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.
Note: We are adding multiplication of elements which can lead to overflow conditions.
Below image is an illustration of the above approach:
Below is the implementation of the above approach:
// 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 long long 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
long long int result = 0;
for ( int i = 0; i < n; i++)
result += (A[i] * B[n - i - 1]);
return result;
} // Driven Code 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;
} |
// 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 long 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
long result = 0 ;
for ( int i = 0 ; i < n; i++)
result += (A[i] * B[n - i - 1 ]);
return result;
}
// Driven Code
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 |
# 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 |
// 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 long 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
long result = 0;
for ( int i = 0; i < n; i++)
result += (a[i] * b[n - i - 1]);
return result;
}
// Driven Code
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. |
<?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. ?> |
<script> // JavaScript 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.
A.sort( function (a,b){
return a - b;
});
B.sort( function (a,b){
return a - b;
});
// Multiplying minimum value of A
// and maximum value of B
let result = 0;
for (let i = 0; i < n; i++)
result += (A[i] * B[n - i - 1]);
return result;
} // Driver Code let A = [ 3, 1, 1 ]; let B = [ 6, 5, 4 ]; let n = A.length; document.write(minValue(A, B, n)); // This code is contributed by souravghosh0416 </script> |
23
Time Complexity: O(n log n).
Auxiliary Space: O(1) because it is using constant space for variables