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* fix some bugs
* delete duplicate files
* format code
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yanglbme
2019-05-09 19:32:54 +08:00
parent 163db8521a
commit 29948363da
368 changed files with 4372 additions and 30841 deletions
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62
DataStructures/Graphs/BFS.java
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@ -1,62 +0,0 @@
import java.util.*;
/**
* Implementation of a Breadth First Search
*
* @author Unknown
*
*/
public class BFS{
/**
* The BFS implemented in code to use.
*
* @param a Structure to perform the search on a graph, adjacency matrix etc.
* @param vertices The vertices to use
* @param source The Source
*/
public static void bfsImplement(byte [][] a,int vertices,int source){ //passing adjacency matrix and no of vertices
byte []b=new byte[vertices]; //flag container containing status of each vertices
Arrays.fill(b,(byte)-1); //status initialization
/* code status
-1 = ready
0 = waiting
1 = processed */
Stack st = new Stack(vertices); //operational stack
st.push(source); //assigning source
while(!st.isEmpty()){
b[st.peek()]=(byte)0; //assigning waiting status
System.out.println(st.peek());
int pop=st.peek();
b[pop]=(byte)1; //assigning processed status
st.pop(); //removing head of the queue
for(int i=0;i<vertices;i++){
if(a[pop][i]!=0 && b[i]!=(byte)0 && b[i]!=(byte)1 ){
st.push(i);
b[i]=(byte)0; //assigning waiting status
}}}
}
/**
* The main method
*
* @param args Command line arguments
*/
public static void main(String args[]){
Scanner in=new Scanner(System.in);
int vertices=in.nextInt(),source=in.nextInt();
byte [][]a=new byte [vertices][vertices];
//initially all elements of a are initialized with value zero
for(int i=0;i<vertices;i++){
int size =in.nextInt();
for(int j=0;j<size;j++){
a[i][in.nextInt()]=1; //taking adjacency entries by assigning 1
}
}
bfsImplement(a,vertices,source); //function call
in.close();
}
}

233
DataStructures/Graphs/ConnectedComponent.java
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@ -1,150 +1,141 @@
package DataStructures.Graphs;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Set;
/**
* A class that counts the number of different connected components in a graph
*
* @author Lukas Keul, Florian Mercks
*
* @author Lukas Keul, Florian Mercks
*/
class Graph<E extends Comparable<E>> {
class Node {
E name;
class Node {
E name;
public Node(E name) {
this.name = name;
}
}
public Node(E name) {
this.name = name;
}
}
class Edge {
Node startNode, endNode;
class Edge {
Node startNode, endNode;
public Edge(Node startNode, Node endNode) {
this.startNode = startNode;
this.endNode = endNode;
}
}
public Edge(Node startNode, Node endNode) {
this.startNode = startNode;
this.endNode = endNode;
}
}
ArrayList<Edge> edgeList;
ArrayList<Node> nodeList;
ArrayList<Edge> edgeList;
ArrayList<Node> nodeList;
public Graph() {
edgeList = new ArrayList<Edge>();
nodeList = new ArrayList<Node>();
}
public Graph() {
edgeList = new ArrayList<Edge>();
nodeList = new ArrayList<Node>();
}
/**
* Adds a new Edge to the graph. If the nodes aren't yet in nodeList, they
* will be added to it.
*
* @param startNode
* the starting Node from the edge
*
* @param endNode
* the ending Node from the edge
*/
public void addEdge(E startNode, E endNode) {
Node start = null, end = null;
for (Node node : nodeList) {
if (startNode.compareTo(node.name) == 0) {
start = node;
}
else if (endNode.compareTo(node.name) == 0) {
end = node;
}
}
if (start == null) {
start = new Node(startNode);
nodeList.add(start);
}
if (end == null) {
end = new Node(endNode);
nodeList.add(end);
}
/**
* Adds a new Edge to the graph. If the nodes aren't yet in nodeList, they
* will be added to it.
*
* @param startNode the starting Node from the edge
* @param endNode the ending Node from the edge
*/
public void addEdge(E startNode, E endNode) {
Node start = null, end = null;
for (Node node : nodeList) {
if (startNode.compareTo(node.name) == 0) {
start = node;
} else if (endNode.compareTo(node.name) == 0) {
end = node;
}
}
if (start == null) {
start = new Node(startNode);
nodeList.add(start);
}
if (end == null) {
end = new Node(endNode);
nodeList.add(end);
}
edgeList.add(new Edge(start, end));
}
edgeList.add(new Edge(start, end));
}
/**
* Main method used for counting the connected components. Iterates through
* the array of nodes to do a depth first search to get all nodes of the
* graph from the actual node. These nodes are added to the array
* markedNodes and will be ignored if they are chosen in the nodeList.
