我在哪里可以找到Java实现的关键路径算法？我相信云端上有一些实现。我已经在谷歌上搜索过，但没有找到任何有效的实现。这就是为什么我要问的原因。
提前致谢。
4个回答
6
这是一个基于此页面提供的解释实现的算法。有一个包装类来保存任务、成本和关键路径成本。它首先计算关键成本，作为所有依赖项的最大关键成本加上自身成本。然后一旦关键成本可用，就使用比较器按照关键成本排序任务，并以依赖关系为决定因素（如果没有依赖关系，则随机选择）。请注意，如果存在循环，则会抛出异常，并且如果任何成本为负，则会失败。
以下是实现代码：
以下是实现代码：
public class CriticalPath {
public static void main(String[] args) {
//The example dependency graph from
//http://www.ctl.ua.edu/math103/scheduling/scheduling_algorithms.htm
HashSet<Task> allTasks = new HashSet<Task>();
Task end = new Task("End", 0);
Task F = new Task("F", 2, end);
Task A = new Task("A", 3, end);
Task X = new Task("X", 4, F, A);
Task Q = new Task("Q", 2, A, X);
Task start = new Task("Start", 0, Q);
allTasks.add(end);
allTasks.add(F);
allTasks.add(A);
allTasks.add(X);
allTasks.add(Q);
allTasks.add(start);
System.out.println("Critical Path: "+Arrays.toString(criticalPath(allTasks)));
}
//A wrapper class to hold the tasks during the calculation
public static class Task{
//the actual cost of the task
public int cost;
//the cost of the task along the critical path
public int criticalCost;
//a name for the task for printing
public String name;
//the tasks on which this task is dependant
public HashSet<Task> dependencies = new HashSet<Task>();
public Task(String name, int cost, Task... dependencies) {
this.name = name;
this.cost = cost;
for(Task t : dependencies){
this.dependencies.add(t);
}
}
@Override
public String toString() {
return name+": "+criticalCost;
}
public boolean isDependent(Task t){
//is t a direct dependency?
if(dependencies.contains(t)){
return true;
}
//is t an indirect dependency
for(Task dep : dependencies){
if(dep.isDependent(t)){
return true;
}
}
return false;
}
}
public static Task[] criticalPath(Set<Task> tasks){
//tasks whose critical cost has been calculated
HashSet<Task> completed = new HashSet<Task>();
//tasks whose ciritcal cost needs to be calculated
HashSet<Task> remaining = new HashSet<Task>(tasks);
//Backflow algorithm
//while there are tasks whose critical cost isn't calculated.
while(!remaining.isEmpty()){
boolean progress = false;
//find a new task to calculate
for(Iterator<Task> it = remaining.iterator();it.hasNext();){
Task task = it.next();
if(completed.containsAll(task.dependencies)){
//all dependencies calculated, critical cost is max dependency
//critical cost, plus our cost
int critical = 0;
for(Task t : task.dependencies){
if(t.criticalCost > critical){
critical = t.criticalCost;
}
}
task.criticalCost = critical+task.cost;
//set task as calculated an remove
completed.add(task);
it.remove();
//note we are making progress
progress = true;
}
}
//If we haven't made any progress then a cycle must exist in
//the graph and we wont be able to calculate the critical path
if(!progress) throw new RuntimeException("Cyclic dependency, algorithm stopped!");
}
//get the tasks
Task[] ret = completed.toArray(new Task[0]);
//create a priority list
Arrays.sort(ret, new Comparator<Task>() {
@Override
public int compare(Task o1, Task o2) {
//sort by cost
int i= o2.criticalCost-o1.criticalCost;
if(i != 0)return i;
//using dependency as a tie breaker
//note if a is dependent on b then
//critical cost a must be >= critical cost of b
if(o1.isDependent(o2))return -1;
if(o2.isDependent(o1))return 1;
return 0;
}
});
return ret;
}
}
- M. Jessup
3
这是Jessup代码的另一个版本。我添加了一些其他功能，现在该代码可以计算最早/最晚开始和完成时间、松弛时间以及节点是否在关键路径上。(我只是添加了这些函数并获得了结果，没有花费太多精力在算法和编码上)
public class CriticalPath {
public static int maxCost;
public static String format = "%1$-10s %2$-5s %3$-5s %4$-5s %5$-5s %6$-5s %7$-10s\n";
public static void main(String[] args) {
// The example dependency graph
HashSet<Task> allTasks = new HashSet<Task>();
Task end = new Task("End", 0);
Task F = new Task("F", 2, end);
Task A = new Task("A", 3, end);
Task X = new Task("X", 4, F, A);
Task Q = new Task("Q", 2, A, X);
Task start = new Task("Start", 0, Q);
allTasks.add(end);
allTasks.add(F);
allTasks.add(A);
allTasks.add(X);
allTasks.add(Q);
allTasks.add(start);
Task[] result = criticalPath(allTasks);
print(result);
// System.out.println("Critical Path: " + Arrays.toString(result));
}
// A wrapper class to hold the tasks during the calculation
