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‎Graph/Basic/03 PrimMinSpanningTreeFunction.cpp

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#include <iostream>
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#define V 8
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#define I 32767
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using namespace std;
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void PrintMST(int T[][V-2], int G[V][V]){
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cout << "\nMinimum Spanning Tree Edges (w/ cost)\n" << endl;
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int sum {0};
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for (int i {0}; i<V-2; i++){
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int c = G[T[0][i]][T[1][i]];
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cout << "[" << T[0][i] << "]---[" << T[1][i] << "] cost: " << c << endl;
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sum += c;
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}
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cout << endl;
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cout << "Total cost of MST: " << sum << endl;
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}
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void PrimsMST(int G[V][V], int n){
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int u;
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int v;
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int min {I};
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int track [V];
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int T[2][V-2] {0};
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// Initial: Find min cost edge
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for (int i {1}; i<V; i++){
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track[i] = I; // Initialize track array with INFINITY
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for (int j {i}; j<V; j++){
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if (G[i][j] < min){
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min = G[i][j];
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u = i;
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v = j;
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}
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}
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}
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T[0][0] = u;
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T[1][0] = v;
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track[u] = track[v] = 0;
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// Initialize track array to track min cost edges
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for (int i {1}; i<V; i++){
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if (track[i] != 0){
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if (G[i][u] < G[i][v]){
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track[i] = u;
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} else {
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track[i] = v;
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}
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}
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}
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// Repeat
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for (int i {1}; i<n-1; i++){
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int k;
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min = I;
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for (int j {1}; j<V; j++){
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if (track[j] != 0 && G[j][track[j]] < min){
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k = j;
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min = G[j][track[j]];
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}
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}
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T[0][i] = k;
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T[1][i] = track[k];
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track[k] = 0;
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// Update track array to track min cost edges
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for (int j {1}; j<V; j++){
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if (track[j] != 0 && G[j][k] < G[j][track[j]]){
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track[j] = k;
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}
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}
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}
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PrintMST(T, G);
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}
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int main() {
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int cost [V][V] {
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{I, I, I, I, I, I, I, I},
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{I, I, 25, I, I, I, 5, I},
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{I, 25, I, 12, I, I, I, 10},
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{I, I, 12, I, 8, I, I, I},
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{I, I, I, 8, I, 16, I, 14},
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{I, I, I, I, 16, I, 20, 18},
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{I, 5, I, I, I, 20, I, I},
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{I, I, 10, I, 14, 18, I, I},
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};
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int n = sizeof(cost[0])/sizeof(cost[0][0]) - 1;
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PrimsMST(cost, n);
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return 0;
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}

‎Graph/Basic/04 KrushalsMinCostSpanningTreeFunction.cpp

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#include <iostream>
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#define I 32767 // Infinity
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#define V 7 // # of vertices in Graph
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#define E 9 // # of edges in Graph
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using namespace std;
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void PrintMCST(int T[][V-1], int A[][E]){
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cout << "\nMinimum Cost Spanning Tree Edges\n" << endl;
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for (int i {0}; i<V-1; i++){
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cout << "[" << T[0][i] << "]-----[" << T[1][i] << "]" << endl;
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}
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cout << endl;
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}
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// Set operations: Union and Find
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void Union(int u, int v, int s[]){
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if (s[u] < s[v]){
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s[u] += s[v];
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s[v] = u;
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} else {
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s[v] += s[u];
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s[u] = v;
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}
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}
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int Find(int u, int s[]){
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int x = u;
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int v = 0;
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while (s[x] > 0){
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x = s[x];
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}
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while (u != x){
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v = s[u];
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s[u] = x;
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u = v;
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}
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return x;
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}
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void KruskalsMCST(int A[3][9]){
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int T[2][V-1]; // Solution array
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int track[E] {0}; // Track edges that are included in solution
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int set[V+1] = {-1, -1, -1, -1, -1, -1, -1, -1}; // Array for finding cycle
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int i {0};
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while (i < V-1){
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int min = I;
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int u {0};
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int v {0};
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int k {0};
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// Find a minimum cost edge
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for (int j {0}; j<E; j++){
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if (track[j] == 0 && A[2][j] < min){
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min = A[2][j];
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u = A[0][j];
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v = A[1][j];
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k = j;
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}
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}
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// Check if the selected min cost edge (u, v) forming a cycle or not
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if (Find(u, set) != Find(v, set)){
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T[0][i] = u;
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T[1][i] = v;
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// Perform union
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Union(Find(u, set), Find(v, set), set);
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i++;
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}
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track[k] = 1;
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}
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PrintMCST(T, A);
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}
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int main() {
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int edges[3][9] = {{ 1, 1, 2, 2, 3, 4, 4, 5, 5},
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{ 2, 6, 3, 7, 4, 5, 7, 6, 7},
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{25, 5, 12, 10, 8, 16, 14, 20, 18}};
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KruskalsMCST(edges);
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return 0;
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}

