Question

C++ program which partitions n positive integers into two disjoint sets with the same sum. Consider all possible subsets of the input numbers.

This is the sample Input 1

6
3 5 20 7 1 14

Output 1

Equal Set: 1 3 7 14

This is the sample Input 2

5
10 8 6 4 2

Output 2

Equal Set: 0

Answer 1

Main.cpp file :

#include <iostream>
#include <string>
#include <sstream>
using namespace std;

class Set {
private:
   class node {
   public:
       int data;
       node* next;
       node(int _data) {
           data = _data;
           next = nullptr;
       }
   };
public:
   node* head = nullptr;
   Set(); // default constructor
   ~Set(); // destructor
   int sum(); // return sum of all elements in the set
   void add(int x); // adds an element to end of set
   void copy(Set& s); // returns a copy of set
   string toString(); // returns a string of elements in subset separated by sapce
};

Set::Set() {
   head = nullptr;
}

Set::~Set() {
   while (head != nullptr) {
       node* temp = head;
       head = head->next;
       delete temp;
   }
}

int Set::sum() {
   int total = 0;
   node* itr = head;
   while (itr != nullptr) {
       total = total + itr->data;
       itr = itr->next;
   }
   return total;
}

void Set::add(int x) {
   if (head == nullptr) {
       head = new node(x);
   }
   else {
       node* itr = head;
       while (itr->next != nullptr) {
           itr = itr->next;
       }
       itr->next = new node(x);
   }
}

void Set::copy(Set& s) {
   node* itr = s.head;
   while (itr != nullptr) {
       this->add(itr->data);
       itr = itr->next;
   }
}

string Set::toString() {
   string str = "";
   node* itr = head;
   while (itr != nullptr) {
       str = str + to_string(itr->data) + " ";
       itr = itr->next;
   }
   return str;
}

int main() {
   cout << "Enter number of inputs followed by inputs separated by a space:" << endl; //prompt for input
   int num_of_input; //number of elements in the set
   string input; //input elements separated by space
   // get input from user
   cin >> num_of_input;
   cin.ignore();
   getline(cin, input);

   // for n element in the set there are 2^n-1 posible subsets
   int num_subset = pow(2, num_of_input) - 1;
   // create an array to hold the subsets
   Set* subsets = new Set[num_subset];
   // create universal set from input
   int* universal = new int[num_of_input];
   stringstream ss;
   ss << input;
   for (int i = 0; i < num_of_input; i++) {
       ss >> universal[i];
   }
   // get total sum of universal set
   int total_sum = 0;
   for (int i = 0; i < num_of_input; i++) {
       total_sum = total_sum + universal[i];
   }
   // disjoint sets should have half the sum of total
   int sum = total_sum / 2;
   // create subsets
   for (int i = 0; i < num_of_input; i++) {
       int offset = pow(2, i) - 1;
       subsets[offset].add(universal[i]);
       for (int j = 0; j < offset; j++) {
           subsets[offset + j + 1].copy(subsets[j]);
           subsets[offset + j + 1].add(universal[i]);
       }
   }
   // print
   cout << "Equal Set: ";
   // set flag
   bool found = false;
   // check for subsets's sum
   for (int i = 0; i < num_subset; i++) {
       if (subsets[i].sum() == sum) {
           cout << subsets[i].toString() << endl;
           found = true;
       }
   }
   if (!found) {
       cout << 0;
   }
   delete[] subsets;
}