The Setstack Computer

Background from Wikipedia: “Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initially controversial, set theory has come to play the role of a foundational theory in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties. Formal versions of set theory also have a foundational role to play as specifying a theoretical ideal of mathematical rigor in proofs.”

Given this importance of sets, being the basis of mathematics, a set of eccentric theorist set off to construct a supercomputer operating on sets instead of numbers. The initial SetStack Alpha is under construction, and they need you to simulate it in order to verify the operation of the prototype. 


The computer operates on a single stack of sets, which is initially empty. After each operation, the
cardinality of the topmost set on the stack is output. The cardinality of a set S is denoted |S| and is the number of elements in S. The instruction set of the SetStack Alpha is PUSH, DUP, UNION, INTERSECT, and ADD.

• PUSH will push the empty set {} on the stack.
• DUP will duplicate the topmost set (pop the stack, and then push that set on the stack twice).
• UNION will pop the stack twice and then push the union of the two sets on the stack.
• INTERSECT will pop the stack twice and then push the intersection of the two sets on the stack.
• ADD will pop the stack twice, add the first set to the second one, and then push the resulting set on the stack.

For illustration purposes, assume that the topmost element of the stack is

A = {{}, {{}}}

and that the next one is

B = {{}, {{{}}}}

For these sets, we have |A| = 2 and |B| = 2. Then:
• UNION would result in the set {{}, {{}}, {{{}}}}. The output is 3.
• INTERSECT would result in the set {{}}. The output is 1.
• ADD would result in the set {{}, {{{}}}, {{},{{}}}}. The output is 3.


Input
An integer 0 ≤ T ≤ 5 on the first line gives the cardinality of the set of test cases. The first line of each test case contains the number of operations 0 ≤ N ≤ 2000. Then follow N lines each containing one of the five commands. It is guaranteed that the SetStack computer can execute all the commands in the sequence without ever popping an empty stack. 

Output

For each operation specified in the input, there will be one line of output consisting of a single integer.
This integer is the cardinality of the topmost element of the stack after the corresponding command has executed. After each test case there will be a line with ‘***’ (three asterisks).

Sample Input
2
9
PUSH
DUP
ADD
PUSH
ADD
DUP
ADD
DUP
UNION
5
PUSH
PUSH
ADD
PUSH
INTERSECT


Sample Output
0
0
1
0
1
1
2
2
2
***
0
0
1
0
0

***

这道题中应用了不少东西：

1.栈，包含头文件<stack> 有关的操作有：取栈顶元素s.top()；入栈s.push(i)；出栈s.pop()。

2.关于集合的两个函数：并集，交集，包含头文件<algorithm>，分别是set_union(s1.begin(),s1.end(),s2.begin(),s2.end(),x)和set_intersection(……)，其中x是保存新集合的位置，有两种情况:s.begin()和 inserter(s,s.begin()) （网上的资料，如果s是vector，采取第一种写法，如果s是set，这样写会产生编译错误，提示不能更改只读类型的值，采取第二种写法）

3.inserter：原理：其内部调用insert() ；功能：在容器的指定位置插入元素；限制：只有提供了inset()成员函数的容器中，inserter才能派上用场. 所有STL容器都提供了inset()函数.；适用：所有STL容器。注意：使用inserter的时候，插入的起始位置是在指定位置的前方。用法：inserter（x，it）其中，x：Container on which the iterator will insert new elements.
Container should be a container class with member insert defined.；it：Iterator pointing to the insertion point.This shall be a mutable iterator (not a const iterator)。
代码如下：

#include<algorithm>
#include<iostream>
#include<vector>
#include<string>
#include<stack>
#include<set>
#include<map>
#define INS(x) inserter(x,x.begin())
#define ALL(x) x.begin(),x.end()
using namespace std;

typedef set<int> Set;
map<Set,int> m_set;
vector<Set> v_set;

int ID(Set s)
{
	if(m_set.count(s)) return m_set[s];
	v_set.push_back(s);
	m_set[s]=v_set.size()-1;
	return m_set[s];
}
int main()
{
	int T;
	cin>>T;
	while(T--)
	{
		int N;
		cin>>N;
		m_set.clear();
		v_set.clear();
		stack<int> s;
		for(int i=0;i<N;i++)
		{
			string op;
			cin>>op;
			Set emp;
			if(op=="PUSH") s.push(ID(emp));
			else if(op=="DUP") s.push(s.top());
			else
			{
				Set x1=v_set[s.top()];s.pop();
				Set x2=v_set[s.top()];s.pop();
				Set x;
				if(op=="UNION")
					set_union(ALL(x1),ALL(x2),INS(x));
				if(op=="INTERSECT")
					set_intersection(ALL(x1),ALL(x2),INS(x));
				if(op=="ADD")
				{
					x=x2;
					x.insert(ID(x1));
				}
				s.push(ID(x));
			}
			cout<<v_set[s.top()].size()<<endl;
		}
		cout<<"***"<<endl;
	}
	return 0;
}