public static class Task {
// the actual cost of the task
public int cost;
// the cost of the task along the critical path
public int criticalCost;
// a name for the task for printing
public String name;
// the earliest start
public int earlyStart;
// the earliest finish
public int earlyFinish;
// the latest start
public int latestStart;
// the latest finish
public int latestFinish;
// the tasks on which this task is dependant
public HashSet<Task> dependencies = new HashSet<Task>();
public Task(String name, int cost, Task... dependencies) {
this.name = name;
this.cost = cost;
for (Task t : dependencies) {
this.dependencies.add(t);
}
this.earlyFinish = -1;
}
public void setLatest() {
latestStart = maxCost - criticalCost;
latestFinish = latestStart + cost;
}
public String[] toStringArray() {
String criticalCond = earlyStart == latestStart ? "Yes" : "No";
String[] toString = { name, earlyStart + "", earlyFinish + "", latestStart + "", latestFinish + "",
latestStart - earlyStart + "", criticalCond };
return toString;
}
public boolean isDependent(Task t) {
// is t a direct dependency?
if (dependencies.contains(t)) {
return true;
}
// is t an indirect dependency
for (Task dep : dependencies) {
if (dep.isDependent(t)) {
return true;
}
}
return false;
}
}
public static Task[] criticalPath(Set<Task> tasks) {
// tasks whose critical cost has been calculated
HashSet<Task> completed = new HashSet<Task>();
// tasks whose critical cost needs to be calculated
HashSet<Task> remaining = new HashSet<Task>(tasks);
// Backflow algorithm
// while there are tasks whose critical cost isn't calculated.
while (!remaining.isEmpty()) {
boolean progress = false;
// find a new task to calculate
for (Iterator<Task> it = remaining.iterator(); it.hasNext();) {
Task task = it.next();
if (completed.containsAll(task.dependencies)) {
// all dependencies calculated, critical cost is max
// dependency
// critical cost, plus our cost
int critical = 0;
for (Task t : task.dependencies) {
if (t.criticalCost > critical) {
critical = t.criticalCost;
}
}
task.criticalCost = critical + task.cost;
// set task as calculated an remove
completed.add(task);
it.remove();
// note we are making progress
progress = true;
}
}
// If we haven't made any progress then a cycle must exist in
// the graph and we wont be able to calculate the critical path
if (!progress)
throw new RuntimeException("Cyclic dependency, algorithm stopped!");
}
// get the cost
maxCost(tasks);
HashSet<Task> initialNodes = initials(tasks);
calculateEarly(initialNodes);
// get the tasks
Task[] ret = completed.toArray(new Task[0]);
// create a priority list
Arrays.sort(ret, new Comparator<Task>() {
@Override
public int compare(Task o1, Task o2) {
return o1.name.compareTo(o2.name);
}
});
return ret;
}
public static void calculateEarly(HashSet<Task> initials) {
for (Task initial : initials) {
initial.earlyStart = 0;
initial.earlyFinish = initial.cost;
setEarly(initial);
}
}
public static void setEarly(Task initial) {
int completionTime = initial.earlyFinish;
for (Task t : initial.dependencies) {
if (completionTime >= t.earlyStart) {
t.earlyStart = completionTime;
t.earlyFinish = completionTime + t.cost;
}
setEarly(t);
}
}
public static HashSet<Task> initials(Set<Task> tasks) {
HashSet<Task> remaining = new HashSet<Task>(tasks);
for (Task t : tasks) {
for (Task td : t.dependencies) {
remaining.remove(td);
}
}
System.out.print("Initial nodes: ");
for (Task t : remaining)
System.out.print(t.name + " ");
System.out.print("\n\n");
return remaining;
}
public static void maxCost(Set<Task> tasks) {
int max = -1;
for (Task t : tasks) {
if (t.criticalCost > max)
max = t.criticalCost;
}
maxCost = max;
System.out.println("Critical path length (cost): " + maxCost);
for (Task t : tasks) {
t.setLatest();
}
}
public static void print(Task[] tasks) {
System.out.format(format, "Task", "ES", "EF", "LS", "LF", "Slack", "Critical?");
for (Task t : tasks)
System.out.format(format, (Object[]) t.toStringArray());
}
}
- mert
1
isDependent(Task t) 函数是做什么的？ - Simon K0
- ThCollignon
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