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Count pairs from an array with absolute difference not less than the minimum element in the pair
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C++ Program for Minimum product pair an array of positive Integers

Last Updated : 02 Aug, 2022
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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 <bits/stdc++.h> 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 <bits/stdc++.h> 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<n; i++)     {        if (arr[i] < first_min)        {           second_min = first_min;           first_min = arr[i];        }        else if (arr[i] < second_min)           second_min = arr[i];     }      return first_min * second_min; }  // 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; }

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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Count pairs from an array with absolute difference not less than the minimum element in the pair
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kartik
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Article Tags :
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  • C++ Programs
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Practice Tags :
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