From d6f670b3909a2c484f3ceada0081d4163a33495c Mon Sep 17 00:00:00 2001
From: Manoel Vilela <manoel.neto@neoway.com.br>
Date: Mon, 17 Nov 2025 02:39:23 -0300
Subject: [PATCH 1/4] feat: add graph_strong_components based on tarjan

---
 src/graph/graph.c         | 12 +++---
 src/graph/graph.h         |  8 ++++
 src/graph/tarjan.c        | 88 ++++++++++++++++++++++++++++++---------
 src/graph/test.c          | 37 ++++++++++++++++
 src/stack/stack-dynamic.c |  4 ++
 src/stack/stack-static.c  |  9 ++++
 src/stack/stack.h         | 10 +++++
 7 files changed, 143 insertions(+), 25 deletions(-)

diff --git a/src/graph/graph.c b/src/graph/graph.c
index 0dd62dbd..e0cd539e 100644
--- a/src/graph/graph.c
+++ b/src/graph/graph.c
@@ -202,17 +202,17 @@ void graph_print(Graph *g) {
         int u = *(int*)iterator_next(it);
         Set *neighbors = (Set*) hash_table_gen_get(g->adj, u, NULL);
         if (g->tarjan) {
-            Iterator *it = set_iterator_items(neighbors);
+            Iterator *neighbors_it = set_iterator_items(neighbors);
             printf("{");
-            while (!iterator_done(it)) {
-                List *list = (List*) iterator_next(it);
+            while (!iterator_done(neighbors_it)) {
+                List *list = (List*) iterator_next(neighbors_it);
                 printf("%d:%s", list->key, graph_edge_type_name((EdgeType)list->data));
-                if (!iterator_done(it)) {
+                if (!iterator_done(neighbors_it)) {
                     printf(", ");
                 }
             }
             printf("}\n");
-            iterator_free(it);
+            iterator_free(neighbors_it);
         } else if (g->weighted) {
             set_print_items(neighbors);
         } else {
@@ -231,8 +231,8 @@ void graph_free(Graph *g) {
 void graph_export_to_dot(Graph *g, const char* filename) {
     FILE *fp = fopen(filename, "w");
     if (fp == NULL) {
-        return;
         fprintf(stderr, "Could not open file %s for writing\n", filename);
+        return;
     }
 
     fprintf(fp, "%s G {\n", g->directed ? "digraph" : "graph");
diff --git a/src/graph/graph.h b/src/graph/graph.h
index d2af8885..b673433c 100644
--- a/src/graph/graph.h
+++ b/src/graph/graph.h
@@ -239,6 +239,14 @@ bool graph_is_dag(Graph *g);
  */
 Graph* graph_tarjan(Graph *g);
 
+/**
+ * @brief Create a array of strong components using tarjan algorithm.
+ * @param g The graph to traverse.
+ * @return array of componentes indexed by node id.
+ * @ingroup DataStructureMethods
+ */
+int* graph_strong_components(Graph *g);
+
 /**
  * This method is defined in acyclical.c because it inherits part of the acyclical code.
  *
diff --git a/src/graph/tarjan.c b/src/graph/tarjan.c
index 918d6376..df53c0c3 100644
--- a/src/graph/tarjan.c
+++ b/src/graph/tarjan.c
@@ -3,12 +3,22 @@
 
 struct TarjanContext {
     Graph* g_tarjan;
+    int *components;
+    Stack* path; // for strong connected components
     int counter_exploration;
     int counter_complete;
     int *exploration;
     int *complete;
 };
 
+void free_tarjan_context(struct TarjanContext *tc) {
+    // keep on memor: g_tarjan + componentes
+    free(tc->exploration);
+    free(tc->complete);
+    stack_free(tc->path);
+    free(tc);
+}
+
 EdgeType tarjan_classify_edge(struct TarjanContext *tc, int parent, int u) {
     if (tc->exploration[u] == 0) {
         return TREE;
@@ -21,13 +31,28 @@ EdgeType tarjan_classify_edge(struct TarjanContext *tc, int parent, int u) {
     }
 }
 
