Given two arrays, A and B, of equal size n, the task is to find the minimum value of A[0] * B[0] + A[1] * B[1] +…+ A[n-1] * B[n-1]. Shuffling of elements of arrays A and B is allowed.
Examples :
Input : A[] = {3, 1, 1} and B[] = {6, 5, 4}.
Output : 23
Minimum value of S = 1*6 + 1*5 + 3*4 = 23.
Input : A[] = { 6, 1, 9, 5, 4 } and B[] = { 3, 4, 8, 2, 4 }
Output : 80.
Minimum value of S = 1*8 + 4*4 + 5*4 + 6*3 + 9*2 = 80.
The idea is to multiply minimum element of one array to maximum element of another array. Algorithm to solve this problem:
- Sort both the arrays A and B.
- Traverse the array and for each element, multiply A[i] and B[n – i – 1] and add to the total.
Below image is an illustration of the above approach:
Below is the implementation of the above approach:
C/C++
// C++ program to calculate minimum sum of product // of two arrays. #include <bits/stdc++.h> using namespace std; // Returns minimum sum of product of two arrays // with permutations allowed int minValue(int A[], int B[], int n) { // Sort A and B so that minimum and maximum // value can easily be fetched. sort(A, A + n); sort(B, B + n); // Multiplying minimum value of A and maximum // value of B int result = 0; for (int i = 0; i < n; i++) result += (A[i] * B[n - i - 1]); return result; } // Driven Program int main() { int A[] = { 3, 1, 1 }; int B[] = { 6, 5, 4 }; int n = sizeof(A) / sizeof(A[0]); cout << minValue(A, B, n) << endl; return 0; } |
chevron_right
filter_none
Java
// java program to calculate minimum // sum of product of two arrays. import java.io.*; import java.util.*; class GFG { // Returns minimum sum of product of two arrays // with permutations allowed static int minValue(int A[], int B[], int n) { // Sort A and B so that minimum and maximum // value can easily be fetched. Arrays.sort(A); Arrays.sort(B); // Multiplying minimum value of A // and maximum value of B int result = 0; for (int i = 0; i < n; i++) result += (A[i] * B[n - i - 1]); return result; } // Driven Program public static void main(String[] args) { int A[] = { 3, 1, 1 }; int B[] = { 6, 5, 4 }; int n = A.length; ; System.out.println(minValue(A, B, n)); } } // This code is contributed by vt_m |
chevron_right
filter_none
Python
# Python program to calculate minimum sum of product # of two arrays. # Returns minimum sum of product of two arrays # with permutations allowed def minValue(A, B, n): # Sort A and B so that minimum and maximum # value can easily be fetched. A.sort() B.sort() # Multiplying minimum value of A and maximum # value of B result = 0 for i in range(n): result += (A[i] * B[n - i - 1]) return result # Driven Program A = [3, 1, 1] B = [6, 5, 4] n = len(A) print minValue(A, B, n) # Contributed by: Afzal Ansari |
chevron_right
filter_none
C#
// C# program to calculate minimum // sum of product of two arrays. using System; class GFG { // Returns minimum sum of product // of two arrays with permutations // allowed static int minValue(int[] a, int[] b, int n) { // Sort A and B so that minimum // and maximum value can easily // be fetched. Array.Sort(a); Array.Sort(b); // Multiplying minimum value of // A and maximum value of B int result = 0; for (int i = 0; i < n; i++) result += (a[i] * b[n - i - 1]); return result; } // Driven Program public static void Main() { int[] a = { 3, 1, 1 }; int[] b = { 6, 5, 4 }; int n = a.Length; Console.Write(minValue(a, b, n)); } } // This code is contributed by nitin mittal. |
chevron_right
filter_none
PHP
<?php // PHP program to calculate minimum // sum of product of two arrays. // Returns minimum sum of // product of two arrays // with permutations allowed function minValue($A, $B, $n) { // Sort A and B so that minimum // and maximum value can easily // be fetched. sort($A); sort($A , $n); sort($B); sort($B , $n); // Multiplying minimum value of // A and maximum value of B $result = 0; for ($i = 0; $i < $n; $i++) $result += ($A[$i] * $B[$n - $i - 1]); return $result; } // Driver Code $A = array( 3, 1, 1 ); $B = array( 6, 5, 4 ); $n = sizeof($A) / sizeof($A[0]); echo minValue($A, $B, $n) ; // This code is contributed by nitin mittal. ?> |
chevron_right
filter_none
Output :
23
Time Complexity : O(n log n).
This article is contributed by Anuj Chauhan(anuj0503). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
Recommended Posts:
- Minimize Cost with Replacement with other allowed
- Maximum sum of pairwise product in an array with negative allowed
- Check if two arrays are permutations of each other
- Check if two arrays are permutations of each other using Mathematical Operation
- Maximum sum from three arrays such that picking elements consecutively from same is not allowed
- Rearrange an array to minimize sum of product of consecutive pair elements
- Minimize cost to Swap two given Arrays
- Minimize the sum calculated by repeatedly removing any two elements and inserting their sum to the Array
- Minimize the sum after choosing elements from the given three arrays
- Count number of triplets with product equal to given number with duplicates allowed
- Minimum sum of product of two arrays
- De-arrangements for minimum product sum of two arrays
- Find maximum path sum in a 2D matrix when exactly two left moves are allowed
- Maximum OR sum of sub-arrays of two different arrays
- Find sub-arrays from given two arrays such that they have equal sum
- Count of possible arrays from prefix-sum and suffix-sum arrays
- Minimize (max(A[i], B[j], C[k]) - min(A[i], B[j], C[k])) of three different sorted arrays
- Minimize count of unequal elements at corresponding indices between given arrays
- Maximum product from array such that frequency sum of all repeating elements in product is less than or equal to 2 * k
- Find Maximum dot product of two arrays with insertion of 0's
