# Find a pair with maximum product in array of Integers

Given an array with both +ive and -ive integers, return a pair with 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} ```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

A Simple Solution is to consider every pair and keep track maximum product. Below is the implementation of this simple solution.

 `// A simple C++ program to find max product pair in ` `// an array of integers ` `#include ` `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, b = arr; ` ` `  `    ``// Traverse through every possible pair ` `    ``// and keep track of max product ` `    ``for` `(``int` `i=0; i 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); ` `    ``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, b = arr; ` `     `  `        ``// 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. `

 ` ``\$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. ` `?> `

Output :
`Max product pair is {6, 7}`

Time Complexity : O(n2)

A Better Solution is to use sorting. Below are detailed steps.
1) Sort input array in increasing order.
2) If all elements are positive, then return product of last two numbers.
3) Else return maximum of products of first two and last two numbers.
Time complexity of this solution is O(nLog n). Thanks to Rahul Jain for suggesting this method.

An Efficient Solution can solve the above problem in single traversal of input array. The idea is to traverse the input array and keep track of following four values.
a) Maximum positive value
b) Second maximum positive value
c) Maximum negative value i.e., a negative value with maximum absolute value
d) Second maximum negative value.
At the end of the loop, compare the products of first two and last two and print the maximum of two products. Below is the implementation of this idea.

 `// A O(n) C++ program to find maximum product pair in an array ` `#include ` `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 << ``" "` `<< arr << endl; ` `        ``return``; ` `    ``} ` ` `  `    ``// Iniitialize maximum and second maximum ` `    ``int` `posa = INT_MIN, posb = INT_MIN; ` ` `  `    ``// Iniitialize 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); ` `    ``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``; ` `        ``} ` `      `  `        ``// Iniitialize maximum and second maximum ` `        ``int` `posa = Integer.MIN_VALUE, ` `            ``posb = Integer.MIN_VALUE; ` `      `  `        ``// Iniitialize 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` ` `  `    ``# Iniitialize maximum and  ` `    ``# second maximum ` `    ``posa ``=` `0` `    ``posb ``=` `0` ` `  `    ``# Iniitialize 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 + ``" "` `+ arr); ` `            ``return``; ` `        ``} ` `     `  `        ``// Iniitialize maximum and ` `        ``// second maximum ` `        ``int` `posa = ``int``.MinValue; ` `        ``int` `posb = ``int``.MaxValue; ` `     `  `        ``// Iniitialize 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.  `

 ` ``\$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  ` `?> `

Output:
`Max product pair is {7, 6}`

Time complexity: O(n)
Auxiliary Space: O(1)

Thanks to Gaurav Ahirwar for suggesting this method.