*
* @return returns the amount of unconnected graphs
*
*/
public int countGraphs() {
int count = 0;
Set<Node> markedNodes = new HashSet<Node>();
/**
* Main method used for counting the connected components. Iterates through
* the array of nodes to do a depth first search to get all nodes of the
* graph from the actual node. These nodes are added to the array
* markedNodes and will be ignored if they are chosen in the nodeList.
*
* @return returns the amount of unconnected graphs
*/
public int countGraphs() {
int count = 0;
Set<Node> markedNodes = new HashSet<Node>();
for (Node n : nodeList) {
if (!markedNodes.contains(n)) {
markedNodes.add(n);
markedNodes.addAll(depthFirstSearch(n, new ArrayList<Node>()));
count++;
}
}
for (Node n : nodeList) {
if (!markedNodes.contains(n)) {
markedNodes.add(n);
markedNodes.addAll(depthFirstSearch(n, new ArrayList<Node>()));
count++;
}
}
return count;
}
return count;
}
/**
* Implementation of depth first search.
*
* @param n
* the actual visiting node
*
* @param visited
* A list of already visited nodes in the depth first search
*
* @return returns a set of visited nodes
*
*/
public ArrayList<Node> depthFirstSearch(Node n, ArrayList<Node> visited) {
visited.add(n);
for (Edge e : edgeList) {
if (e.startNode.equals(n) && !visited.contains(e.endNode)) {
depthFirstSearch(e.endNode, visited);
}
}
return visited;
}
/**
* Implementation of depth first search.
*
* @param n the actual visiting node
* @param visited A list of already visited nodes in the depth first search
* @return returns a set of visited nodes
*/
public ArrayList<Node> depthFirstSearch(Node n, ArrayList<Node> visited) {
visited.add(n);
for (Edge e : edgeList) {
if (e.startNode.equals(n) && !visited.contains(e.endNode)) {
depthFirstSearch(e.endNode, visited);
}
}
return visited;
}
}
public class ConnectedComponent {
public static void main(String[] args) {
Graph graphChars = new Graph();
public static void main(String[] args) {
Graph graphChars = new Graph();
// Graph 1
graphChars.addEdge('a', 'b');
graphChars.addEdge('a', 'e');
graphChars.addEdge('b', 'e');
graphChars.addEdge('b', 'c');
graphChars.addEdge('c', 'd');
graphChars.addEdge('d', 'a');
graphChars.addEdge('x', 'y');
graphChars.addEdge('x', 'z');
graphChars.addEdge('w', 'w');
// Graph 1
graphChars.addEdge('a', 'b');
graphChars.addEdge('a', 'e');
graphChars.addEdge('b', 'e');
graphChars.addEdge('b', 'c');
graphChars.addEdge('c', 'd');
graphChars.addEdge('d', 'a');
Graph graphInts = new Graph();
// Graph 2
graphInts.addEdge(1, 2);
graphInts.addEdge(2, 3);
graphInts.addEdge(2, 4);
graphInts.addEdge(3, 5);
graphInts.addEdge(7, 8);
graphInts.addEdge(8, 10);
graphInts.addEdge(10, 8);
graphChars.addEdge('x', 'y');
graphChars.addEdge('x', 'z');
System.out.println("Amount of different char-graphs: " + graphChars.countGraphs());
System.out.println("Amount of different int-graphs: " + graphInts.countGraphs());
}
graphChars.addEdge('w', 'w');
Graph graphInts = new Graph();
// Graph 2
graphInts.addEdge(1, 2);
graphInts.addEdge(2, 3);
graphInts.addEdge(2, 4);
graphInts.addEdge(3, 5);
graphInts.addEdge(7, 8);
graphInts.addEdge(8, 10);
graphInts.addEdge(10, 8);
System.out.println("Amount of different char-graphs: " + graphChars.countGraphs());
System.out.println("Amount of different int-graphs: " + graphInts.countGraphs());
}
}

18
DataStructures/Graphs/Cycles.java
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@ -1,3 +1,5 @@
package DataStructures.Graphs;
import java.util.Scanner;
import java.util.ArrayList;
@ -5,10 +7,10 @@ import java.util.ArrayList;
class Cycle {
private int nodes, edges;
private int [][] adjacencyMatrix;
private boolean [] visited;
private int[][] adjacencyMatrix;
private boolean[] visited;
ArrayList<ArrayList<Integer>> cycles = new ArrayList<ArrayList<Integer>>();
private boolean [] finalCycles;
private boolean[] finalCycles;
public Cycle() {
Scanner in = new Scanner(System.in);
@ -17,8 +19,8 @@ class Cycle {
System.out.print("Enter the no. of Edges: ");
edges = in.nextInt();
adjacencyMatrix = new int [nodes][nodes];
visited = new boolean [nodes];
adjacencyMatrix = new int[nodes][nodes];
visited = new boolean[nodes];
for (int i = 0; i < nodes; i++) {
visited[i] = false;
@ -26,7 +28,7 @@ class Cycle {
