -3, -4, 2, 0, -5}
Output: {-4,-5}
A Simple Solution is to consider every pair and keep track of the maximum product. Below is the implementation of this simple solution.
C++
// A simple C++ program to find max product pair in
// an array of integers
#include<bits/stdc++.h>
using namespace std;
// Function to find maximum product pair in arr[0..n-1]
void maxProduct(int arr[], int n)
{
if (n < 2)
{
cout << "No pairs exists\n";
return;
}
// Initialize max product pair
int a = arr[0], b = arr[1];
// Traverse through every possible pair
// and keep track of max product
for (int i=0; i<n; i++)
for (int j=i+1; j<n; j++)
if (arr[i]*arr[j] > a*b)
a = arr[i], b = arr[j];
cout << "Max product pair is {" << a << ", "
<< b << "}";
}
// Driver program to test
int main()
{
int arr[] = {1, 4, 3, 6, 7, 0};
int n = sizeof(arr)/sizeof(arr[0]);
maxProduct(arr, n);
return 0;
}
// JAVA Code to Find a pair with maximum
// product in array of Integers
import java.util.*;
class GFG {
// Function to find maximum product pair
// in arr[0..n-1]
static void maxProduct(int arr[], int n)
{
if (n < 2)
{
System.out.println("No pairs exists");
return;
}
// Initialize max product pair
int a = arr[0], b = arr[1];
// Traverse through every possible pair
// and keep track of max product
for (int i = 0; i < n; i++)
for (int j = i + 1; j < n; j++)
if (arr[i] * arr[j] > a * b){
a = arr[i];
b = arr[j];
}
System.out.println("Max product pair is {" +
a + ", " + b + "}");
}
/* Driver program to test above function */
public static void main(String[] args)
{
int arr[] = {1, 4, 3, 6, 7, 0};
int n = arr.length;
maxProduct(arr, n);
}
}
// This code is contributed by Arnav Kr. Mandal.
# A simple Python3 program to find max
# product pair in an array of integers
# Function to find maximum
# product pair in arr[0..n-1]
def maxProduct(arr, n):
if (n < 2):
print("No pairs exists")
return
# Initialize max product pair
a = arr[0]; b = arr[1]
# Traverse through every possible pair
# and keep track of max product
for i in range(0, n):
for j in range(i + 1, n):
if (arr[i] * arr[j] > a * b):
a = arr[i]; b = arr[j]
print("Max product pair is {", a, ",", b, "}",
sep = "")
# Driver Code
arr = [1, 4, 3, 6, 7, 0]
n = len(arr)
maxProduct(arr, n)
# This code is contributed by Smitha Dinesh Semwal.
// C# Code to Find a pair with maximum
// product in array of Integers
using System;
class GFG
{
// Function to find maximum
// product pair in arr[0..n-1]
static void maxProduct(int []arr, int n)
{
if (n < 2)
{
Console.Write("No pairs exists");
return;
}
// Initialize max product pair
int a = arr[0], b = arr[1];
// Traverse through every possible pair
// and keep track of max product
for (int i = 0; i < n; i++)
for (int j = i + 1; j < n; j++)
if (arr[i] * arr[j] > a * b)
{
a = arr[i];
b = arr[j];
}
Console.Write("Max product pair is {" +
a + ", " + b + "}");
}
// Driver Code
public static void Main()
{
int []arr = {1, 4, 3, 6, 7, 0};
int n = arr.Length;
maxProduct(arr, n);
}
}
// This code is contributed by nitin mittal.
