## C++, , disjoint_set.cpp

/**
*
* \file
* \brief [Disjoint Sets Data Structure
* (Disjoint Sets)](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
*
* \author [leoyang429](https://github.com/leoyang429)
*
* \details
* A disjoint set data structure (also called union find or merge find set)
* is a data structure that tracks a set of elements partitioned into a number
* of disjoint (non-overlapping) subsets.
* Some situations where disjoint sets can be used are-
* to find connected components of a graph, kruskal's algorithm for finding
* Minimum Spanning Tree etc.
* There are two operation which we perform on disjoint sets -
* 1) Union
* 2) Find
*
*/

#include <iostream>
#include <vector>

using std::cout;
using std::endl;
using std::vector;

vector<int> root, rank;

/**
*
* Function to create a set
* @param n number of element
*
*/
void CreateSet(int n) {
root = vector<int>(n + 1);
rank = vector<int>(n + 1, 1);
for (int i = 1; i <= n; ++i) {
root[i] = i;
}
}

/**
*
* Find operation takes a number x and returns the set to which this number
* belongs to.
* @param x element of some set
* @return set to which x belongs to
*
*/
int Find(int x) {
if (root[x] == x) {
return x;
}
return root[x] = Find(root[x]);
}

/**
*
* A utility function to check if x and y are from same set or not
* @param x element of some set
* @param y element of some set
*
*/
bool InSameUnion(int x, int y) { return Find(x) == Find(y); }

/**
*
* Union operation combines two disjoint sets to make a single set
* in this union function we pass two elements and check if they are
* from different sets then combine those sets
* @param x element of some set
* @param y element of some set
*
*/
void Union(int x, int y) {
int a = Find(x), b = Find(y);
if (a != b) {
if (rank[a] < rank[b]) {
root[a] = b;
} else if (rank[a] > rank[b]) {
root[b] = a;
} else {
root[a] = b;
++rank[b];
}
}
}

/** Main function */
int main() {
// tests CreateSet & Find
int n = 100;
CreateSet(n);
for (int i = 1; i <= 100; ++i) {
if (root[i] != i) {
cout << "Fail" << endl;
break;
}
}
// tests InSameUnion & Union
cout << "1 and 2 are initially not in the same subset" << endl;
if (InSameUnion(1, 2)) {
cout << "Fail" << endl;
}
Union(1, 2);
cout << "1 and 2 are now in the same subset" << endl;
if (!InSameUnion(1, 2)) {
cout << "Fail" << endl;
}
return 0;
}