System.out.println("Enter the details of each edges <Start Node> <End Node>");
for(int i = 0; i < edges; i++) {
for (int i = 0; i < edges; i++) {
int start, end;
start = in.nextInt();
end = in.nextInt();
@ -50,7 +52,7 @@ class Cycle {
temp.add(curr);
visited[curr] = true;
for (int i = 0; i < nodes; i++) {
if(adjacencyMatrix[curr][i] == 1) {
if (adjacencyMatrix[curr][i] == 1) {
if (i == start) {
cycles.add(new ArrayList<Integer>(temp));
} else {
@ -61,7 +63,7 @@ class Cycle {
}
}
if(temp.size() > 0) {
if (temp.size() > 0) {
temp.remove(temp.size() - 1);
}
visited[curr] = false;

63
DataStructures/Graphs/DFS.java
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@ -1,63 +0,0 @@
import java.util.*;
/**
* Implementation of a Depth First Search
*
* @author Unknown
*
*/
public class DFS{
/**
* Implementation in code of a DFS
*
* @param a structure to be DFS'ed
* @param vertices The vertices
* @param source The source
*/
public static void dfsImplement(byte [][] a,int vertices,int source){ //passing adjacency matrix and no of vertices
byte []b=new byte[vertices]; //flag container containing status of each vertices
Arrays.fill(b,(byte)-1); //status initialization
/* code status
-1 = ready
0 = waiting
1 = processed */
Stack st=new Stack(vertices); //operational stack
st.push(source); //assigning source
while(!st.isEmpty()){
b[st.peek()]=(byte)0; //assigning waiting status
System.out.println(st.peek());
int pop=st.pop();
b[pop]=(byte)1; //assigning processed status
for(int i=0;i<vertices;i++){
if(a[pop][i]!=0 && b[i]!=(byte)0 && b[i]!=(byte)1 ){
st.push(i);
b[i]=(byte)0; //assigning waiting status
}}}
}
/**
* The main method
*
* @param args Command line arguments
*/
public static void main(String args[]){
Scanner in=new Scanner(System.in);
int vertices=in.nextInt(),source=in.nextInt();
byte [][]a=new byte [vertices][vertices];
//initially all elements of a are initialized with value zero
for(int i=0;i<vertices;i++){
int size =in.nextInt();
for(int j=0;j<size;j++){
a[i][in.nextInt()]=1; //taking adjacency entries by assigning 1
}
}
dfsImplement(a,vertices,source); //function call
in.close();
}
}

129
DataStructures/Graphs/FloydWarshall.java
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@ -1,78 +1,73 @@
import java.util.Scanner;
public class FloydWarshall
package DataStructures.Graphs;
import java.util.Arrays;
import java.util.Scanner;
public class FloydWarshall {
private int DistanceMatrix[][];
private int numberofvertices;//number of vertices in the graph
public static final int INFINITY = 999;
public FloydWarshall(int numberofvertices) {
DistanceMatrix = new int[numberofvertices + 1][numberofvertices + 1];//stores the value of distance from all the possible path form the source vertex to destination vertex
Arrays.fill(DistanceMatrix, 0);
this.numberofvertices = numberofvertices;
}
public void floydwarshall(int AdjacencyMatrix[][])//calculates all the distances from source to destination vertex
{
private int DistanceMatrix[][];
private int numberofvertices;//number of vertices in the graph
public static final int INFINITY = 999;
public FloydWarshall(int numberofvertices)
{
DistanceMatrix = new int[numberofvertices + 1][numberofvertices + 1];//stores the value of distance from all the possible path form the source vertex to destination vertex
Arrays.fill(DistanceMatrix, 0);
this.numberofvertices = numberofvertices;
}
public void floydwarshall(int AdjacencyMatrix[][])//calculates all the distances from source to destination vertex
{
for (int source = 1; source <= numberofvertices; source++)
{
for (int destination = 1; destination <= numberofvertices; destination++)
{
DistanceMatrix[source][destination] = AdjacencyMatrix[source][destination];
}
for (int source = 1; source <= numberofvertices; source++) {
for (int destination = 1; destination <= numberofvertices; destination++) {
DistanceMatrix[source][destination] = AdjacencyMatrix[source][destination];
}
for (int intermediate = 1; intermediate <= numberofvertices; intermediate++)
{
for (int source = 1; source <= numberofvertices; source++)
{
for (int destination = 1; destination <= numberofvertices; destination++)
}
for (int intermediate = 1; intermediate <= numberofvertices; intermediate++) {
for (int source = 1; source <= numberofvertices; source++) {