<?php
// A simple PHP program to
// find max product pair in
// an array of integers
// Function to find maximum
// product pair in arr[0..n-1]
function maxProduct( $arr, $n)
{
if ($n < 2)
{
echo "No pairs exists\n";
return;
}
// Initialize max product pair
$a = $arr[0];
$b = $arr[1];
// Traverse through every possible pair
// and keep track of max product
for ($i = 0; $i < $n; $i++)
for ($j = $i + 1; $j < $n; $j++)
{
if ($arr[$i] * $arr[$j] > $a * $b)
{
$a = $arr[$i];
$b = $arr[$j];
}
}
echo "Max product pair is {" , $a , ", ";
echo $b , "}";
}
// Driver Code
$arr = array(1, 4, 3, 6, 7, 0);
$n = count($arr);
maxProduct($arr, $n);
// This code is contributed by anuj_67.
?>
<script>
// A simple Javascript program to find max product pair in
// an array of integers
// Function to find maximum product pair in arr[0..n-1]
function maxProduct(arr, n)
{
if (n < 2)
{
document.write("No pairs exists" + "<br>");
return;
}
// Initialize max product pair
let a = arr[0], b = arr[1];
// Traverse through every possible pair
// and keep track of max product
for (let i=0; i<n; i++)
for (let j=i+1; j<n; j++)
if (arr[i]*arr[j] > a*b)
a = arr[i], b = arr[j];
document.write("Max product pair is {" + a + ", "
+ b + "}");
}
// Driver program to test
let arr = [1, 4, 3, 6, 7, 0];
let n = arr.length;
maxProduct(arr, n);
// This code is contributed by Mayank Tyagi
</script>
OutputMax product pair is {6, 7}
Time Complexity: O(n2)
Auxiliary Space: O(1)
Better Approach:
A Better Solution is to use sorting. Below are detailed steps.
- Sort input array in increasing order.
- If all elements are positive, then return the product of the last two numbers.
- Else return a maximum of products of the first two and last two numbers.
Thanks to Rahul Jain for suggesting this method.
C++14
// C++ code to find a pair with maximum
// product in array of Integers
#include<bits/stdc++.h>
using namespace std;
void maxProduct(vector<int>arr, int n)
{
// Sort the array
sort(arr.begin(), arr.end());
int num1, num2;
// Calculate product of two smallest numbers
int sum1 = arr[0] * arr[1];
// Calculate product of two largest numbers
int sum2 = arr[n - 1] * arr[n - 2];
// Print the pairs whose product is greater
if (sum1 > sum2)
{
num1 = arr[0];
num2 = arr[1];
}
else
{
num1 = arr[n - 2];
num2 = arr[n - 1];
}
cout << ("Max product pair = ")
<< num1 << "," << num2;
}
// Driver Code
int main()
{
vector<int>arr = { 1, 4, 3, 6, 7, 0 };
int n = arr.size();
maxProduct(arr, n);
}
// This code is contributed by Stream_Cipher
// JAVA Code to Find a pair with maximum
// product in array of Integers
import java.util.*;
public class GFG {
static void maxProduct(int arr[], int n)
{
// Sort the array
Arrays.sort(arr);
int num1, num2;
// Calculate product of two smallest numbers
int sum1 = arr[0] * arr[1];
// Calculate product of two largest numbers
int sum2 = arr[n - 1] * arr[n - 2];
// print the pairs whose product is greater
if (sum1 > sum2) {
num1 = arr[0];
num2 = arr[1];
}
else {
num1 = arr[n - 2];
num2 = arr[n - 1];
}
System.out.println("Max product pair = " +
"{" + num1 + "," + num2 + "}");
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 1, 4, 3, 6, 7, 0 };
int n = arr.length;
maxProduct(arr, n);
}
}
// Contributed by Navtika Kumar
# Python code to find a pair with maximum
# product in array of Integers
def maxProduct(arr, n):
# Sort the array
arr.sort()
num1 = num2 = 0
# Calculate product of two smallest numbers
sum1 = arr[0] * arr[1]
# Calculate product of two largest numbers
sum2 = arr[n - 1] * arr[n - 2]
# Print the pairs whose product is greater
if (sum1 > sum2):
num1 = arr[0]
num2 = arr[1]
else:
num1 = arr[n - 2]
num2 = arr[n - 1]
print("Max product pair = {", num1, ",", num2, "}", sep="")
# Driver Code
arr = [1, 4, 3, 6, 7, 0]
n = len(arr)
maxProduct(arr, n)
