chore: import upstream snapshot with attribution

data_structures/disjoint_set.cpp

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+/**
+ *
+ * \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;
+}