for (int destination = 1; destination <= numberofvertices; destination++) {
if (DistanceMatrix[source][intermediate] + DistanceMatrix[intermediate][destination]
< DistanceMatrix[source][destination])
// if the new distance calculated is less then the earlier shortest
// calculated distance it get replaced as new shortest distance
{
if (DistanceMatrix[source][intermediate] + DistanceMatrix[intermediate][destination]
< DistanceMatrix[source][destination])//if the new distance calculated is less then the earlier shortest calculated distance it get replaced as new shortest distance
DistanceMatrix[source][destination] = DistanceMatrix[source][intermediate]
DistanceMatrix[source][destination] = DistanceMatrix[source][intermediate]
+ DistanceMatrix[intermediate][destination];
}
}
}
for (int source = 1; source <= numberofvertices; source++)
System.out.print("\t" + source);
System.out.println();
for (int source = 1; source <= numberofvertices; source++)
{
System.out.print(source + "\t");
for (int destination = 1; destination <= numberofvertices; destination++)
{
System.out.print(DistanceMatrix[source][destination] + "\t");
}
System.out.println();
}
}
public static void main(String... arg)
{
int Adjacency_Matrix[][];
int numberofvertices;
Scanner scan = new Scanner(System.in);
System.out.println("Enter the number of vertices");
numberofvertices = scan.nextInt();
Adjacency_Matrix = new int[numberofvertices + 1][numberofvertices + 1];
System.out.println("Enter the Weighted Matrix for the graph");
for (int source = 1; source <= numberofvertices; source++)
{
for (int destination = 1; destination <= numberofvertices; destination++)
{
Adjacency_Matrix[source][destination] = scan.nextInt();
if (source == destination)
{
Adjacency_Matrix[source][destination] = 0;
continue;
}
if (Adjacency_Matrix[source][destination] == 0)
{
Adjacency_Matrix[source][destination] = INFINITY;
}
}
for (int source = 1; source <= numberofvertices; source++)
System.out.print("\t" + source);
System.out.println();
for (int source = 1; source <= numberofvertices; source++) {
System.out.print(source + "\t");
for (int destination = 1; destination <= numberofvertices; destination++) {
System.out.print(DistanceMatrix[source][destination] + "\t");
}
System.out.println("The Transitive Closure of the Graph");
FloydWarshall floydwarshall = new FloydWarshall(numberofvertices);
floydwarshall.floydwarshall(adjacency_matrix);
scan.close();
System.out.println();
}
}
public static void main(String... arg) {
Scanner scan = new Scanner(System.in);
System.out.println("Enter the number of vertices");
int numberOfVertices = scan.nextInt();
int[][] adjacencyMatrix = new int[numberOfVertices + 1][numberOfVertices + 1];
System.out.println("Enter the Weighted Matrix for the graph");
for (int source = 1; source <= numberOfVertices; source++) {
for (int destination = 1; destination <= numberOfVertices; destination++) {
adjacencyMatrix[source][destination] = scan.nextInt();
if (source == destination) {
adjacencyMatrix[source][destination] = 0;
continue;
}
if (adjacencyMatrix[source][destination] == 0) {
adjacencyMatrix[source][destination] = INFINITY;
}
}
}
System.out.println("The Transitive Closure of the Graph");
FloydWarshall floydwarshall = new FloydWarshall(numberOfVertices);
floydwarshall.floydwarshall(adjacencyMatrix);
scan.close();
}
}

34
DataStructures/Graphs/Graphs.java
View File

@ -1,8 +1,10 @@
package DataStructures.Graphs;
import java.util.ArrayList;
import java.lang.StringBuilder;
class AdjacencyListGraph<E extends Comparable<E>> {
ArrayList<Vertex> verticies;
public AdjacencyListGraph() {
@ -19,7 +21,7 @@ class AdjacencyListGraph<E extends Comparable<E>> {
}
public boolean addAdjacentVertex(Vertex to) {
for (Vertex v: adjacentVerticies) {
for (Vertex v : adjacentVerticies) {
if (v.data.compareTo(to.data) == 0) {
return false; // the edge already exists
}
@ -46,12 +48,12 @@ class AdjacencyListGraph<E extends Comparable<E>> {
* verticies
*
* @param from the data of the vertex the edge is from
* @param to the data of the vertex the edge is going to
* @param to the data of the vertex the edge is going to
* @return returns false if the edge doesn't exist, returns true if the edge exists and is removed
*/
public boolean removeEdge(E from, E to) {