+int update_components(struct TarjanContext *tc, EdgeType edge_type, int u, int v) {
+    if (edge_type == TREE) {
+        int tcu = tc->components[u];
+        int tcv = tc->components[v];
+        return tcu < tcv? tcu: tcv;
+    } else if (stack_has(tc->path, v)) {
+        int tcu = tc->components[u];
+        int exv = tc->exploration[v];
+        return tcu < exv? tcu: exv;
+    }
+    return tc->components[u];
+}
+
+
 static void graph_dfst(
     Graph *g,
     int node,
     struct TarjanContext *tc
 ) {
     tc->exploration[node] = ++tc->counter_exploration;
-
+    tc->components[node] = tc->exploration[node];
+    stack_push(tc->path, node);
     Set* neighbors_set = graph_get_neighbors(g, node);
     Iterator* set_it = set_iterator(neighbors_set);
 
@@ -41,6 +66,13 @@ static void graph_dfst(
         if (edge_type == TREE) {
             graph_dfst(g, neighbor, tc);
         }
+
+        tc->components[node] = update_components(tc, edge_type, node, neighbor);
+    }
+
+    // pop elements for components visited in a cycle
+    if (tc->components[node] == tc->exploration[node]) {
+        while (stack_pop(tc->path) != node);
     }
     set_free(neighbors_set);
     iterator_free(set_it);
@@ -48,36 +80,54 @@ static void graph_dfst(
     tc->complete[node] = ++tc->counter_complete;
 }
 
-
-Graph* graph_tarjan(Graph *g) {
-    struct TarjanContext tc;
+struct TarjanContext* graph_tarjan_explore(Graph *g) {
+    struct TarjanContext *tc = (struct TarjanContext*) malloc(sizeof(struct TarjanContext));
     int max_node_id = graph_max_node_id(g);
-    int *exploration = (int*) malloc(sizeof(int) * (max_node_id + 1));
-    for (int i = 0; i <= max_node_id; i++) {
+    int n = max_node_id + 1;
+    int *exploration = (int*) malloc(n * sizeof(int));
+    int *complete = (int*) malloc(n * sizeof(int));
+    int *components= (int*) malloc(n * sizeof(int));
+
+    // initialize arrays
+    for (int i = 0; i < n; i++) {
         exploration[i] = 0;
-    }
-    int *complete = (int*) malloc(sizeof(int) * (max_node_id + 1));
-    for (int i = 0; i <= max_node_id; i++) {
         complete[i] = 0;
+        components[i] = -1;
     }
 
-    tc.g_tarjan = graph_tarjan_create(graph_is_directed(g));
-    tc.counter_complete = 0;
-    tc.counter_exploration = 0;
-    tc.exploration = exploration;
-    tc.complete = complete;
+    tc->g_tarjan = graph_tarjan_create(graph_is_directed(g));
+    tc->counter_complete = 0;
+    tc->counter_exploration = 0;
+    tc->exploration = exploration;
+    tc->complete = complete;
+    tc->components = components;
+    tc->path = stack_create();
 
     // dfs over each node
     Iterator *nodes = graph_nodes_iterator(g);
     while (!iterator_done(nodes)) {
         int node = *(int*) iterator_next(nodes);
-        if (tc.exploration[node] == 0) {
-            graph_dfst(g, node, &tc);
+        if (tc->exploration[node] == 0) {
+            graph_dfst(g, node, tc);
         }
 
     }
     iterator_free(nodes);
-    free(exploration);
-    free(complete);
-    return tc.g_tarjan;
+    return tc;
+}
+
+Graph* graph_tarjan(Graph *g) {
+    struct TarjanContext *tc= graph_tarjan_explore(g);
+    Graph* g_tarjan = tc->g_tarjan;
+    free(tc->components);
+    free_tarjan_context(tc);
+    return g_tarjan;
+}
+
+int* graph_strong_components(Graph *g) {
+    struct TarjanContext *tc= graph_tarjan_explore(g);
+    int* components = tc->components;
+    graph_free(tc->g_tarjan);
+    free_tarjan_context(tc);
+    return components;
 }
diff --git a/src/graph/test.c b/src/graph/test.c
index a535dc55..7ee8f58e 100644
--- a/src/graph/test.c
+++ b/src/graph/test.c
@@ -197,6 +197,42 @@ void test_graph_tarjan() {
     graph_free(g);
 }
 
