UVA 12096 The SetStack Computer

题目链接：https://vjudge.net/problem/UVA-12096

题目翻译摘自《算法禁赛入门经典》

题目大意

　　有一个专门为了集合运算而设计的“集合栈”计算机。该机器有一个初始为空的栈，并且支持以下操作。

1. PUSH：空集“{}”入栈。
2. DUP：把当前栈顶元素复制一份后再入栈。
3. UNION：出栈两个集合，然后把二者的并集入栈。
4. INTERSECT：出栈两个集合，然后把二者的交集入栈。
5. ADD：出栈两个集合，然后把先出栈的集合加入到后出栈的集合中，把结果入栈。

　　每次操作后，输出栈顶集合的大小（即元素个数）。

　　输入不超过2000个操作，并且保证操作均能顺利进行（不需要对空栈执行出栈操作）。

分析

　　这题用到一个技巧，把遇到的每个集合都存起来，然后给它一个 id，用的时候按照 id 来找集合，这样能大大减少空间占用，效率也能大大提升。

代码如下

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define rFor(i,t,s) for (int i = (t); i >= (s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,inf,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}

template<class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}
 
typedef long long LL;
typedef unsigned long long uLL;
typedef pair< double, double > PDD;
typedef pair< int, int > PII;
typedef pair< int, PII > PIPII;
typedef pair< string, int > PSI;
typedef pair< int, PSI > PIPSI;
typedef set< int > SI;
typedef set< PII > SPII;
typedef vector< int > VI;
typedef vector< VI > VVI;
typedef vector< SI > VSI;
typedef vector< PII > VPII;
typedef map< int, int > MII;
typedef map< int, string > MIS;
typedef map< int, PII > MIPII;
typedef map< PII, int > MPIII;
typedef map< string, int > MSI;
typedef map< string, string > MSS;
typedef map< PII, string > MPIIS;
typedef map< PII, PII > MPIIPII;
typedef multimap< int, int > MMII;
typedef multimap< string, int > MMSI;
//typedef unordered_map< int, int > uMII;
typedef pair< LL, LL > PLL;
typedef vector< LL > VL;
typedef vector< VL > VVL;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-10;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e3 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

int T, N;
string op; 
MSI op_id = {MP("PUSH", 0), MP("DUP", 1), MP("UNION", 2), MP("INTERSECT", 3), MP("ADD", 4)};
map< SI, int > set_id;
VSI elements;
stack< int > st;

void INSERT(SI &x) {
    if(set_id.find(x) == set_id.end()) {
        st.push(elements.size());
        set_id[x] = elements.size();
        elements.PB(x);
    }
    else st.push(set_id[x]);
}

void PUSH() {
    st.push(0);
}

void DUP() {
    st.push(st.top());
}

void UNION() {
    int x = st.top(); st.pop();
    int y = st.top(); st.pop();
    SI z;
    
    set_union(ALL(elements[x]), ALL(elements[y]), INS(z));
    
    INSERT(z);
}

void INTERSECT() {
    int x = st.top(); st.pop();
    int y = st.top(); st.pop();
    SI z;
    
    set_intersection(ALL(elements[x]), ALL(elements[y]), INS(z));
    
    INSERT(z);
}

void ADD() {
    int x = st.top(); st.pop();
    int y = st.top(); st.pop();
    SI z = elements[y];
    
    z.insert(x);
    
    INSERT(z);
}

void (*func[5])() = {PUSH, DUP, UNION, INTERSECT, ADD};

int main(){
    //freopen("MyOutput.txt","w",stdout);
    //freopen("input.txt","r",stdin);
    //INIT();
    cin >> T;
    elements.PB(SI());
    set_id[SI()] = 0;
    
    while(T--) {
        cin >> N;
        st = stack< int >();
        
        Rep(i, N) {
            cin >> op;
            func[op_id[op]]();
            cout << elements[st.top()].size() << endl;
        }
        cout << "***
";
    }
    return 0;
}