Merge pull request #3 from storopoli/storopoli/slides/graphs

feat: Grafos, Caminhos e Ciclos

.github/workflows/clang-format.yml

@@ -12,17 +12,10 @@ jobs:
     steps:
       - name: Checkout code
         uses: actions/checkout@v4
-      - name: Install dependencies
-        run: sudo apt-get install clang-format
-      - name: Check formatting C code
-        run: |
-          find . -type f -name "*.c" -exec clang-format -n -Werror --ferror-limit=1 {} \;
-      - name: Check formatting C++ code
-        run: |
-          find . -type f -name "*.c" -exec clang-format -n -Werror --ferror-limit=1 {} \;
-      - name: Check formatting C header code
-        run: |
-          find . -type f -name "*.c" -exec clang-format -n -Werror --ferror-limit=1 {} \;
-      - name: Check formatting C++ header code
-        run: |
-          find . -type f -name "*.c" -exec clang-format -n -Werror --ferror-limit=1 {} \;
+      - name: Check clang-format
+        uses: DoozyX/[email protected]
+        with:
+          source: '.'
+          extensions: 'c,h'
+          clangFormatVersion: 17
+          style: Google

README.md

@@ -12,7 +12,7 @@
 1. Análise de Algoritmos;
 1. Algoritmos de Busca e Ordenação;
 1. Recursividade;
-1. Algortimos Gulosos; e
+1. Algoritmos Gulosos; e
 1. Problemas P, NP-Completo, e NP-Difícil.
 
 ## Dependências

code/01-graphs-adjacency-list.c

@@ -0,0 +1,23 @@
+#include <stdio.h>
+
+/** Function to create an adjacency list */
+void print_adj_list(int arr[5][5]) {
+  // Initialize to all zeros
+  int adj_list[5][5] = {{0}};
+
+  // Traverse the given matrix
+  // FIXME: add the necessary code here
+}
+
+/** Main Function */
+int main() {
+  // Given matrix
+  int arr[5][5] = {
+      {1, 0, 1, 0, 0}, {0, 1, 0, 0, 0}, {0, 1, 0, 0, 1},
+      {0, 0, 0, 0, 1}, {1, 0, 0, 1, 0},
+  };
+
+  print_adj_list(arr);
+
+  return 0;
+}

code/01-graphs-adjacency-matrix.c

@@ -0,0 +1,45 @@
+#include <stdio.h>
+
+/** N vertices and M edges */
+int N, M;
+
+/** Function to create an adjacency matrix */
+void create_adj_matrix(int adj[][N + 1], int arr[][2]) {
+  // Initialize all value to zero
+  // FIXME: add the necessary code here
+
+  // Traverse the array of edges and update the values
+  // FIXME: add the necessary code here
+}
+
+/** Function to print an adjacency matrix */
+void print_adj_matrix(int adj[][N + 1]) {
+  // Traverse the adj[][]
+  for (int i = 1; i < N + 1; i++) {
+    for (int j = 1; j < N + 1; j++) {
+      // Print the value at adj[i][j]
+      printf("%d ", adj[i][j]);
+    }
+    printf("\n");
+  }
+}
+
+/** Main function */
+int main() {
+  // Number of vertices
+  N = 5;
+
+  // Given edges
+  int arr[][2] = {{1, 2}, {2, 3}, {4, 5}, {1, 5}};
+
+  // Number of edges
+  M = sizeof(arr) / sizeof(arr[0]);
+
+  int adj[N + 1][N + 1];
+
+  create_adj_matrix(adj, arr);
+
+  print_adj_matrix(adj);
+
+  return 0;
+}