+void test_graph_strong_components() {
+    puts("== Graph strong components ");
+
+    Graph *g = graph_create();
+
+    printf(":: input graph: \n");
+    graph_add_edge(g, 1, 2);
+    graph_add_edge(g, 1, 3);
+    graph_add_edge(g, 2, 3);
+    graph_add_edge(g, 3, 4);
+    graph_add_edge(g, 4, 1);
+    graph_add_edge(g, 5, 1);
+
+    graph_print(g);
+
+    printf(":: strong components: \n");
+
+    int *components = graph_strong_components(g);
+    int n = graph_max_node_id(g) + 1;
+    for (int u = 0; u < n; u++) {
+        if (components[u] >= 0) {
+            printf("%d -> %d\n", u, components[u]);
+        }
+    }
+
+    // expected: two components {1, 2, 3, 4} and {5}
+    assert(components[1] == components[2]);
+    assert(components[2] == components[3]);
+    assert(components[3] == components[4]);
+    assert(components[3] == components[4]);
+    assert(components[1] != components[5]);
+
+    free(components);
+    graph_free(g);
+}
+
 void test_graph_export() {
     char cwd[PATH_MAX];
     getcwd(cwd, sizeof(cwd));
@@ -345,6 +381,7 @@ int main(int argc, char *argv[]) {
     test_dfs();
     test_graph_acyclical();
     test_graph_tarjan();
+    test_graph_strong_components();
     test_graph_topological_sort();
     test_graph_dijkstra(extra_tests);
     if (should_run_extra_tests(argc, argv)) {
diff --git a/src/stack/stack-dynamic.c b/src/stack/stack-dynamic.c
index b049a7e5..6b953082 100644
--- a/src/stack/stack-dynamic.c
+++ b/src/stack/stack-dynamic.c
@@ -40,6 +40,10 @@ int stack_pop(Stack *s) {
     return list_pop_head(&s->list);
 }
 
+bool stack_has(Stack *s, int data) {
+    return list_search(s->list, data) != NULL;
+}
+
 void stack_print(Stack* s) {
     printf("<STACK: ");
     list_print(s->list);
diff --git a/src/stack/stack-static.c b/src/stack/stack-static.c
index 0469e12f..83a370b8 100644
--- a/src/stack/stack-static.c
+++ b/src/stack/stack-static.c
@@ -50,6 +50,15 @@ void stack_print(Stack* s) {
     printf("]>");
 }
 
+bool stack_has(Stack *s, int data) {
+    for (int i = 0; i < s->n; i++) {
+        if (s->v[i] == data) {
+            return true;
+        }
+    }
+    return false;
+}
+
 void stack_println(Stack* s) {
     stack_print(s);
     printf("\n");
diff --git a/src/stack/stack.h b/src/stack/stack.h
index 700e7c66..bf9b0380 100644
--- a/src/stack/stack.h
+++ b/src/stack/stack.h
@@ -56,6 +56,16 @@ void stack_push(Stack* s, int data);
  */
 int stack_pop(Stack* s);
 
+/**
+ * @brief Check if element is on the stack.
+ *
+ * @param s The stack to check.
+ * @param data The data to check on stack.
+ * @return true if element exists, false otherwise.
+ * @ingroup DataStructureMethods
+ */
+bool stack_has(Stack* s, int data);
+
 /**
  * @brief Prints the elements of a stack to the console.
  *

From 20df77f22aba9217ecffded65f6009a7e40b6604 Mon Sep 17 00:00:00 2001
From: Manoel Vilela <manoel.neto@neoway.com.br>
Date: Mon, 17 Nov 2025 03:35:42 -0300
Subject: [PATCH 2/4] feat: add graph_edges_ordered

---
 src/graph/graph.c      | 57 ++++++++++++++++++++++++++++++++++++++++++
 src/graph/graph.h      |  7 ++++++
 src/graph/test.c       | 29 +++++++++++++++++++++
 src/list/single/list.c |  2 ++
 src/set/set.c          |  4 +++
 src/set/set.h          |  8 ++++++
 6 files changed, 107 insertions(+)

diff --git a/src/graph/graph.c b/src/graph/graph.c
index e0cd539e..649d2ae1 100644
--- a/src/graph/graph.c
+++ b/src/graph/graph.c
@@ -76,6 +76,63 @@ List* graph_edges(Graph *g) {
     return edges;
 }
 
