POJ 2553 The Bottom of a Graph

题目链接：https://vjudge.net/problem/POJ-2553
题目大意

　　给定有向图 G，对于 G 中一个点 v，如果 v 所能到达的点都能到达 v，那么称 v 为一个 sink 点，求 G 中所有的 sink 点。
分析

　　Tarjan 算法求出度为 0 的 SCC 的模板题。
代码如下

  1 #include <cmath>
  2 #include <ctime>
  3 #include <iostream>
  4 #include <string>
  5 #include <vector>
  6 #include <cstdio>
  7 #include <cstdlib>
  8 #include <cstring>
  9 #include <queue>
 10 #include <map>
 11 #include <set>
 12 #include <algorithm>
 13 #include <cctype>
 14 #include <stack>
 15 #include <deque>
 16 #include <list>
 17 #include <sstream>
 18 #include <cassert>
 19 using namespace std;
 20  
 21 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
 22 #define Rep(i,n) for (int i = 0; i < (n); ++i)
 23 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
 24 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
 25 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
 26 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 27 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 28 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 29  
 30 #define pr(x) cout << #x << " = " << x << "  "
 31 #define prln(x) cout << #x << " = " << x << endl
 32  
 33 #define LOWBIT(x) ((x)&(-x))
 34  
 35 #define ALL(x) x.begin(),x.end()
 36 #define INS(x) inserter(x,x.begin())
 37 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 38 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
 39 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 40 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 41  
 42 #define ms0(a) memset(a,0,sizeof(a))
 43 #define msI(a) memset(a,inf,sizeof(a))
 44 #define msM(a) memset(a,-1,sizeof(a))
 45 
 46 #define MP make_pair
 47 #define PB push_back
 48 #define ft first
 49 #define sd second
 50  
 51 template<typename T1, typename T2>
 52 istream &operator>>(istream &in, pair<T1, T2> &p) {
 53     in >> p.first >> p.second;
 54     return in;
 55 }
 56  
 57 template<typename T>
 58 istream &operator>>(istream &in, vector<T> &v) {
 59     for (auto &x: v)
 60         in >> x;
 61     return in;
 62 }
 63  
 64 template<typename T1, typename T2>
 65 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 66     out << "[" << p.first << ", " << p.second << "]" << "
";
 67     return out;
 68 }
 69 
 70 inline int gc(){
 71     static const int BUF = 1e7;
 72     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 73     
 74     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 75     return *bg++;
 76 } 
 77 
 78 inline int ri(){
 79     int x = 0, f = 1, c = gc();
 80     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
 81     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 82     return x*f;
 83 }
 84 
 85 template<class T>
 86 inline string toString(T x) {
 87     ostringstream sout;
 88     sout << x;
 89     return sout.str();
 90 }
 91 
 92 inline int toInt(string s) {
 93     int v;
 94     istringstream sin(s);
 95     sin >> v;
 96     return v;
 97 }
 98 
 99 //min <= aim <= max
100 template<typename T>
101 inline bool BETWEEN(const T aim, const T min, const T max) {
102     return min <= aim && aim <= max;
103 }
104  
105 typedef long long LL;
106 typedef unsigned long long uLL;
107 typedef pair< double, double > PDD;
108 typedef pair< int, int > PII;
109 typedef pair< int, PII > PIPII;
110 typedef pair< string, int > PSI;
111 typedef pair< int, PSI > PIPSI;
112 typedef set< int > SI;
113 typedef set< PII > SPII;
114 typedef vector< int > VI;
115 typedef vector< double > VD;
116 typedef vector< VI > VVI;
117 typedef vector< SI > VSI;
118 typedef vector< PII > VPII;
119 typedef map< int, int > MII;