# This code is contributed by subhammahato348.
// C# code to Find a pair with maximum
// product in array of Integers
using System;
class GFG{
static void maxProduct(int []arr, int n)
{
// Sort the array
Array.Sort(arr);
int num1, num2;
// Calculate product of two
// smallest numbers
int sum1 = arr[0] * arr[1];
// Calculate product of two
// largest numbers
int sum2 = arr[n - 1] * arr[n - 2];
// Print the pairs whose
// product is greater
if (sum1 > sum2)
{
num1 = arr[0];
num2 = arr[1];
}
else
{
num1 = arr[n - 2];
num2 = arr[n - 1];
}
Console.Write("Max product pair = " +
"{" + num1 + "," + num2 + "}");
}
// Driver Code
public static void Main(String[] args)
{
int []arr = { 1, 4, 3, 6, 7, 0 };
int n = arr.Length;
maxProduct(arr, n);
}
}
// This code is contributed by shivanisinghss2110
<script>
// Javascript code to Find a pair with maximum
// product in array of Integers
function maxProduct(arr, n)
{
// Sort the array
arr.sort(function(a, b){return a - b});
let num1, num2;
// Calculate product of two smallest numbers
let sum1 = arr[0] * arr[1];
// Calculate product of two largest numbers
let sum2 = arr[n - 1] * arr[n - 2];
// print the pairs whose product is greater
if (sum1 > sum2)
{
num1 = arr[0];
num2 = arr[1];
}
else
{
num1 = arr[n - 2];
num2 = arr[n - 1];
}
document.write("Max product pair = " +
"{" + num1 + "," + num2 + "}");
}
// Driver Code
let arr = [ 1, 4, 3, 6, 7, 0 ];
let n = arr.length;
maxProduct(arr, n);
// This code is contributed by avanitrachhadiya2155
</script>
OutputMax product pair = 6,7
Time Complexity: O(nlog n)
Auxiliary Space: O(1)
Efficient Approach:
An Efficient Solution can solve the above problem in a single traversal of the input array. The idea is to traverse the input array and keep track of the following four values.
- Maximum positive value
- Second maximum positive value
- Maximum negative value i.e., a negative value with maximum absolute value
- Second maximum negative value.
At the end of the loop, compare the products of the first two and last two and print the maximum of two products. Below is the implementation of this idea.
C++
// A O(n) C++ program to find maximum product pair in an array
#include<bits/stdc++.h>
using namespace std;
// Function to find maximum product pair in arr[0..n-1]
void maxProduct(int arr[], int n)
{
if (n < 2)
{
cout << "No pairs exists\n";
return;
}
if (n == 2)
{
cout << arr[0] << " " << arr[1] << endl;
return;
}
// Initialize maximum and second maximum
int posa = INT_MIN, posb = INT_MIN;
// Initialize minimum and second minimum
int nega = INT_MIN, negb = INT_MIN;
// Traverse given array
for (int i = 0; i < n; i++)
{
// Update maximum and second maximum if needed
if (arr[i] > posa)
{
posb = posa;
posa = arr[i];
}
else if (arr[i] > posb)
posb = arr[i];
// Update minimum and second minimum if needed
if (arr[i] < 0 && abs(arr[i]) > abs(nega))
{
negb = nega;
nega = arr[i];
}
else if(arr[i] < 0 && abs(arr[i]) > abs(negb))
negb = arr[i];
}
if (nega*negb > posa*posb)
cout << "Max product pair is {" << nega << ", "
<< negb << "}";
else
cout << "Max product pair is {" << posa << ", "
<< posb << "}";
}
// Driver program to test above function
int main()
{
int arr[] = {1, 4, 3, 6, 7, 0};
int n = sizeof(arr)/sizeof(arr[0]);
maxProduct(arr, n);
return 0;
}
// JAVA Code to Find a pair with maximum
// product in array of Integers
import java.util.*;
class GFG {
// Function to find maximum product pair
// in arr[0..n-1]
