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。
- PUSH:空集“{}”入栈。
- DUP:把当前栈顶元素复制一份后再入栈。
- UNION:出栈两个集合,然后把二者的并集入栈。
- INTERSECT:出栈两个集合,然后把二者的交集入栈。
- 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
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 #include <bits/stdc++.h> 2 using namespace std; 3 4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); 5 #define Rep(i,n) for (int i = 0; i < (n); ++i) 6 #define For(i,s,t) for (int i = (s); i <= (t); ++i) 7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i) 8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i) 9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i) 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i) 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i) 12 13 #define pr(x) cout << #x << " = " << x << " " 14 #define prln(x) cout << #x << " = " << x << endl 15 16 #define LOWBIT(x) ((x)&(-x)) 17 18 #define ALL(x) x.begin(),x.end() 19 #define INS(x) inserter(x,x.begin()) 20 21 #define ms0(a) memset(a,0,sizeof(a)) 22 #define msI(a) memset(a,inf,sizeof(a)) 23 #define msM(a) memset(a,-1,sizeof(a)) 24 25 #define MP make_pair 26 #define PB push_back 27 #define ft first 28 #define sd second 29 30 template<typename T1, typename T2> 31 istream &operator>>(istream &in, pair<T1, T2> &p) { 32 in >> p.first >> p.second; 33 return in; 34 } 35 36 template<typename T> 37 istream &operator>>(istream &in, vector<T> &v) { 38 for (auto &x: v) 39 in >> x; 40 return in; 41 } 42 43 template<typename T1, typename T2> 44 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) { 45 out << "[" << p.first << ", " << p.second << "]" << " "; 46 return out; 47 } 48 49 inline int gc(){ 50 static const int BUF = 1e7; 51 static char buf[BUF], *bg = buf + BUF, *ed = bg; 52 53 if(bg == ed) fread(bg = buf, 1, BUF, stdin); 54 return *bg++; 55 } 56 57 inline int ri(){ 58 int x = 0, f = 1, c = gc(); 59 for(; c<48||c>57; f = c=='-'?-1:f, c=gc()); 60 for(; c>47&&c<58; x = x*10 + c - 48, c=gc()); 61 return x*f; 62 } 63 64 template<class T> 65 inline string toString(T x) { 66 ostringstream sout; 67 sout << x; 68 return sout.str(); 69 } 70 71 typedef long long LL; 72 typedef unsigned long long uLL; 73 typedef pair< double, double > PDD; 74 typedef pair< int, int > PII; 75 typedef pair< int, PII > PIPII; 76 typedef pair< string, int > PSI; 77 typedef pair< int, PSI > PIPSI; 78 typedef set< int > SI; 79 typedef set< PII > SPII; 80 typedef vector< int > VI; 81 typedef vector< VI > VVI; 82 typedef vector< SI > VSI; 83 typedef vector< PII > VPII; 84 typedef map< int, int > MII; 85 typedef map< int, string > MIS; 86 typedef map< int, PII > MIPII; 87 typedef map< PII, int > MPIII; 88 typedef map< string, int > MSI; 89 typedef map< string, string > MSS; 90 typedef map< PII, string > MPIIS; 91 typedef map< PII, PII > MPIIPII; 92 typedef multimap< int, int > MMII; 93 typedef multimap< string, int > MMSI; 94 //typedef unordered_map< int, int > uMII; 95 typedef pair< LL, LL > PLL; 96 typedef vector< LL > VL; 97 typedef vector< VL > VVL; 98 typedef priority_queue< int > PQIMax; 99 typedef priority_queue< int, VI, greater< int > > PQIMin; 100 const double EPS = 1e-10; 101 const LL inf = 0x7fffffff; 102 const LL infLL = 0x7fffffffffffffffLL; 103 const LL mod = 1e9 + 7; 104 const int maxN = 1e3 + 7; 105 const LL ONE = 1; 106 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 107 const LL oddBits = 0x5555555555555555; 108 109 int T, N; 110 string op; 111 MSI op_id = {MP("PUSH", 0), MP("DUP", 1), MP("UNION", 2), MP("INTERSECT", 3), MP("ADD", 4)}; 112 map< SI, int > set_id; 113 VSI elements; 114 stack< int > st; 115 116 void INSERT(SI &x) { 117 if(set_id.find(x) == set_id.end()) { 118 st.push(elements.size()); 119 set_id[x] = elements.size(); 120 elements.PB(x); 121 } 122 else st.push(set_id[x]); 123 } 124 125 void PUSH() { 126 st.push(0); 127 } 128 129 void DUP() { 130 st.push(st.top()); 131 } 132 133 void UNION() { 134 int x = st.top(); st.pop(); 135 int y = st.top(); st.pop(); 136 SI z; 137 138 set_union(ALL(elements[x]), ALL(elements[y]), INS(z)); 139 140 INSERT(z); 141 } 142 143 void INTERSECT() { 144 int x = st.top(); st.pop(); 145 int y = st.top(); st.pop(); 146 SI z; 147 148 set_intersection(ALL(elements[x]), ALL(elements[y]), INS(z)); 149 150 INSERT(z); 151 } 152 153 void ADD() { 154 int x = st.top(); st.pop(); 155 int y = st.top(); st.pop(); 156 SI z = elements[y]; 157 158 z.insert(x); 159 160 INSERT(z); 161 } 162 163 void (*func[5])() = {PUSH, DUP, UNION, INTERSECT, ADD}; 164 165 int main(){ 166 //freopen("MyOutput.txt","w",stdout); 167 //freopen("input.txt","r",stdin); 168 //INIT(); 169 cin >> T; 170 elements.PB(SI()); 171 set_id[SI()] = 0; 172 173 while(T--) { 174 cin >> N; 175 st = stack< int >(); 176 177 Rep(i, N) { 178 cin >> op; 179 func[op_id[op]](); 180 cout << elements[st.top()].size() << endl; 181 } 182 cout << "*** "; 183 } 184 return 0; 185 }