Vertex fromV = null;
for (Vertex v: verticies) {
for (Vertex v : verticies) {
if (from.compareTo(v.data) == 0) {
fromV = v;
break;
@ -60,17 +62,18 @@ class AdjacencyListGraph<E extends Comparable<E>> {
if (fromV == null) return false;
return fromV.removeAdjacentVertex(to);
}
/**
* this method adds an edge to the graph between two specified
* verticies
* verticies
*
* @param from the data of the vertex the edge is from
* @param to the data of the vertex the edge is going to
* @param to the data of the vertex the edge is going to
* @return returns true if the edge did not exist, return false if it already did
*/
public boolean addEdge(E from, E to) {
Vertex fromV = null, toV = null;
for (Vertex v: verticies) {
for (Vertex v : verticies) {
if (from.compareTo(v.data) == 0) { // see if from vertex already exists
fromV = v;
} else if (to.compareTo(v.data) == 0) { // see if to vertex already exists
@ -91,17 +94,18 @@ class AdjacencyListGraph<E extends Comparable<E>> {
/**
* this gives a list of verticies in the graph and their adjacencies
*
*
* @return returns a string describing this graph
*/
@Override
public String toString() {
StringBuilder sb = new StringBuilder();
for (Vertex v: verticies) {
for (Vertex v : verticies) {
sb.append("Vertex: ");
sb.append(v.data);
sb.append("\n");
sb.append("Adjacent verticies: ");
for (Vertex v2: v.adjacentVerticies) {
for (Vertex v2 : v.adjacentVerticies) {
sb.append(v2.data);
sb.append(" ");
}
@ -112,18 +116,18 @@ class AdjacencyListGraph<E extends Comparable<E>> {
}
public class Graphs {
public static void main(String args[]) {
AdjacencyListGraph<Integer> graph = new AdjacencyListGraph<>();
public static void main(String args[]) {
AdjacencyListGraph<Integer> graph = new AdjacencyListGraph<>();
assert graph.addEdge(1, 2);
assert graph.addEdge(1, 5);
assert graph.addEdge(2, 5);
assert !graph.addEdge(1, 2);
assert !graph.addEdge(1, 2);
assert graph.addEdge(2, 3);
assert graph.addEdge(3, 4);
assert graph.addEdge(4, 1);
assert !graph.addEdge(2, 3);
System.out.println(graph);
}
}

174
DataStructures/Graphs/KruskalsAlgorithm.java
View File

@ -1,174 +0,0 @@
// Java program for Kruskal's algorithm to find Minimum Spanning Tree
// of a given connected, undirected and weighted graph
import java.util.*;
import java.lang.*;
import java.io.*;
class Graph
{
// A class to represent a graph edge
class Edge implements Comparable<Edge>
{
int src, dest, weight;
// Comparator function used for sorting edges based on
// their weight
public int compareTo(Edge compareEdge)
{
return this.weight-compareEdge.weight;
}
};
// A class to represent a subset for union-find
class subset
{
int parent, rank;
};
int V, E; // V-> no. of vertices & E->no.of edges
Edge edge[]; // collection of all edges
// Creates a graph with V vertices and E edges
Graph(int v, int e)
{
V = v;
E = e;
edge = new Edge[E];
for (int i=0; i<e; ++i)
edge[i] = new Edge();
}
// A utility function to find set of an element i
// (uses path compression technique)
int find(subset subsets[], int i)
{
// find root and make root as parent of i (path compression)
if (subsets[i].parent != i)
subsets[i].parent = find(subsets, subsets[i].parent);
return subsets[i].parent;
}
// A function that does union of two sets of x and y
// (uses union by rank)
void Union(subset subsets[], int x, int y)
{
int xroot = find(subsets, x);
int yroot = find(subsets, y);
// Attach smaller rank tree under root of high rank tree
// (Union by Rank)
if (subsets[xroot].rank < subsets[yroot].rank)
subsets[xroot].parent = yroot;
else if (subsets[xroot].rank > subsets[yroot].rank)
subsets[yroot].parent = xroot;
// If ranks are same, then make one as root and increment
// its rank by one
else
{
subsets[yroot].parent = xroot;
subsets[xroot].rank++;
}
}
// The main function to construct MST using Kruskal's algorithm
void KruskalMST()
{
Edge result[] = new Edge[V]; // Tnis will store the resultant MST
int e = 0; // An index variable, used for result[]
int i = 0; // An index variable, used for sorted edges
for (i=0; i<V; ++i)
result[i] = new Edge();
// Step 1: Sort all the edges in non-decreasing order of their
// weight. If we are not allowed to change the given graph, we
// can create a copy of array of edges
Arrays.sort(edge);
// Allocate memory for creating V ssubsets