static void maxProduct(int arr[], int n)
{
if (n < 2)
{
System.out.println("No pairs exists");
return;
}
if (n == 2)
{
System.out.println(arr[0] + " " + arr[1]);
return;
}
// Initialize maximum and second maximum
int posa = Integer.MIN_VALUE,
posb = Integer.MIN_VALUE;
// Initialize minimum and second minimum
int nega = Integer.MIN_VALUE,
negb = Integer.MIN_VALUE;
// Traverse given array
for (int i = 0; i < n; i++)
{
// Update maximum and second maximum
// if needed
if (arr[i] > posa)
{
posb = posa;
posa = arr[i];
}
else if (arr[i] > posb)
posb = arr[i];
// Update minimum and second minimum
// if needed
if (arr[i] < 0 && Math.abs(arr[i]) >
Math.abs(nega))
{
negb = nega;
nega = arr[i];
}
else if(arr[i] < 0 && Math.abs(arr[i])
> Math.abs(negb))
negb = arr[i];
}
if (nega * negb > posa * posb)
System.out.println("Max product pair is {"
+ nega + ", " + negb + "}");
else
System.out.println("Max product pair is {"
+ posa + ", " + posb + "}");
}
/* Driver program to test above function */
public static void main(String[] args)
{
int arr[] = {1, 4, 3, 6, 7, 0};
int n = arr.length;
maxProduct(arr, n);
}
}
// This code is contributed by Arnav Kr. Mandal.
# A O(n) Python 3 program to find
# maximum product pair in an array
# Function to find maximum product
# pair in arr[0..n-1]
def maxProduct(arr, n):
if (n < 2):
print("No pairs exists")
return
if (n == 2):
print(arr[0] ," " , arr[1])
return
# Initialize maximum and
# second maximum
posa = 0
posb = 0
# Initialize minimum and
# second minimum
nega = 0
negb = 0
# Traverse given array
for i in range(n):
# Update maximum and second
# maximum if needed
if (arr[i] > posa):
posb = posa
posa = arr[i]
elif (arr[i] > posb):
posb = arr[i]
# Update minimum and second
# minimum if needed
if (arr[i] < 0 and abs(arr[i]) > abs(nega)):
negb = nega
nega = arr[i]
elif(arr[i] < 0 and abs(arr[i]) > abs(negb)):
negb = arr[i]
if (nega * negb > posa * posb):
print("Max product pair is {" ,
nega ,", ", negb , "}")
else:
print( "Max product pair is {" ,
posa ,", " ,posb , "}")
# Driver Code
if __name__ =="__main__":
arr = [1, 4, 3, 6, 7, 0]
n = len(arr)
maxProduct(arr, n)
# This code is contributed
# by ChitraNayal
// C# Code to Find a pair with maximum
// product in array of Integers
using System;
class GFG {
// Function to find maximum
// product pair in arr[0..n-1]
static void maxProduct(int []arr, int n)
{
if (n < 2)
{
Console.WriteLine("No pairs exists");
return;
}
if (n == 2)
{
Console.WriteLine(arr[0] + " " + arr[1]);
return;
}
// Initialize maximum and
// second maximum
int posa = int.MinValue;
int posb = int.MaxValue;
// Initialize minimum and
// second minimum
int nega = int.MinValue;
int negb = int.MaxValue;
// Traverse given array
for (int i = 0; i < n; i++)
{
// Update maximum and
// second maximum
// if needed
if (arr[i] > posa)
{
posb = posa;
posa = arr[i];
}
else if (arr[i] > posb)
posb = arr[i];
// Update minimum and
// second minimum if
// needed
if (arr[i] < 0 && Math.Abs(arr[i]) >
Math.Abs(nega))
{
negb = nega;
nega = arr[i];
}
else if(arr[i] < 0 &&
Math.Abs(arr[i]) >
Math.Abs(negb))
negb = arr[i];
}
if (nega * negb > posa * posb)
Console.WriteLine("Max product pair is {"
+ nega + ", " + negb + "}");
else
Console.WriteLine("Max product pair is {"
+ posa + ", " + posb + "}");
}
// Driver Code
public static void Main()
{
int []arr = {1, 4, 3, 6, 7, 0};
int n = arr.Length;
maxProduct(arr, n);
}
}
// This code is contributed by anuj_67.