+int graph_edges_count(Graph *g) {
+    Iterator *nodes = graph_nodes_iterator(g);
+    int n_edges = 0;
+    while (!iterator_done(nodes)) {
+        int node = *(int*) iterator_next(nodes);
+        Set* neighbors = graph_get_neighbors(g, node);
+        n_edges += set_size(neighbors);
+        set_free(neighbors);
+    }
+    iterator_free(nodes);
+    return n_edges;
+}
+
+// compare edges in descending order
+int _compare_edge_weight(const void *a, const void *b) {
+    int x = *((const int*)a + 2);
+    int y = *((const int*)b + 2);
+    if (x < y) {
+        return 1;
+    } else if (x > y) {
+        return -1;
+    } else {
+        return 0;
+    }
+}
+
+// return a list of edges ordered in ascending order
+List* graph_edges_ordered(Graph *g) {
+    int edges_count = graph_edges_count(g);
+    int edges_by_weight[edges_count][3];
+    List *edges = graph_edges(g);
+    Iterator *it = list_iterator(edges);
+    int rows = 0;
+    while (!iterator_done(it)) {
+        List *edge = (List*) iterator_next(it);
+        int u = edge->key;
+        int v = edge->data;
+        int w = graph_get_edge_weight(g, u, v);
+        edges_by_weight[rows][0] = u;
+        edges_by_weight[rows][1] = v;
+        edges_by_weight[rows][2] = w;
+        rows++;
+    }
+    iterator_free(it);
+    list_free(edges);
+
+    qsort(edges_by_weight, edges_count, sizeof(int) * 3, _compare_edge_weight);
+    List *edges_ordered = list_create();
+    for (int i = 0; i < edges_count; i++) {
+        int u = edges_by_weight[i][0];
+        int v = edges_by_weight[i][1];
+        edges_ordered = list_insert_with_key(edges_ordered, u, v);
+    }
+
+    return edges_ordered;
+
+}
 
 size_t graph_size(Graph *g) {
     return hash_table_gen_size(g->adj);
diff --git a/src/graph/graph.h b/src/graph/graph.h
index b673433c..68982a3a 100644
--- a/src/graph/graph.h
+++ b/src/graph/graph.h
@@ -208,6 +208,13 @@ Iterator* graph_nodes_iterator(Graph *g);
  */
 List* graph_edges(Graph *g);
 
+/**
+ * @brief List with edges of the graph with (key,data) ordered ascending.
+ * @param g The graph to traverse.
+ * @ingroup DataStructureMethods
+ */
+List* graph_edges_ordered(Graph *g);
+
 /**
  * @brief Get the maximum node id on the graph.
  * @return maximum node id on the graph.
diff --git a/src/graph/test.c b/src/graph/test.c
index 7ee8f58e..b9165f8d 100644
--- a/src/graph/test.c
+++ b/src/graph/test.c
@@ -197,6 +197,34 @@ void test_graph_tarjan() {
     graph_free(g);
 }
 
+void test_graph_edges_ordered() {
+    Graph* g = graph_create();
+    graph_add_edge_with_weight(g, 2, 4, 15);
+    graph_add_edge_with_weight(g, 1, 6, 14);
+    graph_add_edge_with_weight(g, 2, 3, 10);
+    graph_add_edge_with_weight(g, 1, 2, 7);
+    graph_add_edge_with_weight(g, 1, 3, 9);
+    printf(":: graph");
+    graph_print(g);
+
+
+    List *expected = list_create();
+    expected = list_append_with_key(expected, 1, 2);
+    expected = list_append_with_key(expected, 1, 3);
+    expected = list_append_with_key(expected, 2, 3);
+    expected = list_append_with_key(expected, 1, 6);
+    expected = list_append_with_key(expected, 2, 4);
+
+    List *edges_ordered = graph_edges_ordered(g);
+    printf("Edges ordered: "); list_println(edges_ordered);
+    printf("Edges expected: "); list_println(expected);
+    assert(list_equal(edges_ordered, expected));
+
+    graph_free(g);
+    list_free(expected);
+    list_free(edges_ordered);
+}
+
 void test_graph_strong_components() {
     puts("== Graph strong components ");
 
@@ -384,6 +412,7 @@ int main(int argc, char *argv[]) {
     test_graph_strong_components();
     test_graph_topological_sort();
     test_graph_dijkstra(extra_tests);
+    test_graph_edges_ordered();
     if (should_run_extra_tests(argc, argv)) {
         test_graph_export();
     }
diff --git a/src/list/single/list.c b/src/list/single/list.c
index 60d8f581..6fc8d484 100644
--- a/src/list/single/list.c
+++ b/src/list/single/list.c
@@ -472,6 +472,8 @@ List* list_from_iterator(Iterator *it) {
     return l;
 }
 