120 typedef map< LL, int > MLLI;
121 typedef map< int, string > MIS;
122 typedef map< int, PII > MIPII;
123 typedef map< PII, int > MPIII;
124 typedef map< string, int > MSI;
125 typedef map< string, string > MSS;
126 typedef map< PII, string > MPIIS;
127 typedef map< PII, PII > MPIIPII;
128 typedef multimap< int, int > MMII;
129 typedef multimap< string, int > MMSI;
130 //typedef unordered_map< int, int > uMII;
131 typedef pair< LL, LL > PLL;
132 typedef vector< LL > VL;
133 typedef vector< VL > VVL;
134 typedef priority_queue< int > PQIMax;
135 typedef priority_queue< int, VI, greater< int > > PQIMin;
136 const double EPS = 1e-8;
137 const LL inf = 0x3fffffff;
138 const LL infLL = 0x3fffffffffffffffLL;
139 const LL mod = 20100713;
140 const int maxN = 5e3 + 7;
141 const LL ONE = 1;
142 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
143 const LL oddBits = 0x5555555555555555;
144 
145 struct Edge{
146     int from, to;
147     
148     Edge() {}
149     Edge(int x, int y) : from(x), to(y) {}
150 };
151 
152 istream& operator>> (istream& in, Edge &x) {
153     in >> x.from >> x.to;
154     return in;
155 }
156 
157 template<typename T>
158 ostream &operator<<(ostream &out, const vector<T> &v) {
159     Rep(i, v.size()) {
160         if(i) out << " ";
161         out << v[i];
162     }
163     out << endl;
164     return out;
165 }
166 
167 int N, M;
168 VI V[maxN], ans;
169 vector< Edge > E;
170 
171 void addEdge(Edge &x) {
172     V[x.from].PB(E.size());
173     E.PB(x);
174 }
175 
176 stack< int > sk; // 递归处理 SCC (强连通分量)
177 bool insk[maxN]; // 是否在栈中 
178 
179 int scc[maxN], sccid; // 存每个点对应SCC的编号 
180 int in[maxN], out[maxN]; // SCC的入度与出度 
181 
182 int Time;
183 int tp[maxN]; // timestamp，时间戳
184 int facr[maxN]; // The farthest ancestor that can be reached，每个节点最远的返回的祖先 
185 // S ：当前节点号
186 // 划分SCC并缩点 
187 void Tarjan(int S) {
188     tp[S] = facr[S] = ++Time;
189     sk.push(S);
190     insk[S] = 1;
191     
192     Rep(i, V[S].size()) {
193         Edge &e = E[V[S][i]];
194         
195         if(!tp[e.to]) {
196             Tarjan(e.to);
197             facr[S] = min(facr[S], facr[e.to]);
198         }
199         else if(insk[e.to]) facr[S] = min(facr[S], tp[e.to]); // 必须要保证在栈中，不然不能保证是一块SCC 
200     }
201     
202     if(facr[S] == tp[S]) {
203         ++sccid;
204         while(!sk.empty()) {
205             int tmp = sk.top(); sk.pop();
206             
207             insk[tmp] = 0;
208             scc[tmp] = sccid;
209             if(tmp == S) break;
210         } 
211     }
212 }
213 
214 void init() {
215     For(i, 1, N) V[i].clear();
216     E.clear();
217     ans.clear();
218     
219     while(!sk.empty()) sk.pop();
220     ms0(insk);
221     
222     ms0(scc); sccid = 0;
223     //ms0(in); 
224     ms0(out);
225     
226     Time = 0;
227     ms0(tp);
228     ms0(facr);
229 }
230 
231 int main(){
232     //freopen("MyOutput.txt","w",stdout);
233     //freopen("input.txt","r",stdin);
234     INIT();
235     while(cin >> N && N) {
236         init();
237         cin >> M;
238         For(i, 1, M) {
239             Edge t;
240             cin >> t;
241             addEdge(t);
242         }
243         
244         For(i, 1, N) if(!tp[i]) Tarjan(i);
245         
246         For(i, 1, N) {
247             Rep(j, V[i].size()) {
248                 Edge &e = E[V[i][j]];
249                 if(scc[e.from] != scc[e.to]) ++out[scc[e.from]];
250             }
251         }
252         
253         For(i, 1, N) if(!out[scc[i]]) ans.PB(i); 
254         
255         sort(ALL(ans));
256         cout << ans;
257     }
258     return 0;
259 }
View Code