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# Dependency Algorithm - find a minimum set of packages to install

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Dependency Algorithm - find a minimum set of packages to install

Represent the constraints.

```X : A&(E|C)
A : E&(Y|N)
E : B&(Z|Y)
C : A|K
```

Prepare two list target and result.
Add the node X to target.

```target = X, result=[]
```

Add single node X to the result.
Replace node X with its dependent in the target.

```target = A&(E|C), result=[X]
```

Add single node A to result.
Replace node A with its dependent in the target.

```target = E&(Y|N)&(E|C), result=[X, A]
```

Single node E must be true.
So (E|C) is always true.
Remove it from the target.

```target = E&(Y|N), result=[X, A]
```

Add single node E to result.
Replace node E with its dependent in the target.

```target = B&(Z|Y)&(Y|N), result=[X, A, E]
```

Add single node B to result.
Replace node B with its dependent in the target.

```target = (Z|Y)&(Y|N), result=[X, A, E, B]
```

There are no single node any more.
Then expand the target expression.

expanded = Z&Y|Z&N|Y&Y|Y&N

Y&Y equals to Y.

```expanded = Z&Y|Z&N|Y|Y&N
```

Choose the term that has smallest number of nodes.
Add all nodes in the term to the target.

```target = , result=[X, A, E, B, Y]
```
```package stackoverflow.dependency;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;

public class Dependency {

public static class Node {
final String name;
final List<String> and = new ArrayList<>();
final List<String> or = new ArrayList<>();

Node(String name) {
this.name = name;
}

public Node and(String... and) {
for (String e : and)
return this;
}

public Node or(String... or) {
for (String e : or)
return this;
}

@Override
public String toString() {
return name + " and" + and + " or" + or;
}
}

final Map<String, Node> map = new HashMap<>();

public Node node(String name) {
Node node = map.get(name);
if (node == null)
map.put(name, node = new Node(name));
return node;
}

@Override
public String toString() {
StringBuilder sb = new StringBuilder();
for (Node e : map.values())
sb.append(e).append("\n");
return sb.toString();
}

public Node get(String name) {
return map.get(name);
}

static void expand(List<List<String>> targetOr, int index, List<String> set, List<Set<String>> expanded) {
int size = targetOr.size();
if (index >= size)
else
for (String s : targetOr.get(index)) {
expand(targetOr, index + 1, set, expanded);
set.remove(set.size() - 1);
}
}

public List<String> dependents(String start) {
List<String> targetAnd = new ArrayList<>();
List<List<String>> targetOr = new ArrayList<>();
List<String> result = new ArrayList<>();
while (!targetAnd.isEmpty()) {
System.out.println("target=AND" + targetAnd + " OR" + targetOr + ", result=" + result);
String single = targetAnd.remove(0);
Node singleNode = get(single);
for (Iterator<List<String>> i = targetOr.iterator(); i.hasNext(); )
if (i.next().contains(single))
i.remove();
System.out.println("target=AND" + targetAnd + " OR" + targetOr + ", result=" + result);
if (singleNode.or.size() > 0)
}
if (!targetOr.isEmpty()) {
List<Set<String>> expanded = new ArrayList<>();
expand(targetOr, 0, new ArrayList<>(), expanded);
System.out.println("expanded=OR" + expanded);
int min = Integer.MAX_VALUE;
Set<String> minSet = null;
for (Set<String> set : expanded)
if (set.size() < min) {
min = set.size();
minSet = set;
}
}
return result;
}

public static void main(String[] args) {
Dependency d = new Dependency();
d.node("X").and("A").or("E", "C");
d.node("E").and("B").or("Y", "Z");
d.node("A").and("E").or("H", "Y");
d.node("C").or("A", "K");
d.node("Z");
d.node("B");
d.node("H");
d.node("K");
System.out.println(d);
List<String> result = d.dependents("X");
System.out.println(result);
}
}

```
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