+
+// O(n^2): insertion sort
 void list_sort(List **list) {
     List* list_sorted = list_create();
     Iterator* it = list_iterator_data(*list);
diff --git a/src/set/set.c b/src/set/set.c
index c7920b5c..45740b28 100644
--- a/src/set/set.c
+++ b/src/set/set.c
@@ -21,6 +21,10 @@ Set* set_create() {
     return set;
 }
 
+int set_size(Set *set) {
+    return hash_table_size(set->memory);
+}
+
 Set* set_copy(Set *set) {
     Set *set_new = set_create();
     hash_table_free(set_new->memory);
diff --git a/src/set/set.h b/src/set/set.h
index 688c548a..a469f594 100644
--- a/src/set/set.h
+++ b/src/set/set.h
@@ -41,6 +41,14 @@ Set* set_create();
  */
 Set* set_init(int set_size, ...);
 
+/**
+ * @brief Get a the size of the set
+ * @param set to count
+ * @return number of elements
+ * @ingroup DataStructureMethods
+ */
+int set_size(Set *set);
+
 /**
  * @brief Create a set as copy of another
  * @param set to copy

From c7ad70d0337ca48b07a7f8bb733b4401faee3497 Mon Sep 17 00:00:00 2001
From: Manoel Vilela <manoel.neto@neoway.com.br>
Date: Mon, 17 Nov 2025 04:10:09 -0300
Subject: [PATCH 3/4] feat(set): Implement Disjoint Set (Union-Find) data
 structure

This commit introduces a new Disjoint Set (Union-Find) data structure
to the  module.

- Added  and  implementing the
  Disjoint Set with , ,
   (with path compression), and
   (with union by rank).
- Updated  to include the new source files and
  ensure proper compilation of dependencies.
- Added comprehensive unit tests for the Disjoint Set functionality
  in .
---
 src/set/Makefile       |  4 +--
 src/set/set-disjoint.c | 61 ++++++++++++++++++++++++++++++++++++++++++
 src/set/set-disjoint.h | 43 +++++++++++++++++++++++++++++
 src/set/test.c         | 56 ++++++++++++++++++++++++++++++++++++++
 4 files changed, 162 insertions(+), 2 deletions(-)
 create mode 100644 src/set/set-disjoint.c
 create mode 100644 src/set/set-disjoint.h

diff --git a/src/set/Makefile b/src/set/Makefile
index d536de3c..3f36180c 100644
--- a/src/set/Makefile
+++ b/src/set/Makefile
@@ -14,7 +14,7 @@ INCLUDE := -I../ -L../list/single -L../hash-table/
 
 # targets to compile
 TEST_TARGET = test
-TARGETS = set.o
+TARGETS = set.o set-disjoint.o
 LIBRARY_OBJS = $(TARGETS)
 
 TEST_BINARY = $(TEST_TARGET).$(EXTENSION)
@@ -25,7 +25,7 @@ LIBRARY_TARGET = libset.a
 all: compile
 	@echo > /dev/null
 
-compile: $(TARGETS) $(TEST_TARGET).o $(MAIN_TARGET).o
+compile: deps $(TARGETS) $(TEST_TARGET).o $(MAIN_TARGET).o
 
