Divide 1 to n into two groups with minimum sum difference

4

Given a positive integer n such that n > 2. Divide numbers from 1 to n in two groups such that absolute difference of sum of each group is minimum. Print any two groups with their size in first line and in next line print elements of that group.

Examples:

Input : 5
Output : 2
         5 2
         3
         4 3 1
Here sum of group 1 is 7 and sum of group 2 is 8.
Their absolute difference is 1 which is minimum.
We can have multiple correct answers. (1, 2, 5) and 
(3, 4) is another such group.

Input : 6
Output : 2
         6 4
         4
         5 3 2 1

We can always divide sum of n integers in two groups such that their absolute difference of their sum is 0 or 1. So sum of group at most differ by 1. We define sum of group1 as half of n elements sum.

Now run a loop from n to 1 and insert i into group1 if inserting an element doesn’t exceed group1 sum otherwise insert that i into group2.

C++

// CPP program to divide n integers
// in two groups such that absolute
// difference of their sum is minimum
#include <bits/stdc++.h>
using namespace std;

// To print vector along size
void printVector(vector<int> v)
{
    // Print vector size
    cout << v.size() << endl;

    // Print vector elements
    for (int i = 0; i < v.size(); i++)
        cout << v[i] << " ";

    cout << endl;
}

// To divide n in two groups such that
// absolute difference of their sum is 
// minimum
void findTwoGroup(int n)
{
    // Find sum of all elements upto n
    int sum = n * (n + 1) / 2;

    // Sum of elements of group1
    int group1Sum = sum / 2;

    vector<int> group1, group2;

    for (int i = n; i > 0; i--) {

        // If sum is greater then or equal
        // to 0 include i in group 1
        // otherwise include in group2
        if (group1Sum - i >= 0) {

            group1.push_back(i);

            // Decrease sum of group1
            group1Sum -= i;
        }
        else {
            group2.push_back(i);
        }
    }

    // Print both the groups
    printVector(group1);
    printVector(group2);
}

// Driver program to test above functions
int main()
{
    int n = 5;
    findTwoGroup(n);
    return 0;
}

Java

// Java program to divide n integers
// in two groups such that absolute
// difference of their sum is minimum
import java.io.*;
import java.util.*;

class GFG 
{
    // To print vector along size
    static void printVector(Vector<Integer> v)
    {
        // Print vector size
        System.out.println(v.size());
    
        // Print vector elements
        for (int i = 0; i < v.size(); i++)
            System.out.print(v.get(i) + " ");
    
        System.out.println();
    }
    
    // To divide n in two groups such that
    // absolute difference of their sum is 
    // minimum
    static void findTwoGroup(int n)
    {
        // Find sum of all elements upto n
        int sum = n * (n + 1) / 2;
    
        // Sum of elements of group1
        int group1Sum = sum / 2;
    
        Vector<Integer> group1 = new Vector<Integer>();
        Vector<Integer> group2 = new Vector<Integer>();
    
        for (int i = n; i > 0; i--) {
    
            // If sum is greater then or equal
            // to 0 include i in group1
            // otherwise include in group2
            if (group1Sum - i >= 0) {
    
                group1.add(i);
    
                // Decrease sum of group1
                group1Sum -= i;
            }
            else {
                group2.add(i);
            }
        }
    
        // Print both the groups
        printVector(group1);
        printVector(group2);
    }
    
    // Driver code
    public static void main (String[] args) 
    {
        int n = 5;
        findTwoGroup(n);
    }
}

// This code is contributed by Gitanjali.

Python3

# Python program to divide n integers
# in two groups such that absolute
# difference of their sum is minimum
import math

# To print vector along size
def printVector( v):

    # Print vector size
    print(len(v))

    # Print vector elements
    for i in range( 0, len(v)):
        print(v[i] , end =  " ")

    print()


# To divide n in two groups such that
# absolute difference of their sum is 
# minimum
def findTwoGroup(n):

    # Find sum of all elements upto n
    sum = n * (n + 1) / 2

    # Sum of elements of group1
    group1Sum = sum / 2

    group1=[]
    group2=[]
    for i in range(n, 0, -1):

        # If sum is greater then or equal
        # to 0 include i in group 1
        # otherwise include in group2
        if (group1Sum - i >= 0) :
            group1.append(i)

            # Decrease sum of group1
            group1Sum -= i
        
        else :
            group2.append(i)

    # Print both the groups
    printVector(group1)
    printVector(group2)

# driver code
n = 5
findTwoGroup(n)

# This code is contributed by Gitanjali.


Output:

2
5 2
3
4 3 1

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