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https://github.com/TheAlgorithms/C
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Christian Bender
GitHub
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130
data_structures/graphs/Bellman-Ford.c
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130
data_structures/graphs/Bellman-Ford.c
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@ -0,0 +1,130 @@
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#include<stdio.h>
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#include<stdlib.h>
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#include<limits.h>
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#include<string.h>
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//Structure for storing edge
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struct Edge{
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int src,dst,weight;
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};
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//Structure for storing a graph
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struct Graph{
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int vertexNum;
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int edgeNum;
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struct Edge* edges;
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};
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//Constructs a graph with V vertices and E edges
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void createGraph(struct Graph* G,int V,int E){
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G->vertexNum = V;
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G->edgeNum = E;
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G->edges = (struct Edge*) malloc(E * sizeof(struct Edge));
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}
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//Adds the given edge to the graph
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void addEdge(struct Graph* G, int src, int dst, int weight){
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static int ind;
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struct Edge newEdge;
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newEdge.src = src;
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newEdge.dst = dst;
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newEdge.weight = weight;
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G->edges[ind++]= newEdge;
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}
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//Utility function to find minimum distance vertex in mdist
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int minDistance(int mdist[], int vset[], int V){
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int minVal = INT_MAX, minInd ;
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for(int i=0; i<V;i++)
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if(vset[i] == 0 && mdist[i] < minVal){
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minVal = mdist[i];
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minInd = i;
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}
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return minInd;
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}
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//Utility function to print distances
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void print(int dist[], int V){
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printf("\nVertex Distance\n");
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for(int i = 0; i < V; i++){
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if(dist[i] != INT_MAX)
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printf("%d\t%d\n",i,dist[i]);
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else
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printf("%d\tINF",i);
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}
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}
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//The main function that finds the shortest path from given source
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//to all other vertices using Bellman-Ford.It also detects negative
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//weight cycle
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void BellmanFord(struct Graph* graph, int src){
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int V = graph->vertexNum;
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int E = graph->edgeNum;
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int dist[V];
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//Initialize distances array as INF for all except source
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//Intialize source as zero
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for(int i=0; i<V; i++)
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dist[i] = INT_MAX;
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dist[src] = 0;
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//Calculate shortest path distance from source to all edges
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//A path can contain maximum (|V|-1) edges
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for(int i=0; i<=V-1; i++)
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for(int j = 0; j<E; j++){
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int u = graph->edges[j].src;
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int v = graph->edges[j].dst;
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int w = graph->edges[j].weight;
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if(dist[u]!=INT_MAX && dist[u] + w < dist[v])
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dist[v] = dist[u] + w;
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}
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//Iterate inner loop once more to check for negative cycle
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for(int j = 0; j<E; j++){
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int u = graph->edges[j].src;
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int v = graph->edges[j].dst;
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int w = graph->edges[j].weight;
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if(dist[u]!=INT_MAX && dist[u] + w < dist[v]){
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printf("Graph contains negative weight cycle. Hence, shortest distance not guaranteed.");
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return;
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}
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}
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print(dist, V);
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return;
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}
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//Driver Function
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int main(){
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int V,E,gsrc;
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int src,dst,weight;
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struct Graph G;
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printf("Enter number of vertices: ");
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scanf("%d",&V);
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printf("Enter number of edges: ");
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scanf("%d",&E);
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createGraph(&G,V,E);
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for(int i=0; i<E; i++){
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printf("\nEdge %d \nEnter source: ",i+1);
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scanf("%d",&src);
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printf("Enter destination: ");
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scanf("%d",&dst);
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printf("Enter weight: ");
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scanf("%d",&weight);
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addEdge(&G, src, dst, weight);
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}
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printf("\nEnter source:");
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scanf("%d",&gsrc);
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BellmanFord(&G,gsrc);
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return 0;
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}
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114
data_structures/graphs/Dijkstra.c
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114
data_structures/graphs/Dijkstra.c
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@ -0,0 +1,114 @@
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#include<stdio.h>
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#include<stdlib.h>
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#include<limits.h>
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#include<string.h>
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//Structure for storing a graph
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struct Graph{
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int vertexNum;
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int** edges;
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};
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//Constructs a graph with V vertices and E edges
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void createGraph(struct Graph* G,int V){
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G->vertexNum = V;
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G->edges =(int**) malloc(V * sizeof(int*));
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for(int i=0; i<V; i++){
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G->edges[i] = (int*) malloc(V * sizeof(int));
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for(int j=0; j<V; j++)
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G->edges[i][j] = INT_MAX;
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G->edges[i][i] = 0;
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}
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}
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//Adds the given edge to the graph
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void addEdge(struct Graph* G, int src, int dst, int weight){
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G->edges[src][dst] = weight;
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}
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//Utility function to find minimum distance vertex in mdist
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int minDistance(int mdist[], int vset[], int V){
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int minVal = INT_MAX, minInd ;
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for(int i=0; i<V;i++)
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if(vset[i] == 0 && mdist[i] < minVal){
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minVal = mdist[i];
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minInd = i;
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}
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return minInd;