 deps:
 	make clean library -C ../list/single CFLAGS=-DLIST_PRINT_KEY
diff --git a/src/set/set-disjoint.c b/src/set/set-disjoint.c
new file mode 100644
index 00000000..73b71edc
--- /dev/null
+++ b/src/set/set-disjoint.c
@@ -0,0 +1,61 @@
+#include "set-disjoint.h"
+#include "../utils/check_alloc.h"
+#include <stdlib.h>
+
+struct DisjointSet {
+    int *parent;
+    int *rank;
+    int n;
+};
+
+DisjointSet *set_disjoint_create(int n) {
+    DisjointSet *ds = (DisjointSet *)malloc(sizeof(DisjointSet));
+    check_alloc(ds);
+    ds->n = n;
+    ds->parent = (int *)malloc(sizeof(int) * n);
+    check_alloc(ds->parent);
+    ds->rank = (int *)malloc(sizeof(int) * n);
+    check_alloc(ds->rank);
+    for (int i = 0; i < n; i++) {
+        ds->parent[i] = i;
+        ds->rank[i] = 0;
+    }
+    return ds;
+}
+
+void set_disjoint_destroy(DisjointSet **ds) {
+    if (ds == NULL || *ds == NULL) {
+        return;
+    }
+    free((*ds)->parent);
+    (*ds)->parent = NULL;
+    free((*ds)->rank);
+    (*ds)->rank = NULL;
+    free(*ds);
+    *ds = NULL;
+}
+
+// Find with path compression
+int set_disjoint_find(DisjointSet *ds, int i) {
+    if (ds->parent[i] != i) {
+        ds->parent[i] = set_disjoint_find(ds, ds->parent[i]);
+    }
+    return ds->parent[i];
+}
+
+// Union by rank
+void set_disjoint_union(DisjointSet *ds, int i, int j) {
+    int root_i = set_disjoint_find(ds, i);
+    int root_j = set_disjoint_find(ds, j);
+
+    if (root_i != root_j) {
+        if (ds->rank[root_i] < ds->rank[root_j]) {
+            ds->parent[root_i] = root_j;
+        } else if (ds->rank[root_i] > ds->rank[root_j]) {
+            ds->parent[root_j] = root_i;
+        } else {
+            ds->parent[root_j] = root_i;
+            ds->rank[root_i]++;
+        }
+    }
+}
diff --git a/src/set/set-disjoint.h b/src/set/set-disjoint.h
new file mode 100644
index 00000000..4b231217
--- /dev/null
+++ b/src/set/set-disjoint.h
@@ -0,0 +1,43 @@
+#ifndef SET_DISJOINT_H
+#define SET_DISJOINT_H
+
+/**
+ * @brief A disjoint-set data structure.
+ * @see https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+ */
+typedef struct DisjointSet DisjointSet;
+
+/**
+ * @brief Creates a new disjoint-set data structure with n elements.
+ *
+ * @param[in] n The number of elements.
+ * @return A pointer to the new disjoint-set.
+ */
+DisjointSet *set_disjoint_create(int n);
+
+/**
+ * @brief Destroys a disjoint-set data structure.
+ *
+ * @param[in,out] ds A pointer to a pointer to the disjoint-set.
+ */
+void set_disjoint_destroy(DisjointSet **ds);
+
+/**
+ * @brief Finds the representative of the set containing element i.
+ *
+ * @param[in] ds The disjoint-set.
+ * @param[in] i The element to find.
+ * @return The representative of the set containing i.
+ */
+int set_disjoint_find(DisjointSet *ds, int i);
+
+/**
+ * @brief Merges the sets containing elements i and j.
+ *
+ * @param[in,out] ds The disjoint-set.
+ * @param[in] i The first element.
+ * @param[in] j The second element.
+ */
+void set_disjoint_union(DisjointSet *ds, int i, int j);
+
+#endif /* SET_DISJOINT_H */
diff --git a/src/set/test.c b/src/set/test.c
index 704fe6cc..191f0c22 100644
--- a/src/set/test.c
+++ b/src/set/test.c
@@ -1,6 +1,7 @@
 #include <stdio.h>
 #include <assert.h>
 #include "set.h"
+#include "set-disjoint.h"
 
 void test_set_contains() {
     printf("\n== test set_contains\n\n");
@@ -133,6 +134,60 @@ void test_set_iterator() {
 }
 