subset subsets[] = new subset[V];
for(i=0; i<V; ++i)
subsets[i]=new subset();
// Create V subsets with single elements
for (int v = 0; v < V; ++v)
{
subsets[v].parent = v;
subsets[v].rank = 0;
}
i = 0; // Index used to pick next edge
// Number of edges to be taken is equal to V-1
while (e < V - 1)
{
// Step 2: Pick the smallest edge. And increment the index
// for next iteration
Edge next_edge = new Edge();
next_edge = edge[i++];
int x = find(subsets, next_edge.src);
int y = find(subsets, next_edge.dest);
// If including this edge does't cause cycle, include it
// in result and increment the index of result for next edge
if (x != y)
{
result[e++] = next_edge;
Union(subsets, x, y);
}
// Else discard the next_edge
}
// print the contents of result[] to display the built MST
System.out.println("Following are the edges in the constructed MST");
for (i = 0; i < e; ++i)
System.out.println(result[i].src+" -- "+result[i].dest+" == "+
result[i].weight);
}
// Driver Program
public static void main (String[] args)
{
/* Let us create following weighted graph
10
0--------1
| \ |
6| 5\ |15
| \ |
2--------3
4 */
int V = 4; // Number of vertices in graph
int E = 5; // Number of edges in graph
Graph graph = new Graph(V, E);
// add edge 0-1
graph.edge[0].src = 0;
graph.edge[0].dest = 1;
graph.edge[0].weight = 10;
// add edge 0-2
graph.edge[1].src = 0;
graph.edge[1].dest = 2;
graph.edge[1].weight = 6;
// add edge 0-3
graph.edge[2].src = 0;
graph.edge[2].dest = 3;
graph.edge[2].weight = 5;
// add edge 1-3
graph.edge[3].src = 1;
graph.edge[3].dest = 3;
graph.edge[3].weight = 15;
// add edge 2-3
graph.edge[4].src = 2;
graph.edge[4].dest = 3;
graph.edge[4].weight = 4;
graph.KruskalMST();
}
}

214
DataStructures/Graphs/MatrixGraphs.java
View File

@ -1,145 +1,147 @@
package DataStructures.Graphs;
public class MatrixGraphs {
public static void main(String args[]) {
AdjacencyMatrixGraph graph = new AdjacencyMatrixGraph(10);
graph.addEdge(1, 2);
graph.addEdge(1, 5);
graph.addEdge(2, 5);
graph.addEdge(1, 2);
graph.addEdge(2, 3);
graph.addEdge(3, 4);
graph.addEdge(4, 1);
graph.addEdge(2, 3);
System.out.println(graph);
}
public static void main(String args[]) {
AdjacencyMatrixGraph graph = new AdjacencyMatrixGraph(10);
graph.addEdge(1, 2);
graph.addEdge(1, 5);
graph.addEdge(2, 5);
graph.addEdge(1, 2);
graph.addEdge(2, 3);
graph.addEdge(3, 4);
graph.addEdge(4, 1);
graph.addEdge(2, 3);
System.out.println(graph);
}
}
class AdjacencyMatrixGraph {
private int _numberOfVertices;
private int _numberOfEdges;
private int[][] _adjacency;
private int _numberOfVertices;
private int _numberOfEdges;
private int[][] _adjacency;
static final int EDGE_EXIST = 1;
static final int EDGE_NONE = 0;
static final int EDGE_EXIST = 1;
static final int EDGE_NONE = 0;
public AdjacencyMatrixGraph(int givenNumberOfVertices) {
this.setNumberOfVertices(givenNumberOfVertices);
this.setNumberOfEdges(0);
this.setAdjacency(new int[givenNumberOfVertices][givenNumberOfVertices]);
for (int i = 0; i < givenNumberOfVertices; i++) {
for (int j = 0; j < givenNumberOfVertices; j++) {
this.adjacency()[i][j] = AdjacencyMatrixGraph.EDGE_NONE;
}
}
}
public AdjacencyMatrixGraph(int givenNumberOfVertices) {
this.setNumberOfVertices(givenNumberOfVertices);
this.setNumberOfEdges(0);
this.setAdjacency(new int[givenNumberOfVertices][givenNumberOfVertices]);
for (int i = 0; i < givenNumberOfVertices; i++) {
for (int j = 0; j < givenNumberOfVertices; j++) {
this.adjacency()[i][j] = AdjacencyMatrixGraph.EDGE_NONE;
}
}
}
private void setNumberOfVertices(int newNumberOfVertices) {
this._numberOfVertices = newNumberOfVertices;
}
private void setNumberOfVertices(int newNumberOfVertices) {
this._numberOfVertices = newNumberOfVertices;
}
public int numberOfVertices() {
return this._numberOfVertices;
}
public int numberOfVertices() {
return this._numberOfVertices;
}
private void setNumberOfEdges(int newNumberOfEdges) {
this._numberOfEdges = newNumberOfEdges;
}
private void setNumberOfEdges(int newNumberOfEdges) {
this._numberOfEdges = newNumberOfEdges;
}
public int numberOfEdges() {
return this._numberOfEdges;
}
public int numberOfEdges() {
return this._numberOfEdges;
}
private void setAdjacency(int[][] newAdjacency) {
this._adjacency = newAdjacency;
}