code/02-graphs-eulerian-path.c

@@ -0,0 +1,80 @@
+#include <stdio.h>
+
+/** Number of vertices in the graph */
+#define N 5
+/** Maximum length of the path */
+#define MAX_PATH_LENGTH 20
+
+/** Find Eulerian Path in a graph
+ * @param graph Adjacency matrix of the graph
+ */
+void find_path(int graph[N][N]) {
+  int numofadj[N];
+  int stack[N];
+  int path[MAX_PATH_LENGTH];
+  int top = 0;
+  int path_length = 0;
+
+  // Find out number of edges each vertex has
+  // FIXME: Add the code here
+
+  // Find out how many vertex has odd number edges
+  // FIXME: Add the code here
+
+  // If number of vertex with odd number of edges is greater than two return "No
+  // Solution".
+  // FIXME: Add the code here
+
+  // If there is a path find the path
+  // Initialize empty stack and path take the starting current as discussed
+  // FIXME: Add the code here
+
+  // Loop will run until there is element in the stack or current edge has some
+  // neighbour.
+  // FIXME: Add the code here
+
+  // If the current vertex has at least one neighbour add the current vertex
+  // to stack, remove the edge between them and set the current to its
+  // neighbour.
+  // FIXME: Add the code here
+
+  // Add the last vertex to the path
+  // FIXME: Add the code here
+
+  // Print the path
+  // FIXME: Add the code here
+}
+
+int main() {
+  // Test case 1
+  int graph1[N][N] = {{0, 1, 0, 0, 1},
+                      {1, 0, 1, 1, 0},
+                      {0, 1, 0, 1, 0},
+                      {0, 1, 1, 0, 0},
+                      {1, 0, 0, 0, 0}};
+
+  printf("Test Case 1:\n");
+  find_path(graph1);
+
+  // Test case 2
+  int graph2[N][N] = {{0, 1, 0, 1, 1},
+                      {1, 0, 1, 0, 1},
+                      {0, 1, 0, 1, 1},
+                      {1, 1, 1, 0, 0},
+                      {1, 0, 1, 0, 0}};
+
+  printf("Test Case 2:\n");
+  find_path(graph2);
+
+  // Test case 3
+  int graph3[N][N] = {{0, 1, 0, 0, 1},
+                      {1, 0, 1, 1, 1},
+                      {0, 1, 0, 1, 0},
+                      {0, 1, 1, 0, 1},
+                      {1, 1, 0, 1, 0}};
+
+  printf("Test Case 3:\n");
+  find_path(graph3);
+
+  return 0;
+}

code/02-graphs-hamiltonian-cycle.c

@@ -0,0 +1,61 @@
+#include <stdio.h>
+
+/** Number of vertices in the graph */
+#define N 5
+
+/** A utility function to print solution */
+void print_solution(int path[]) {
+  printf("Solution Exists: ");
+
+  for (int i = 0; i < N; i++) printf("%d ", path[i]);
+
+  // Let us print the first vertex again to show the complete cycle
+  printf("%d ", path[0]);
+  printf("\n");
+  printf("\n");
+}
+
+/** This function solves the Hamiltonian cycle problem using Backtracking.
+ * It returns false if there is no Hamiltonian Cycle possible,
+ * otherwise return true and prints the path.
+ */
+int hamiltonian_cycle(int graph[N][N]) {
+  // FIXME: Implement the function
+  // print_solution(path);
+  return 1;
+}
+
+/** Main function */
+int main() {
+  /* Let us create the following graph
+     (0)--(1)--(2)
+      |   / \   |
+      |  /   \  |
+      | /     \ |
+     (3)-------(4)    */
+  int graph1[N][N] = {
+      {0, 1, 0, 1, 0}, {1, 0, 1, 1, 1}, {0, 1, 0, 0, 1},
+      {1, 1, 0, 0, 1}, {0, 1, 1, 1, 0},
+  };
+
+  // Print the solution
+  printf("Test Case 1:\n");
+  hamiltonian_cycle(graph1);
+
+  /* Let us create the following graph
+     (0)--(1)--(2)
+      |   / \   |
+      |  /   \  |
+      | /     \ |
+     (3)       (4)    */
+  int graph2[N][N] = {
+      {0, 1, 0, 1, 0}, {1, 0, 1, 1, 1}, {0, 1, 0, 0, 1},
+      {1, 1, 0, 0, 0}, {0, 1, 1, 0, 0},
+  };
+
+  // Print the solution
+  printf("Test Case 2:\n");
+  hamiltonian_cycle(graph2);
+
+  return 0;
+}