 
+void test_set_disjoint() {
+    printf("\n== test set_disjoint\n\n");
+    int n = 10;
+    DisjointSet *ds = set_disjoint_create(n);
+
+    // Initially, each element is in its own set
+    for (int i = 0; i < n; i++) {
+        assert(set_disjoint_find(ds, i) == i);
+    }
+
+    // Union some elements
+    set_disjoint_union(ds, 0, 1);
+    set_disjoint_union(ds, 2, 3);
+    set_disjoint_union(ds, 0, 2); // This should connect 0, 1, 2, 3
+
+    // Verify unions
+    assert(set_disjoint_find(ds, 0) == set_disjoint_find(ds, 1));
+    assert(set_disjoint_find(ds, 0) == set_disjoint_find(ds, 2));
+    assert(set_disjoint_find(ds, 0) == set_disjoint_find(ds, 3));
+    assert(set_disjoint_find(ds, 1) == set_disjoint_find(ds, 2));
+    assert(set_disjoint_find(ds, 1) == set_disjoint_find(ds, 3));
+    assert(set_disjoint_find(ds, 2) == set_disjoint_find(ds, 3));
+
+    // Elements not involved in unions should still be in their own sets
+    assert(set_disjoint_find(ds, 4) == 4);
+    assert(set_disjoint_find(ds, 5) == 5);
+
+    // Further unions
+    set_disjoint_union(ds, 4, 5);
+    set_disjoint_union(ds, 6, 7);
+    set_disjoint_union(ds, 8, 9);
+    set_disjoint_union(ds, 4, 6); // This should connect 4, 5, 6, 7
+
+    assert(set_disjoint_find(ds, 4) == set_disjoint_find(ds, 5));
+    assert(set_disjoint_find(ds, 4) == set_disjoint_find(ds, 6));
+    assert(set_disjoint_find(ds, 4) == set_disjoint_find(ds, 7));
+
+    // Union the two large sets
+    set_disjoint_union(ds, 0, 4); // Connects 0,1,2,3 with 4,5,6,7
+
+    assert(set_disjoint_find(ds, 0) == set_disjoint_find(ds, 4));
+    assert(set_disjoint_find(ds, 1) == set_disjoint_find(ds, 5));
+    assert(set_disjoint_find(ds, 2) == set_disjoint_find(ds, 6));
+    assert(set_disjoint_find(ds, 3) == set_disjoint_find(ds, 7));
+
+    // Check that 8 and 9 are still separate
+    assert(set_disjoint_find(ds, 8) == set_disjoint_find(ds, 9));
+    assert(set_disjoint_find(ds, 0) != set_disjoint_find(ds, 8));
+
+    set_disjoint_destroy(&ds);
+    assert(ds == NULL);
+}
+
+
 int main(void) {
     printf("== Tests over Set data stucture");
     test_set_contains();
@@ -143,5 +198,6 @@ int main(void) {
     test_set_union();
     test_set_difference();
     test_set_iterator();
+    test_set_disjoint();
     return 0;
 }

From d809da73b76ce934e06b3992972759010307898e Mon Sep 17 00:00:00 2001
From: Manoel Vilela <manoel.neto@neoway.com.br>
Date: Mon, 17 Nov 2025 04:34:18 -0300
Subject: [PATCH 4/4] feat: add graph_kruskal

---
 src/graph/Makefile     |  2 +-
 src/graph/graph.h      |  8 ++++++++
 src/graph/kruskal.c    | 24 ++++++++++++++++++++++++
 src/graph/test.c       | 22 ++++++++++++++++++++++
 src/set/set-disjoint.c | 14 ++++----------
 src/set/set-disjoint.h |  4 ++--
 src/set/test.c         |  3 +--
 7 files changed, 62 insertions(+), 15 deletions(-)
 create mode 100644 src/graph/kruskal.c

diff --git a/src/graph/Makefile b/src/graph/Makefile
index 98890acc..9bc0a2c4 100644
--- a/src/graph/Makefile
+++ b/src/graph/Makefile
@@ -14,7 +14,7 @@ INCLUDE := -I../ -L../list/single  -L../hash-table -L../set -L../queue -L../stac
 
 # targets to compile
 TEST_TARGET = test
-TARGETS = graph.o bfs.o dfs.o acyclical.o tarjan.o dijkstra.o
+TARGETS = graph.o bfs.o dfs.o acyclical.o tarjan.o dijkstra.o kruskal.o
 LIBRARY_OBJS = $(TARGETS)
 
 TEST_BINARY = $(TEST_TARGET).$(EXTENSION)
diff --git a/src/graph/graph.h b/src/graph/graph.h
index 68982a3a..217889e1 100644
--- a/src/graph/graph.h
+++ b/src/graph/graph.h
@@ -273,6 +273,14 @@ List* graph_topological_sort(Graph *g);
  */
 Graph* graph_dijkstra(Graph* g, int source);
 