<?php
// A O(n) PHP program to find maximum
// product pair in an array
// Function to find maximum product
// pair in arr[0..n-1]
function maxProduct(&$arr, $n)
{
if ($n < 2)
{
echo("No pairs exists\n");
return;
}
if ($n == 2)
{
echo ($arr[0]);
echo (" ");
echo($arr[1]);
echo("\n");
return;
}
// Initialize maximum and
// second maximum
$posa = 0;
$posb = 0;
// Initialize minimum and
// second minimum
$nega = 0;
$negb = 0;
// Traverse given array
for ($i = 0; $i < $n; $i++)
{
// Update maximum and second
// maximum if needed
if ($arr[$i] > $posa)
{
$posb = $posa;
$posa = $arr[$i];
}
else if ($arr[$i] > $posb)
$posb = $arr[$i];
// Update minimum and second
// minimum if needed
if ($arr[$i] < 0 &&
abs($arr[$i]) > abs($nega))
{
$negb = $nega;
$nega = $arr[$i];
}
else if($arr[$i] < 0 &&
abs($arr[$i]) > abs($negb))
$negb = $arr[$i];
}
if ($nega * $negb > $posa * $posb)
{
echo("Max product pair is {");
echo $nega;
echo(", ");
echo ($negb);
echo ("}");
}
else
{
echo("Max product pair is {");
echo $posa;
echo(", ");
echo ($posb);
echo ("}");
}
}
// Driver Code
$arr = array(1, 4, 3, 6, 7, 0);
$n = sizeof($arr);
maxProduct($arr, $n);
// This code is contributed
// by Shivi_Aggarwal
?>
<script>
// JAVAscript Code to Find a pair with maximum
// product in array of Integers
// Function to find maximum product pair
// in arr[0..n-1]
function maxProduct(arr,n)
{
if (n < 2)
{
document.write("No pairs exists");
return;
}
if (n == 2)
{
document.write(arr[0] + " " + arr[1]);
return;
}
// Initialize maximum and second maximum
let posa = Number.MIN_VALUE,
posb = Number.MIN_VALUE;
// Initialize minimum and second minimum
let nega = Number.MIN_VALUE,
negb = Number.MIN_VALUE;
// Traverse given array
for (let i = 0; i < n; i++)
{
// Update maximum and second maximum
// if needed
if (arr[i] > posa)
{
posb = posa;
posa = arr[i];
}
else if (arr[i] > posb)
posb = arr[i];
// Update minimum and second minimum
// if needed
if (arr[i] < 0 && Math.abs(arr[i]) >
Math.abs(nega))
{
negb = nega;
nega = arr[i];
}
else if(arr[i] < 0 && Math.abs(arr[i])
> Math.abs(negb))
negb = arr[i];
}
if (nega * negb > posa * posb)
document.write("Max product pair is {"
+ nega + ", " + negb + "}");
else
document.write("Max product pair is {"
+ posa + ", " + posb + "}");
}
/* Driver program to test above function */
let arr=[1, 4, 3, 6, 7, 0];
let n = arr.length;
maxProduct(arr, n);
// This code is contributed by rag2127
</script>
OutputMax product pair is {7, 6}
Time complexity: O(n)
Auxiliary Space: O(1)
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