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]
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
Australia
UK
UAE
Singapore
Canada
New
Zealand
Malaysia
USA
India
South
Africa
Ireland
Saudi
Arab
Qatar
Kuwait
Hongkong
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