‎Graph/Basic/05 DepthFirstSearchUsingRecursion.cpp

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#include <iostream>
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using namespace std;
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void DFS(int u, int A[][8], int n){
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static int visited[8] {0};
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if (visited[u] == 0){
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cout << u << ", " << flush;
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visited[u] = 1;
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for (int v=1; v<n; v++){
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if (A[u][v] == 1 && visited[v] == 0){
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DFS(v, A, n);
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}
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}
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}
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}
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int main (){
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int A[8][8] = {{0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 1, 1, 1, 0, 0, 0},
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{0, 1, 0, 1, 0, 0, 0, 0},
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{0, 1, 1, 0, 1, 1, 0, 0},
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{0, 1, 0, 1, 0, 1, 0, 0},
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{0, 0, 0, 1, 1, 0, 1, 1},
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{0, 0, 0, 0, 0, 1, 0, 0},
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{0, 0, 0, 0, 0, 1, 0, 0}};
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cout << "Vertex: 4 -> " << flush;
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DFS(4, A, 8);
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cout << endl;
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return 0;
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}

‎Graph/Basic/06 BreadthFirstSearchUsingSTLQueue.cpp

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#include <iostream>
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#include <stack>
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using namespace std;
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// Based on Lecture
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void DFS(int u, int A[][8], int n) {
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// Initialize visit tracking array and stack
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int visited[8] {0};
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stack<int> stk;
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stk.emplace(u);
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// Visit start vertex u
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cout << u << ", " << flush;
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visited[u] = 1; // Visited vertex u
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// Initial Adjacent vertex
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int v = 0;
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while (!stk.empty()){
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while (v < n){
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if (A[u][v] == 1 && visited[v] == 0){
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stk.push(u); // Suspend exploring current vertex u
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u = v; // Update current vertex as the next adjacent vertex
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// Visit current vertex u
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cout << u << ", " << flush;
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visited[u] = 1;
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v = -1; // Increment will make this 0
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}
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v++;
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}
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v = u; // Can set v = 0 but setting v = u is better
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u = stk.top(); // Return to previous suspended vertex
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stk.pop();
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}
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}
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// Simpler and adds elements to stack from end
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void dfs(int u, int A[][8], int n){
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int visited[8] {0};
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stack<int> stk;
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stk.emplace(u);
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while (!stk.empty()){
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u = stk.top();
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stk.pop();
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if (visited[u] != 1){
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cout << u << ", " << flush;
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visited[u] = 1;
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for (int v=n-1; v>=0; v--){
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if (A[u][v] == 1 && visited[v] == 0){
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stk.emplace(v);
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}
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}
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}
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}
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}
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int main (){
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int A[8][8] = {{0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 1, 1, 1, 0, 0, 0},
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{0, 1, 0, 1, 0, 0, 0, 0},
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{0, 1, 1, 0, 1, 1, 0, 0},
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{0, 1, 0, 1, 0, 1, 0, 0},
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{0, 0, 0, 1, 1, 0, 1, 1},
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{0, 0, 0, 0, 0, 1, 0, 0},
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{0, 0, 0, 0, 0, 1, 0, 0}};
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int u = 5;
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cout << "DFS Vertex: " << u << " -> " << flush;
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DFS(u, A, 8);
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cout << endl;
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cout << "dfs Vertex: " << u << " -> " << flush;
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dfs(u, A, 8);
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cout << endl;
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return 0;
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}

‎Graph/Basic/07 BreadthFirstSearchUsingSTLQueue.cpp

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#include <iostream>
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#include <queue>
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using namespace std;
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void BFS(int vtx, int A[][8], int n){
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queue<int> Q;
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int visited[8] {0};
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// Initial
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cout << vtx << ", " << flush; // Visit vertex
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visited[vtx] = 1;
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Q.emplace(vtx);
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// Explore
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while (!Q.empty()){
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int u = Q.front(); // Vertex u for exploring
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Q.pop();
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for (int v=1; v<=n; v++){ // Adjacent vertices of vertex u
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if (A[u][v] == 1 && visited[v] == 0){ // Adjacent vertex and not visited
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cout << v << ", " << flush; // Visit vertex
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visited[v] = 1;
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Q.emplace(v);
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}
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}
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}
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cout << endl;
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}
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int main (){
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int A[8][8] = {{0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 1, 1, 1, 0, 0, 0},
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{0, 1, 0, 1, 0, 0, 0, 0},
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{0, 1, 1, 0, 1, 1, 0, 0},
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{0, 1, 0, 1, 0, 1, 0, 0},
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{0, 0, 0, 1, 1, 0, 1, 1},
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{0, 0, 0, 0, 0, 1, 0, 0},
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{0, 0, 0, 0, 0, 1, 0, 0}};
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cout << "Vertex: 1 -> " << flush;
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BFS(1, A, 8);
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cout << "Vertex: 4 -> " << flush;
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BFS(4, A, 8);
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return 0;
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}

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