public static void main(String[] args) {
In in = new In("jobsPC1.txt");
int N = in.readInt();
in.readLine();
EdgeWeightedDigraph G;
G = new EdgeWeightedDigraph(2 * N + 2);
int s = 2 * N, t = 2 * N + 1;
for (int i = 0; i < N; ++i) {
String[] a = in.readLine().split("\\s+");
double duration = Double.parseDouble(a[0]);
G.addEdge(new DirectedEdge(i, i + N, duration));
G.addEdge(new DirectedEdge(s, i, 0.0));
G.addEdge(new DirectedEdge(i + N, t, 0.0));
for (int j = 1; j < a.length; ++j) {
G.addEdge(new DirectedEdge(i + N, Integer.parseInt(a[j]), 0));
}
}
StdOut.println(G);
MyAcyclicLP lp = new MyAcyclicLP(G, s);
StdOut.println("Start times: ");
for (int i = 0; i < N; ++i) StdOut.printf("%4d: %5.1f\n", i, lp.distTo(i));
StdOut.printf("%5.1f\n", lp.distTo(t));
for (DirectedEdge e : lp.pathTo(t)) {
StdOut.print(e + " ");
}
StdOut.println();
}
public DepthFirstOrder(EdgeWeightedDigraph G) {
pre = new int[G.V()];
post = new int[G.V()];
postorder = new Queue<Integer>();
preorder = new Queue<Integer>();
marked = new boolean[G.V()];
for (int v = 0; v < G.V(); v++) if (!marked[v]) dfs(G, v);
}
public EdgeWeightedDirectedCycle(EdgeWeightedDigraph G) {
marked = new boolean[G.V()];
onStack = new boolean[G.V()];
edgeTo = new DirectedEdge[G.V()];
for (int v = 0; v < G.V(); v++) if (!marked[v]) dfs(G, v);
// check that digraph has a cycle
assert check(G);
}
/**
* Método recursivo usado para la obtención de todos los caminos posibles dentro de un árbol. Si
* un nodo tiene un outdegree igual a 0, es una hoja, y el camino ha terminado. De lo contrario,
* debe continuar buscando caminos entre los nodos adyacentes al primer nodo mencionado.
*
* @param G Grafo dirigido y con pesos sobre el cual se están buscando caminos.
* @param node Nodo que se está visitando actualmente.
* @param weight Peso actual del camino.
* @param path Representaoión como String del camino que se ha seguido hasta el nodo actual.
*/
private void getPaths(EdgeWeightedDigraph G, Integer node, double weight, String path) {
if (G.outdegree(node) == 0) this.paths.put(weight, path);
else
for (DirectedEdge edge : G.adj(node))
this.getPaths(
G,
edge.to(),
weight + edge.weight(),
path + "| " + edge.from() + " -> " + edge.to() + " | ");
}
private boolean findNegativeCycle(){
int V = edgeTo.length;
EdgeWeightedDigraph spt;
spt = new EdgeWeightedDigraph(V);
for (int v = 0 ; v < V ; v++ ) {
if(edgeTo[v] !=null)
spt.addEdge(edgeTo[v]);
}
EdgeWeightedCycleFinder cf ;
cf = new EdgeWeightedCycleFinder(spt);
cycle = cf.cycle();
}
public DijkstraSP(EdgeWeightedDigraph G , int s){
edgeTo =new DirectedEdge[G.V()];
distTo =new double[G.V()];
pq = new IndexMinPQ<Double>(G.V());
for(int v = 0 ; v < G.V() ; v++) distTo[v] = Double.POSITIVE_INFINITY;
distTo[s]=0;
pq.insert(s,0.0);
while(!pq.isEmpty()){
relax(G,pq.delMin());
}
}
public AcyclicLP(EdgeWeightedDigraph G, int s) {
distTo = new double[G.V()];
edgeTo = new DirectedEdge[G.V()];
for (int v = 0; v < G.V(); v++) distTo[v] = Double.NEGATIVE_INFINITY;
distTo[s] = 0.0;
// relax vertices in toplogical order
Topological topological = new Topological(G);
for (int v : topological.order()) {
for (DirectedEdge e : G.adj(v)) relax(e);
}
}
public SingleSourceShortestPaths(EdgeWeightedDigraph G, int source) {
this.source = source;
this.distTo = new double[G.V()];
this.edgeTo = new DirectedEdge[G.V()];
for (int v = 0; v < G.V(); ++v) {
this.distTo[v] = Double.POSITIVE_INFINITY;
}
this.distTo[this.source] = 0.0;
}
public AcyclicSP(EdgeWeightedDigraph G ,int s){
edgeTo = new DirectedEdge[G.V()];
distTo = new double[G.V()];
for(int v = 0 ; v < G.V() ; v++){
distTo[v] = Double.POSITIVE_INFINITY;
}
distTo[s] = 0.0;
Topological top = new Topological(G);
for(int v:top.order()){
relax(G,v);
}
}
private void findNegativeCycle(){
int V = edgeTo.length;
EdgeWeightedDigraph spt ;
spt = new EdgeWeightedDigraph;
for (int v = 0 ; v < V ; v++ ) {
if(edgeTo[v] !=null ){
spt.addEdge(edgeTo[v]);
}
}
EdgeWeightedCycleFinder cf;
cf = new EdgeWeightedCycleFinder(spt);
cycle = cf.cycle();//cycle()方法来自4.2界
}
private void relax(EdgeWeightedDigraph G ,int v){
for(DirectedEdge e:G.adj(v)){
int w = e.to();
if(distTo[w]>distTo[v]+e.weight()){
distTo[w] = distTo[v]+e.weight();
edgeTo[w] = e;
if(!onQ[w]){
q.enqueue(w);
onQ[w] = true;
}
}
if(cost++ %G.V() == 0 ) findNegativeCycle();
}
}
/**
* Initializes a new edge-weighted digraph that is a deep copy of <tt>G</tt>.
