Adley — Mon, 26 Sep 2011 08:02:00 GMT

�W�卡��（Descartes�Q�积的定义：
设A,B为集合，用A中元素�ؓ�W�一元素�Q�B中元素�ؓ�W�二元素构成的有序对�Q�所有这��L��有序对组成的集合叫做A与B的笛卡尔�U�，��C��AxB.

�W�卡��积的符号化为：

AxB={|x∈A∧y∈B}

例如�Q�A={a,b},B={0,1,2},�?/span>

AxB={,,,,,,}

BxA={<0,a>,<0,b>,<1,a>,<1,b>,<2,a>,<2,b>}

�W�卡��积的运��性质

1.对�Q意集合A�Q�根据定义有

AxΦ =Φ �Q?#934; xA=Φ

2.一般地��_��W�卡��积�q�算不满��交换律�Q�即

AxB≠BxA(当A≠Φ ∧B≠Φ∧A≠B�?

Java�c?/span>

public final class Descartes {

private List> finalSet = new LinkedList>(); //�W�卡��积

private List> newStates = new LinkedList>(); //状态集合，被用来计��笛卡尔�U�的中间状�?/span>

private boolean abort = false; //遇空�l�止

public final Descartes compute(List inputSet) {

if (abort) {

return this;

}

//�I�集防�M

if (inputSet == null || inputSet.size() == 0) {

finalSet = new LinkedList>();//�I�集

abort = true;

return this;

}

if (finalSet.size() == 0) {//如果finalSet为空�Q�则把输入的集合当做finalSet

for (Long element : inputSet) {

List set = new LinkedList();

set.add(element);

finalSet.add(set);

}

} else {

for (List originalSet : finalSet) {

for (Long set : inputSet) {

List newState = new LinkedList();

newState.addAll(originalSet); //把初始中的每个集合拿出来和输入的集合的每个元素组合成一个新的集�?/span>

newState.add(set);

newStates.add(newState);

}

if (newStates.size() > 0) {

finalSet = newStates;

newStates = new LinkedList>();

}

return this;

}

public final List> getResult() {

return finalSet;

}

��试代码

public final class DescartesTest {

public static void main(String[] args) {

Descartes descartes = new Descartes();

List set1 = new LinkedList();

set1.add(1l);

set1.add(2l);

List set2 = new LinkedList();

set2.add(2l);

set2.add(3l);

List set3= new LinkedList();

set3.add(2l);

set3.add(3l);

descartes.compute(set1).compute(set2).compute(set3);

System.out.println(descartes.getResult());

}

}
输出�Q?br />[[1, 2, 2], [1, 2, 3], [1, 3, 2], [1, 3, 3], [2, 2, 2], [2, 2, 3], [2, 3, 2], [2, 3, 3]]

Adley 2011-09-26 16:02 发表评论

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