private void setAdjacency(int[][] newAdjacency) {
this._adjacency = newAdjacency;
}
private int[][] adjacency() {
return this._adjacency;
}
private int[][] adjacency() {
return this._adjacency;
}
private boolean adjacencyOfEdgeDoesExist(int from, int to) {
return (this.adjacency()[from][to] != AdjacencyMatrixGraph.EDGE_NONE);
}
private boolean adjacencyOfEdgeDoesExist(int from, int to) {
return (this.adjacency()[from][to] != AdjacencyMatrixGraph.EDGE_NONE);
}
public boolean vertexDoesExist(int aVertex) {
if (aVertex >= 0 && aVertex < this.numberOfVertices()) {
return true;
} else {
return false;
}
}
public boolean vertexDoesExist(int aVertex) {
if (aVertex >= 0 && aVertex < this.numberOfVertices()) {
return true;
} else {
return false;
}
}
public boolean edgeDoesExist(int from, int to) {
if (this.vertexDoesExist(from) && this.vertexDoesExist(to)) {
return (this.adjacencyOfEdgeDoesExist(from, to));
}
public boolean edgeDoesExist(int from, int to) {
if (this.vertexDoesExist(from) && this.vertexDoesExist(to)) {
return (this.adjacencyOfEdgeDoesExist(from, to));
}
return false;
}
return false;
}
/**
/**
* This method adds an edge to the graph between two specified
* vertices
* vertices
*
* @param from the data of the vertex the edge is from
* @param to the data of the vertex the edge is going to
* @param to the data of the vertex the edge is going to
* @return returns true if the edge did not exist, return false if it already did
*/
public boolean addEdge(int from, int to) {
if (this.vertexDoesExist(from) && this.vertexDoesExist(to)) {
if (!this.adjacencyOfEdgeDoesExist(from, to)) {
this.adjacency()[from][to] = AdjacencyMatrixGraph.EDGE_EXIST;
this.adjacency()[to][from] = AdjacencyMatrixGraph.EDGE_EXIST;
this.setNumberOfEdges(this.numberOfEdges() + 1);
return true;
}
}
public boolean addEdge(int from, int to) {
if (this.vertexDoesExist(from) && this.vertexDoesExist(to)) {
if (!this.adjacencyOfEdgeDoesExist(from, to)) {
this.adjacency()[from][to] = AdjacencyMatrixGraph.EDGE_EXIST;
this.adjacency()[to][from] = AdjacencyMatrixGraph.EDGE_EXIST;
this.setNumberOfEdges(this.numberOfEdges() + 1);
return true;
}
}
return false;
}
return false;
}
/**
/**
* this method removes an edge from the graph between two specified
* vertices
* vertices
*
* @param from the data of the vertex the edge is from
* @param to the data of the vertex the edge is going to
* @param to the data of the vertex the edge is going to
* @return returns false if the edge doesn't exist, returns true if the edge exists and is removed
*/
public boolean removeEdge(int from, int to) {
if(!this.vertexDoesExist(from) || !this.vertexDoesExist(to)) {
if (this.adjacencyOfEdgeDoesExist(from, to)) {
this.adjacency()[from][to] = AdjacencyMatrixGraph.EDGE_NONE;
this.adjacency()[to][from] = AdjacencyMatrixGraph.EDGE_NONE;
this.setNumberOfEdges(this.numberOfEdges() - 1);
return true;
}
}
return false;
}
public boolean removeEdge(int from, int to) {
if (!this.vertexDoesExist(from) || !this.vertexDoesExist(to)) {
if (this.adjacencyOfEdgeDoesExist(from, to)) {
this.adjacency()[from][to] = AdjacencyMatrixGraph.EDGE_NONE;
this.adjacency()[to][from] = AdjacencyMatrixGraph.EDGE_NONE;
this.setNumberOfEdges(this.numberOfEdges() - 1);
return true;
}
}
return false;
}
/**
* this gives a list of vertices in the graph and their adjacencies
*
*
* @return returns a string describing this graph
*/
public String toString() {
String s = new String();
s = " ";
for (int i = 0; i < this.numberOfVertices(); i++) {
s = s + String.valueOf(i) + " ";
}
s = s + " \n";
public String toString() {
String s = new String();
s = " ";
for (int i = 0; i < this.numberOfVertices(); i++) {
s = s + String.valueOf(i) + " ";
}
s = s + " \n";
for (int i = 0; i < this.numberOfVertices(); i++) {
s = s + String.valueOf(i) + " : ";
for (int j = 0; j < this.numberOfVertices(); j++) {
s = s + String.valueOf(this._adjacency[i][j]) + " ";
}
s = s + "\n";
}
return s;
}
for (int i = 0; i < this.numberOfVertices(); i++) {
s = s + String.valueOf(i) + " : ";
for (int j = 0; j < this.numberOfVertices(); j++) {
s = s + String.valueOf(this._adjacency[i][j]) + " ";
}
s = s + "\n";
}
return s;
}
}

96
DataStructures/Graphs/PrimMST.java
View File

@ -1,97 +1,91 @@
// A Java program for Prim's Minimum Spanning Tree (MST) algorithm.
