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# C++ Program for Minimum product pair an array of positive Integers

Given an array of positive integers. We are required to write a program to print the minimum product of any two numbers of the given array.
Examples:

```Input : 11 8 5 7 5 100
Output : 25
Explanation : The minimum product of any
two numbers will be 5 * 5 = 25.

Input : 198 76 544 123 154 675
Output : 7448
Explanation : The minimum product of any
two numbers will be 76 * 123 = 7448.```

Simple Approach : A simple approach will be to run two nested loops to generate all possible pair of elements and keep track of the minimum product.
Time Complexity: O( n * n)
Auxiliary Space: O( 1 )
Better Approach: An efficient approach will be to first sort the given array and print the product of first two numbers, sorting will take O(n log n). Answer will be then a[0] * a[1] .

## C++

 `// C++ program to calculate minimum``// product of a pair``#include ``using` `namespace` `std;` `// Function to calculate minimum product``// of pair``int` `printMinimumProduct(``int` `arr[], ``int` `n)``{``    ``//Sort the array``    ``sort(arr,arr+n);``    ` `    ``// Returning the product of first two numbers``    ``return` `arr[0] * arr[1];``}` `// Driver program to test above function``int` `main()``{``    ``int` `a[] = { 11, 8 , 5 , 7 , 5 , 100 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);``    ``cout << printMinimumProduct(a,n);``    ``return` `0;``}` `// This code is contributed by Pushpesh Raj`

Output

`25`

Time Complexity: O( n * log(n))
Auxiliary Space: O( 1 )
Best Approach: The idea is linearly traverse given array and keep track of minimum two elements. Finally return product of two minimum elements.
Below is the implementation of above approach.

## C++

 `// C++ program to calculate minimum``// product of a pair``#include ``using` `namespace` `std;` `// Function to calculate minimum product``// of pair``int` `printMinimumProduct(``int` `arr[], ``int` `n)``{``    ``// Initialize first and second``    ``// minimums. It is assumed that the``    ``// array has at least two elements.``    ``int` `first_min = min(arr[0], arr[1]);``    ``int` `second_min = max(arr[0], arr[1]);` `    ``// Traverse remaining array and keep``    ``// track of two minimum elements (Note``    ``// that the two minimum elements may``    ``// be same if minimum element appears``    ``// more than once)``    ``// more than once)``    ``for` `(``int` `i=2; i

Output

`25`

Time Complexity: O(n)
Auxiliary Space: O(1) Please refer complete article on Minimum product pair an array of positive Integers for more details!

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