Divide array in two Subsets such that sum of square of sum of both subsets is maximum
Given an integer array arr[], the task is to divide this array into two non-empty subsets such that the sum of the square of the sum of both the subsets is maximum and sizes of both the subsets must not differ by more than 1.
Examples:
Input: arr[] = {1, 2, 3}
Output: 26
Explanation:
Sum of Subset Pairs are as follows
(1)2 + (2 + 3)2 = 26
(2)2 + (1 + 3)2 = 20
(3)2 + (1 + 2)2 = 18
Maximum among these is 26, Therefore the required sum is 26
Input: arr[] = {7, 2, 13, 4, 25, 8}
Output: 2845
Approach: The task is to maximize the sum of a2 + b2 where a and b are the sum of the two subsets and a + b = C (constant), i.e., the sum of the entire array. The maximum sum can be achieved by sorting the array and dividing the first N/2 – 1 smaller elements in one subset and the rest N/2 + 1 elements in the other subset. In this way, the sum can be maximized while keeping the difference in size at most 1.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int maxSquareSubsetSum( int * A, int N)
{
int sub1 = 0, sub2 = 0;
sort(A, A + N);
for ( int i = 0; i < N; i++) {
if (i < (N / 2) - 1)
sub1 += A[i];
else
sub2 += A[i];
}
return sub1 * sub1 + sub2 * sub2;
}
int main()
{
int arr[] = { 7, 2, 13, 4, 25, 8 };
int N = sizeof (arr) / sizeof (arr[0]);
cout << maxSquareSubsetSum(arr, N);
return 0;
}
|
Java
import java.util.*;
class GFG
{
static int maxSquareSubsetSum( int []A, int N)
{
int sub1 = 0 , sub2 = 0 ;
Arrays.sort(A);
for ( int i = 0 ; i < N; i++)
{
if (i < (N / 2 ) - 1 )
sub1 += A[i];
else
sub2 += A[i];
}
return sub1 * sub1 + sub2 * sub2;
}
public static void main (String[] args)
{
int arr[] = { 7 , 2 , 13 , 4 , 25 , 8 };
int N = arr.length;
System.out.println(maxSquareSubsetSum(arr, N));
}
}
|
Python3
def maxSquareSubsetSum(A, N) :
sub1 = 0 ; sub2 = 0 ;
A.sort();
for i in range (N) :
if (i < (N / / 2 ) - 1 ) :
sub1 + = A[i];
else :
sub2 + = A[i];
return sub1 * sub1 + sub2 * sub2;
if __name__ = = "__main__" :
arr = [ 7 , 2 , 13 , 4 , 25 , 8 ];
N = len (arr);
print (maxSquareSubsetSum(arr, N));
|
C#
using System;
class GFG
{
static int maxSquareSubsetSum( int []A, int N)
{
int sub1 = 0, sub2 = 0;
Array.Sort(A);
for ( int i = 0; i < N; i++)
{
if (i < (N / 2) - 1)
sub1 += A[i];
else
sub2 += A[i];
}
return sub1 * sub1 + sub2 * sub2;
}
public static void Main()
{
int []arr = { 7, 2, 13, 4, 25, 8 };
int N = arr.Length;
Console.WriteLine(maxSquareSubsetSum(arr, N));
}
}
|
Javascript
<script>
function bblSort(arr){
for ( var i = 0; i < arr.length; i++){
for ( var j = 0; j < ( arr.length - i -1 ); j++){
if (arr[j] > arr[j+1]){
var temp = arr[j]
arr[j] = arr[j + 1]
arr[j+1] = temp
}
}
}
return arr;
}
function maxSquareSubsetSum(A , N) {
var sub1 = 0, sub2 = 0;
A = bblSort(A);
for (i = 0; i < N; i++) {
if (i < (N / 2) - 1)
sub1 += A[i];
else
sub2 += A[i];
}
return sub1 * sub1 + sub2 * sub2;
}
var arr = [ 7, 2, 13, 4, 25, 8 ];
var N = arr.length;
document.write(maxSquareSubsetSum(arr, N));
</script>
|
Time Complexity: O(N*log(N))
Auxiliary Space: O(1)
Last Updated :
17 Oct, 2022
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