+/**
+ * @brief Run kruskal algorithm to get the minimum-span tree.
+ * @param g The graph to traverse.
+ * @return a new graph with the minimum span tree.
+ * @ingroup DataStructureMethods
+ */
+Graph* graph_kruskal(Graph* g);
+
 /**
  * @brief Run dijkstra algorithm and calculate the minimum distance.
  * @param g The graph to traverse.
diff --git a/src/graph/kruskal.c b/src/graph/kruskal.c
new file mode 100644
index 00000000..579d2c2e
--- /dev/null
+++ b/src/graph/kruskal.c
@@ -0,0 +1,24 @@
+#include "graph.h"
+#include "../set/set-disjoint.h"
+
+Graph* graph_kruskal(Graph *g) {
+    Graph *g_kruskal = graph_create();
+    DisjointSet *components = set_disjoint_create(graph_max_node_id(g) + 1);
+    List *edges = graph_edges_ordered(g);
+    Iterator *it = list_iterator(edges);
+
+    while (!iterator_done(it)) {
+        List *edge = (List*) iterator_next(it);
+        int u = edge->key;
+        int v = edge->data;
+        if (set_disjoint_find(components, u) != set_disjoint_find(components, v)) {
+            graph_add_edge_with_weight(g_kruskal, u, v, graph_get_edge_weight(g, u, v));
+            set_disjoint_union(components, u, v);
+        }
+    }
+
+    set_disjoint_free(components);
+    iterator_free(it);
+    list_free(edges);
+    return g_kruskal;
+}
diff --git a/src/graph/test.c b/src/graph/test.c
index b9165f8d..fe862fcc 100644
--- a/src/graph/test.c
+++ b/src/graph/test.c
@@ -389,6 +389,27 @@ void test_graph_dijkstra(bool extra_tests) {
     graph_free(dijkstra_result);
 }
 
+void test_graph_kruskal() {
+    puts("== Graph kruskal test");
+    Graph *g = graph_create();
+    graph_add_edge_with_weight(g, 1, 2, 10);
+    graph_add_edge_with_weight(g, 1, 3, 20);
+    graph_add_edge_with_weight(g, 2, 3, 5);
+    graph_add_edge_with_weight(g, 3, 4, 30);
+    graph_add_edge_with_weight(g, 4, 1, 9);
+    graph_add_edge_with_weight(g, 5, 1, 7);
+
+    printf(":: input graph\n");
+    graph_print(g);
+
+    printf(":: kruskal tree\n");
+    Graph *g_kruskal = graph_kruskal(g);
+    graph_print(g_kruskal);
+
+    graph_free(g);
+    graph_free(g_kruskal);
+}
+
 
 bool should_run_extra_tests(int argc, char *argv[]) {
     // Iterate through the command-line arguments starting from argv[1]
@@ -413,6 +434,7 @@ int main(int argc, char *argv[]) {
     test_graph_topological_sort();
     test_graph_dijkstra(extra_tests);
     test_graph_edges_ordered();
+    test_graph_kruskal();
     if (should_run_extra_tests(argc, argv)) {
         test_graph_export();
     }
diff --git a/src/set/set-disjoint.c b/src/set/set-disjoint.c
index 73b71edc..7097104b 100644
--- a/src/set/set-disjoint.c
+++ b/src/set/set-disjoint.c
@@ -23,16 +23,10 @@ DisjointSet *set_disjoint_create(int n) {
     return ds;
 }
 
-void set_disjoint_destroy(DisjointSet **ds) {
-    if (ds == NULL || *ds == NULL) {
-        return;
-    }
-    free((*ds)->parent);
-    (*ds)->parent = NULL;
-    free((*ds)->rank);
-    (*ds)->rank = NULL;
-    free(*ds);
-    *ds = NULL;
+void set_disjoint_free(DisjointSet *ds) {
+    free(ds->parent);
+    free(ds->rank);
+    free(ds);
 }
 
 // Find with path compression
diff --git a/src/set/set-disjoint.h b/src/set/set-disjoint.h
index 4b231217..52e40509 100644
--- a/src/set/set-disjoint.h
+++ b/src/set/set-disjoint.h
@@ -16,11 +16,11 @@ typedef struct DisjointSet DisjointSet;
 DisjointSet *set_disjoint_create(int n);
 
 /**
- * @brief Destroys a disjoint-set data structure.
+ * @brief Free a disjoint-set data structure.
  *
  * @param[in,out] ds A pointer to a pointer to the disjoint-set.
  */
-void set_disjoint_destroy(DisjointSet **ds);
+void set_disjoint_free(DisjointSet *ds);
 
 /**
  * @brief Finds the representative of the set containing element i.
diff --git a/src/set/test.c b/src/set/test.c
index 191f0c22..5d92d5e0 100644
--- a/src/set/test.c
+++ b/src/set/test.c
@@ -183,8 +183,7 @@ void test_set_disjoint() {
     assert(set_disjoint_find(ds, 8) == set_disjoint_find(ds, 9));
     assert(set_disjoint_find(ds, 0) != set_disjoint_find(ds, 8));
 
-    set_disjoint_destroy(&ds);
-    assert(ds == NULL);
+    set_disjoint_free(ds);
 }