Given an array of n positive integers. We are required to write a program to print the minimum product of k integers of the given array.
Examples:
Input : 198 76 544 123 154 675 k = 2 Output : 9348 We get minimum product after multiplying 76 and 123. Input : 11 8 5 7 5 100 k = 4 Output : 1400
The idea is simple, we find the smallest k elements and print multiplication of them. In below implementation, we have used simple Heap based approach where we insert array elements into a min heap and then find product of top k elements.
C++
// CPP program to find minimum product of // k elements in an array #include <bits/stdc++.h> using namespace std; int minProduct( int arr[], int n, int k) { priority_queue< int , vector< int >, greater< int > > pq; for ( int i = 0; i < n; i++) pq.push(arr[i]); int count = 0, ans = 1; // One by one extract items from max heap while (pq.empty() == false && count < k) { ans = ans * pq.top(); pq.pop(); count++; } return ans; } // Driver code int main() { int arr[] = {198, 76, 544, 123, 154, 675}; int k = 2; int n = sizeof (arr) / sizeof (arr[0]); cout << "Minimum product is " << minProduct(arr, n, k); return 0; } |
Python3
# Python3 program to find minimum # product of k elements in an array import math import heapq def minProduct(arr, n, k): heapq.heapify(arr) count = 0 ans = 1 # One by one extract # items from min heap while ( arr ) and count < k: x = heapq.heappop(arr) ans = ans * x count = count + 1 return ans; # Driver method arr = [ 198 , 76 , 544 , 123 , 154 , 675 ] k = 2 n = len (arr) print ( "Minimum product is" , minProduct(arr, n, k)) |
Output:
Minimum product is 9348
Time Complexity : O(n * log n)
Note that the above problem can be solved in O(n) time using methods discussed here and here.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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