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Merge pull request #44 from arpanjain97/master
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Christian Bender
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116
Dynamic Programming/Bellman-Ford.cpp
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116
Dynamic Programming/Bellman-Ford.cpp
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#include<iostream>
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#include<limits.h>
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using namespace std;
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//Wrapper class for storing an edge
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class Edge{
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public: int src,dst,weight;
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};
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//Wrapper class for storing a graph
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class Graph{
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public:
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int vertexNum,edgeNum;
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Edge* edges;
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//Constructs a graph with V vertices and E edges
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Graph(int V,int E){
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this->vertexNum = V;
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this->edgeNum = E;
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this->edges =(Edge*) malloc(E * sizeof(Edge));
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}
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//Adds the given edge to the graph
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void addEdge(int src, int dst, int weight){
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static int edgeInd = 0;
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if(edgeInd < this->edgeNum){
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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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this->edges[edgeInd++] = newEdge;
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}
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}
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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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cout<<"\nVertex Distance"<<endl;
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for(int i = 0; i < V; i++){
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if( dist[i] != INT_MAX)
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cout<<i<<"\t"<<dist[i]<<endl;
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else
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cout<<i<<"\tINF"<<endl;
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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(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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cout<<"Graph contains negative weight cycle. Hence, shortest distance not guaranteed."<<endl;
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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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cout<<"Enter number of vertices: ";
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cin>>V;
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cout<<"Enter number of edges: ";
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cin>>E;
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Graph G(V,E);
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for(int i=0; i<E; i++){
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cout<<"\nEdge "<<i+1<<"\nEnter source: ";
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cin>>src;
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cout<<"Enter destination: ";
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cin>>dst;
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cout<<"Enter weight: ";
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cin>>weight;
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G.addEdge(src, dst, weight);
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}
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cout<<"\nEnter source: ";
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cin>>gsrc;
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BellmanFord(G,gsrc);
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return 0;
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}
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106
Dynamic Programming/Floyd-Warshall.cpp
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106
Dynamic Programming/Floyd-Warshall.cpp
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#include<iostream>
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#include<limits.h>
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#include<string.h>
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using namespace std;
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//Wrapper class for storing a graph
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class Graph{
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public:
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int vertexNum;
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int** edges;
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//Constructs a graph with V vertices and E edges
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Graph(int V){
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this->vertexNum = V;
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this->edges =(int**) malloc(V * sizeof(int*));
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for(int i=0; i<V; i++){
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this->edges[i] = (int*) malloc(V * sizeof(int));
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for(int j=0; j<V; j++)
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this->edges[i][j] = INT_MAX;
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this->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(int src, int dst, int weight){
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this->edges[src][dst] = weight;
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}
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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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cout<<"\nThe Distance matrix for Floyd - Warshall"<<endl;
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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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cout<<dist[i*V+j]<<"\t";
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else
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cout<<"INF"<<"\t";
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}
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cout<<endl;
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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(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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cout<<"Enter number of vertices: ";
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cin>>V;
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cout<<"Enter number of edges: ";
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cin>>E;
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Graph G(V);
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for(int i=0; i<E; i++){
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cout<<"\nEdge "<<i+1<<"\nEnter source: ";
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cin>>src;
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cout<<"Enter destination: ";
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cin>>dst;
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cout<<"Enter weight: ";
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cin>>weight;
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G.addEdge(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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107
Greedy Algorithms/Dijkstra.cpp
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107
Greedy Algorithms/Dijkstra.cpp
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#include<iostream>
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#include<limits.h>
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using namespace std;
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//Wrapper class for storing a graph
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class Graph{
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public:
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int vertexNum;
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int** edges;
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//Constructs a graph with V vertices and E edges
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Graph(int V){
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this->vertexNum = V;
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this->edges =(int**) malloc(V * sizeof(int*));
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for(int i=0; i<V; i++)
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this->edges[i] = (int*) calloc(V, sizeof(int));
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}
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//Adds the given edge to the graph
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void addEdge(int src, int dst, int weight){
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this->edges[src][dst] = weight;
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}
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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[], bool 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] == false && 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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cout<<"\nVertex Distance"<<endl;
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for(int i = 0; i < V; i++){
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if( dist[i] != INT_MAX)
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cout<<i<<"\t"<<dist[i]<<endl;
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else
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cout<<i<<"\tINF"<<endl;
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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(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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bool 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] = false;
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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] = true;
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for(int v=0; v<V; v++){
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if(!vset[v] && graph.edges[u][v] && 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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cout<<"Enter number of vertices: ";
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cin>>V;
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cout<<"Enter number of edges: ";
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cin>>E;
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Graph G(V);
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for(int i=0; i<E; i++){
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cout<<"\nEdge "<<i+1<<"\nEnter source: ";
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cin>>src;
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cout<<"Enter destination: ";
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cin>>dst;
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cout<<"Enter weight: ";
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cin>>weight;
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G.addEdge(src, dst, weight);
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}
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cout<<"\nEnter source:";
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cin>>gsrc;
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Dijkstra(G,gsrc);
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return 0;
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}
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