//adjacency matrix representation of the graph
package DataStructures.Graphs;
import java.lang.*;
class PrimMST
{
/**
* A Java program for Prim's Minimum Spanning Tree (MST) algorithm.
* adjacency matrix representation of the graph
*/
class PrimMST {
// Number of vertices in the graph
private static final int V=5;
private static final int V = 5;
// A utility function to find the vertex with minimum key
// value, from the set of vertices not yet included in MST
int minKey(int key[], Boolean mstSet[])
{
int minKey(int key[], Boolean mstSet[]) {
// Initialize min value
int min = Integer.MAX_VALUE, min_index=-1;
int min = Integer.MAX_VALUE, min_index = -1;
for (int v = 0; v < V; v++)
if (mstSet[v] == false && key[v] < min)
{
if (mstSet[v] == false && key[v] < min) {
min = key[v];
min_index = v;
}
return min_index;
}
// A utility function to print the constructed MST stored in
// parent[]
void printMST(int parent[], int n, int graph[][])
{
void printMST(int parent[], int n, int graph[][]) {
System.out.println("Edge Weight");
for (int i = 1; i < V; i++)
System.out.println(parent[i]+" - "+ i+" "+
graph[i][parent[i]]);
System.out.println(parent[i] + " - " + i + " " +
graph[i][parent[i]]);
}
// Function to construct and print MST for a graph represented
// using adjacency matrix representation
void primMST(int graph[][])
{
void primMST(int graph[][]) {
// Array to store constructed MST
int parent[] = new int[V];
// Key values used to pick minimum weight edge in cut
int key[] = new int [V];
int key[] = new int[V];
// To represent set of vertices not yet included in MST
Boolean mstSet[] = new Boolean[V];
// Initialize all keys as INFINITE
for (int i = 0; i < V; i++)
{
for (int i = 0; i < V; i++) {
key[i] = Integer.MAX_VALUE;
mstSet[i] = false;
}
// Always include first 1st vertex in MST.
key[0] = 0; // Make key 0 so that this vertex is
// picked as first vertex
// picked as first vertex
parent[0] = -1; // First node is always root of MST
// The MST will have V vertices
for (int count = 0; count < V-1; count++)
{
for (int count = 0; count < V - 1; count++) {
// Pick thd minimum key vertex from the set of vertices
// not yet included in MST
int u = minKey(key, mstSet);
// Add the picked vertex to the MST Set
mstSet[u] = true;
// Update key value and parent index of the adjacent
// vertices of the picked vertex. Consider only those
// vertices which are not yet included in MST
for (int v = 0; v < V; v++)
// graph[u][v] is non zero only for adjacent vertices of m
// mstSet[v] is false for vertices not yet included in MST
// Update the key only if graph[u][v] is smaller than key[v]
if (graph[u][v]!=0 && mstSet[v] == false &&
graph[u][v] < key[v])
{
parent[v] = u;
if (graph[u][v] != 0 && mstSet[v] == false &&
graph[u][v] < key[v]) {
parent[v] = u;
key[v] = graph[u][v];
}
}
// print the constructed MST
printMST(parent, V, graph);
}
public static void main (String[] args)
{
public static void main(String[] args) {
/* Let us create the following graph
2 3
(0)--(1)--(2)
@ -101,13 +95,13 @@ class PrimMST
(3)-------(4)
9 */
PrimMST t = new PrimMST();
int graph[][] = new int[][] {{0, 2, 0, 6, 0},
{2, 0, 3, 8, 5},
{0, 3, 0, 0, 7},
{6, 8, 0, 0, 9},
{0, 5, 7, 9, 0},
};
int graph[][] = new int[][]{{0, 2, 0, 6, 0},
{2, 0, 3, 8, 5},
{0, 3, 0, 0, 7},
{6, 8, 0, 0, 9},
{0, 5, 7, 9, 0},
};
// Print the solution
t.primMST(graph);
}