*
* @param G the edge-weighted digraph to copy
*/
public EdgeWeightedDigraph(EdgeWeightedDigraph G) {
this(G.V());
this.E = G.E();
for (int v = 0; v < G.V(); v++) {
// reverse so that adjacency list is in same order as original
Stack<DirectedEdge> reverse = new Stack<DirectedEdge>();
for (DirectedEdge e : G.adj[v]) {
reverse.push(e);
}
for (DirectedEdge e : reverse) {
adj[v].add(e);
}
}
}
/** @param args */
public static void main(String[] args) {
// TODO Auto-generated method stub
In in = new In("E:\\jwork\\algs4-data\\tinyEWDAG.txt");
EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
int s = 5;
AcyclicLP sp = new AcyclicLP(G, s);
for (int i = 0; i < G.V(); i++) {
System.out.printf(s + "-" + i + ":%.2f\n", sp.distTo(i));
for (DirectedEdge edge : sp.pathTo(i)) {
System.out.print(edge + " ");
}
System.out.println();
}
}
// check that algorithm computes either the topological order or finds a directed cycle
private void dfs(EdgeWeightedDigraph G, int v) {
onStack[v] = true;
marked[v] = true;
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
// short circuit if directed cycle found
if (cycle != null) return;
// found new vertex, so recur
else if (!marked[w]) {
edgeTo[w] = e;
dfs(G, w);
}
// trace back directed cycle
else if (onStack[w]) {
cycle = new Stack<DirectedEdge>();
while (e.from() != w) {
cycle.push(e);
e = edgeTo[e.from()];
}
cycle.push(e);
}
}
onStack[v] = false;
}
public BellmanFordSP(EdgeWeightedDigraph G ,int s){
distTo = new double[G.V()];
edgeTo = new DirectedEdge[G.V()];
onQ = new boolean[G.V()];
queue = new Queue<Integer>();
for(int v = 0 ; v < G.V() ; v++) distTo[v] = Double.POSITIVE_INFINITY;
distTo[s] = 0.0;
onQ[s]=true;
while(!queue.isEmpty() && !hasNegativeCycle()){
int v = queue.dequeue();
onQ[v] = false;
relax(G,v);
}
}
public static void main(String[] args) {
// create random DAG with V vertices and E edges; then add F random edges
int V = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
int F = Integer.parseInt(args[2]);
EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
int[] vertices = new int[V];
for (int i = 0; i < V; i++) vertices[i] = i;
StdRandom.shuffle(vertices);
for (int i = 0; i < E; i++) {
int v, w;
do {
v = StdRandom.uniform(V);
w = StdRandom.uniform(V);
} while (v >= w);
double weight = Math.random();
G.addEdge(new DirectedEdge(v, w, weight));
}
// add F extra edges
for (int i = 0; i < F; i++) {
int v = (int) (Math.random() * V);
int w = (int) (Math.random() * V);
double weight = Math.random();
G.addEdge(new DirectedEdge(v, w, weight));
}
StdOut.println(G);
// find a directed cycle
EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(G);
if (finder.hasCycle()) {
StdOut.print("Cycle: ");
for (DirectedEdge e : finder.cycle()) {
StdOut.print(e + " ");
}
StdOut.println();
}
// or give topologial sort
else {
StdOut.println("No directed cycle");
}
}
public void relax(EdgeWeightedDigraph G , int v){//vertex relaxation
for(DirectedEdge e: G.adj(v)){//没有遍历树,只是遍历了从v指向的所有边(edges)
int w = e.to();
if(distTo[w]>distTo[v]+e.weight){
distTo[w]=distTo[v]+e.weight;
edgeTo[w]=e;
}
}
}
private void relax(EdgeWeightedDigraph G, int v) {
for (DirectedEdge edge : G.adj(v)) {
int w = edge.to();
if (distTo[w] < distTo[v] + edge.weight()) {
distTo[w] = distTo[v] + edge.weight();
edgeTo[w] = edge;
}
}
}
public static void main(String[] args) {
In in = new In(args[0]);
