From a69051ac53b24635086a9ad792e2e132d53d887c Mon Sep 17 00:00:00 2001
From: Sagar Pandya <sagar.pandya1999@gmail.com>
Date: Fri, 8 Jan 2021 15:11:34 +0530
Subject: [PATCH] namespaces added datatype changed for big number
 documentation improved

---
 graph/connected_components_with_dsu.cpp | 122 +++++++++++++++++-------
 1 file changed, 89 insertions(+), 33 deletions(-)

diff --git a/graph/connected_components_with_dsu.cpp b/graph/connected_components_with_dsu.cpp
index 50d0c4242..5317361b2 100644
--- a/graph/connected_components_with_dsu.cpp
+++ b/graph/connected_components_with_dsu.cpp
@@ -1,56 +1,112 @@
-#include <iostream>
-#include <set>
-#include <vector>
+/**
+ * @file
+ * @brief [Disjoint union](https://en.wikipedia.org/wiki/Disjoint_union)
+ *
+ * @details
+ * The Disjoint union is the technique to find connected component in graph efficiently.
+ *
+ * ### Algorithm
+ * In Graph, if you have to find out the number of connected components, there are 2 options
+ * 1. Depth first search
+ * 2. Disjoint union
+ * 1st option is inefficient, Disjoint union is the most optimal way to find this.
+ */
+#include <iostream> /// for io operations
+#include <set>    /// for std::set
+#include <vector> /// for std::vector
 
-int number_of_nodes;  // denotes number of nodes;
-std::vector<int> parent;
-std::vector<int> connected_set_size;
-void make_set() {  // function the initialize every node as it's own parent
-    for (int i = 1; i <= number_of_nodes; i++) {
+/**
+ * @namespace graph
+ * @brief Graph Algorithms
+ */
+namespace graph {
+
+/**
+ * @namespace disjoint_union
+ * @brief Function for [Disjoint union] (https://en.wikipedia.org/wiki/Disjoint_union) implementation
+ */
+namespace disjoint_union {
+
+int64_t number_of_nodes;                  // denotes number of nodes
+std::vector<int64_t> parent;              // parent of each node
+std::vector<int64_t> connected_set_size;  // size of each set
+/**
+ * @brief function the initialize every node as it's own parent
+ * @returns void
+ */
+void make_set() {
+    for (int64_t i = 1; i <= number_of_nodes; i++) {
         parent[i] = i;
         connected_set_size[i] = 1;
     }
 }
-// To find the component where following node belongs to
-int find_set(int v) {
-    if (v == parent[v]) {
-        return v;
+/**
+ * @brief To find the component where following node belongs to
+ * @param val parent of val should be found
+ * @return parent of val
+ */
+int64_t find_set(int64_t val) {
+    while (parent[val] != val) {
+        parent[val] = parent[parent[val]];
+        val = parent[val];
     }
-    return parent[v] = find_set(parent[v]);
+    return val;
 }
+/**
+ * @brief To join 2 components to belong to one
+ * @param node1 1st component
+ * @param node2 2nd component
+ * @returns void
+ */
+void union_sets(int64_t node1, int64_t node2) {
+    node1 = find_set(node1);  // find the parent of node1
+    node2 = find_set(node2);  // find the parent of node2
 
-void union_sets(int a, int b) {  // To join 2 components to belong to one
-    a = find_set(a);
-    b = find_set(b);
-    if (a != b) {
-        if (connected_set_size[a] < connected_set_size[b]) {
-            std::swap(a, b);
+    // If parents of both nodes are not same, combine them
+    if (node1 != node2) {
+        if (connected_set_size[node1] < connected_set_size[node2]) {
+            std::swap(node1, node2);  // swap both components
         }
-        parent[b] = a;
-        connected_set_size[a] += connected_set_size[b];
+        parent[node2] = node1;  // make node1 as parent of node2.
+        connected_set_size[node1] +=
+            connected_set_size[node2];  // sum the size of both as they combined
     }
 }
-
-int no_of_connected_components() {  // To find total no of connected components
-    std::set<int> temp;  // temp set to count number of connected components
-    for (int i = 1; i <= number_of_nodes; i++) temp.insert(find_set(i));
-    return temp.size();
+/**
+ * @brief To find total no of connected components
+ * @return Number of connected components
+ */
+int64_t no_of_connected_components() {
+    std::set<int64_t> temp;  // temp set to count number of connected components
+    for (int64_t i = 1; i <= number_of_nodes; i++) temp.insert(find_set(i));
+    return temp.size();  // return the size of temp set
 }
-
-// All critical/corner cases have been taken care of.
-// Input your required values: (not hardcoded)
-int main() {
+/**
+ * @brief Test Implementations
+ * @returns void
+ */
+static void test() {
     std::cin >> number_of_nodes;
     parent.resize(number_of_nodes + 1);
     connected_set_size.resize(number_of_nodes + 1);
     make_set();
-    int edges = 0;
+    int64_t edges = 0;
     std::cin >> edges;  // no of edges in the graph
     while (edges--) {
-        int node_a = 0, node_b = 0;
+        int64_t node_a = 0, node_b = 0;
         std::cin >> node_a >> node_b;
         union_sets(node_a, node_b);
     }
     std::cout << no_of_connected_components() << std::endl;
-    return 0;
 }
+} // namespace disjoint_union
+} // namespace graph
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    graph::disjoint_union::test();  // Execute the tests
+    return 0;
+}
\ No newline at end of file