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}
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//Utility function to print distances
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void print(int dist[], int V){
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printf("\nVertex Distance\n");
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for(int i = 0; i < V; i++){
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if(dist[i] != INT_MAX)
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printf("%d\t%d\n",i,dist[i]);
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else
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printf("%d\tINF",i);
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}
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}
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//The main function that finds the shortest path from given source
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//to all other vertices using Dijkstra's Algorithm.It doesn't work on negative
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//weights
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void Dijkstra(struct Graph* graph, int src){
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int V = graph->vertexNum;
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int mdist[V]; //Stores updated distances to vertex
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int vset[V]; // vset[i] is true if the vertex i included
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// in the shortest path tree
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//Initialise mdist and vset. Set distance of source as zero
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for(int i=0; i<V; i++)
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mdist[i] = INT_MAX, vset[i] = 0;
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mdist[src] = 0;
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//iterate to find shortest path
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for(int count = 0; count<V-1; count++){
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int u = minDistance(mdist,vset,V);
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vset[u] = 1;
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for(int v=0; v<V; v++){
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if(!vset[v] && graph->edges[u][v]!=INT_MAX && mdist[u] + graph->edges[u][v] < mdist[v])
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mdist[v] = mdist[u] + graph->edges[u][v];
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}
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}
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print(mdist, V);
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return;
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}
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//Driver Function
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int main(){
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int V,E,gsrc;
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int src,dst,weight;
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struct Graph G;
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printf("Enter number of vertices: ");
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scanf("%d",&V);
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printf("Enter number of edges: ");
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scanf("%d",&E);
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createGraph(&G,V);
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for(int i=0; i<E; i++){
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printf("\nEdge %d \nEnter source: ",i+1);
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scanf("%d",&src);
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printf("Enter destination: ");
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scanf("%d",&dst);
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printf("Enter weight: ");
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scanf("%d",&weight);
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addEdge(&G, src, dst, weight);
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}
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printf("\nEnter source:");
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scanf("%d",&gsrc);
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Dijkstra(&G,gsrc);
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return 0;
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}
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104
data_structures/graphs/Floyd-Warshall.c
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104
data_structures/graphs/Floyd-Warshall.c
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@ -0,0 +1,104 @@
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#include<stdio.h>
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#include<stdlib.h>
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#include<limits.h>
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#include<string.h>
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//Structure for storing a graph
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struct Graph{
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int vertexNum;
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int** edges;
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};
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//Constructs a graph with V vertices and E edges
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void createGraph(struct Graph* G,int V){
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G->vertexNum = V;
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G->edges =(int**) malloc(V * sizeof(int*));
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for(int i=0; i<V; i++){
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G->edges[i] = (int*) malloc(V * sizeof(int));
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for(int j=0; j<V; j++)
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G->edges[i][j] = INT_MAX;
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G->edges[i][i] = 0;
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}
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}
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//Adds the given edge to the graph
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void addEdge(struct Graph* G, int src, int dst, int weight){
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G->edges[src][dst] = weight;
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}
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//Utility function to print distances
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void print(int dist[], int V){
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printf("\nThe Distance matrix for Floyd - Warshall\n");
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for(int i = 0; i < V; i++){
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for(int j=0; j<V; j++){
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if(dist[i*V+j] != INT_MAX)
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printf("%d\t",dist[i*V+j]);
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else
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printf("INF\t");
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}
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printf("\n");
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}
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}
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//The main function that finds the shortest path from a vertex
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//to all other vertices using Floyd-Warshall Algorithm.
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void FloydWarshall(struct Graph* graph){
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int V = graph->vertexNum;
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int dist[V][V];
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//Initialise distance array
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for(int i=0; i<V; i++)
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for(int j=0; j<V; j++)
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dist[i][j] = graph->edges[i][j];
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//Calculate distances
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for(int k=0; k<V; k++)
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//Choose an intermediate vertex
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for(int i=0; i<V; i++)
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//Choose a source vertex for given intermediate
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for(int j=0; j<V; j++)
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//Choose a destination vertex for above source vertex
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if(dist[i][k] != INT_MAX && dist[k][j] != INT_MAX && dist[i][k] + dist[k][j] < dist[i][j])
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//If the distance through intermediate vertex is less than direct edge then update value in distance array
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dist[i][j] = dist[i][k] + dist[k][j];
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//Convert 2d array to 1d array for print
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int dist1d[V*V];
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for(int i=0; i<V; i++)
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for(int j=0; j<V; j++)
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dist1d[i*V+j] = dist[i][j];
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print(dist1d,V);
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}
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//Driver Function
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int main(){
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int V,E;
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int src,dst,weight;
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struct Graph G;
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printf("Enter number of vertices: ");
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scanf("%d",&V);
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printf("Enter number of edges: ");
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scanf("%d",&E);
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createGraph(&G,V);
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for(int i=0; i<E; i++){
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printf("\nEdge %d \nEnter source: ",i+1);
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scanf("%d",&src);
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printf("Enter destination: ");
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scanf("%d",&dst);
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printf("Enter weight: ");
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scanf("%d",&weight);
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addEdge(&G, src, dst, weight);
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}
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FloydWarshall(&G);
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return 0;
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}
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