int s = Integer.parseInt(args[1]);
EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
AcyclicLP lp = new AcyclicLP(G, s);
for (int v = 0; v < G.V(); v++) {
if (lp.hasPathTo(v)) {
StdOut.printf("%d to %d (%.2f) ", s, v, lp.distTo(v));
for (DirectedEdge e : lp.pathTo(v)) {
StdOut.print(e + " ");
}
StdOut.println();
} else {
StdOut.printf("%d to %d no path\n", s, v);
}
}
}
private void relax(EdgeWeightedDigraph G ,int v){
for(DirectedEdge e:G.adj(V)){
int w = e.to();
if(distTo[w]>distTo[v]+e.weight()){
distTo[w] = distTo[v]+e.weight();
edgeTo[w] = e;
if(pq.contains(w)) pq.change(w,distTo[w]);
else pq.insert(w,distTo[w]);
}
}
}
// run DFS in edge-weighted digraph G from vertex v and compute preorder/postorder
private void dfs(EdgeWeightedDigraph G, int v) {
marked[v] = true;
pre[v] = preCounter++;
preorder.enqueue(v);
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
if (!marked[w]) {
dfs(G, w);
}
}
postorder.enqueue(v);
post[v] = postCounter++;
}
public static void main(String[] args){
int N = StdIn.readInt();StdIn.readLine();
EdgeWeightedDigraph G ;
G = new EdgeWeightedDigraph(2*N+2);
int s = 2*N ,t = 2*N+1;
for(int i = 0 ; i < N ; i++){
String[] a = StdIn.readLine().split("\\s+");
double duration = Double.parseDouble(a[0]);
G.addEdge(new DirectedEdge(i,i+N,duration));
G.addEdge(new DirectedEdge(s,i,0.0));
G.addEdge(new DirectedEdge(i+N,t,0.0));
for(int j = 1 ; j < a.length ; j++){
int sucessor = Integer.parseInt(a[j]);
G.addEdge(new DirectedEdge(i+N,sucessor,0.0));
}
}
AcyclicSP lp = new AcyclicSP(G,s);
StdOut.println("START TIME:");
for(int i = 0 ; i < N ; i++){
StdOut.printf("%4d:%5.1f\n",i,lp.distTo(i));
StdOut.printf("finish time :%5.1f\n",lp.distTo(t));
}
}
public AcyclicLP(EdgeWeightedDigraph G, int s) {
this.s = s;
distTo = new double[G.V()];
for (int i = 0; i < distTo.length; i++) {
distTo[i] = INFINITY;
}
edgeTo = new DirectedEdge[G.V()];
EdgeWeightedTopologicalOrder order = new EdgeWeightedTopologicalOrder(G);
int count = 0;
int kb = Integer.MAX_VALUE;
edgeTo[s] = null;
distTo[s] = 0; /* initialize*/
for (int i : order.reversePost()) {
if (i == s) {
kb = count;
}
if (count < kb) {
count++;
continue;
}
relax(G, i);
}
}
/**
* Reads the precedence constraints from standard input and prints a feasible schedule to standard
* output.
*/
public static void main(String[] args) {
// number of jobs
int N = StdIn.readInt();
// source and sink
int source = 2 * N;
int sink = 2 * N + 1;
// build network
EdgeWeightedDigraph G = new EdgeWeightedDigraph(2 * N + 2);
for (int i = 0; i < N; i++) {
double duration = StdIn.readDouble();
G.addEdge(new DirectedEdge(source, i, 0.0));
G.addEdge(new DirectedEdge(i + N, sink, 0.0));
G.addEdge(new DirectedEdge(i, i + N, duration));
// precedence constraints
int M = StdIn.readInt();
for (int j = 0; j < M; j++) {
int precedent = StdIn.readInt();
G.addEdge(new DirectedEdge(N + i, precedent, 0.0));
}
}
// compute longest path
AcyclicLP lp = new AcyclicLP(G, source);
// print results
StdOut.println(" job start finish");
StdOut.println("--------------------");
for (int i = 0; i < N; i++) {
StdOut.printf("%4d %7.1f %7.1f\n", i, lp.distTo(i), lp.distTo(i + N));
}
StdOut.printf("Finish time: %7.1f\n", lp.distTo(sink));
}
DisjkstraAllPairsSP(EdgeWeightedDigraph G){
all = new DijkstraSP[G.V()];
for(int v = 0 ; v < G.V() ; v++){
all[v] = new DijkstraSP(G,v);
}
}