POJ 3687 Labeling Balls

Posted 2022-06-15 zaq19970105

题目链接：https://vjudge.net/problem/POJ-3687

题目大意

　　有 N 个重量互不相同的球，标记为 1 ~ N，现给定 M 个重量约束条件，将 1 ~ N 单位的重量分配给每个球，如果能成功分配，输出重量序列（字典序尽量小），不能则输出 -1。

分析

　　一种错误的想法是先建立拓扑图，然后拓扑排序，每次取序号最小的节点从小到大分配重量，但这是不对的，这里举个反例：5 4 · 5 1 4 2 1 3 2 3。

　　正解是建立逆向拓扑图，然后拓扑排序，每次取序号最大的节点从大到小分配重量。因为这样分配一旦分配好节点就可以扔掉，转化为子问题，而子问题并不会对已扔掉的节点产生影响。

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,0x3f,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 << "]" << "\n";
 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< char > VC;
116 typedef vector< double > VD;
117 typedef vector< VI > VVI;
118 typedef vector< SI > VSI;
119 typedef vector< PII > VPII;
120 typedef map< int, int > MII;
121 typedef map< LL, int > MLLI;
122 typedef map< int, string > MIS;
123 typedef map< int, PII > MIPII;
124 typedef map< PII, int > MPIII;
125 typedef map< string, int > MSI;
126 typedef map< char, int > MCI;
127 typedef map< string, string > MSS;
128 typedef map< PII, string > MPIIS;
129 typedef map< PII, PII > MPIIPII;
130 typedef multimap< int, int > MMII;
131 typedef multimap< string, int > MMSI;
132 //typedef unordered_map< int, int > uMII;
133 typedef pair< LL, LL > PLL;
134 typedef vector< LL > VL;
135 typedef vector< VL > VVL;
136 typedef priority_queue< int > PQIMax;
137 typedef priority_queue< int, VI, greater< int > > PQIMin;
138 const double EPS = 1e-8;
139 const LL inf = 0x3fffffff;
140 const LL infLL = 0x3fffffffffffffffLL;
141 const LL mod = 1e9 + 7;
142 const int maxN = 2e2 + 7;
143 const LL ONE = 1;
144 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
145 const LL oddBits = 0x5555555555555555;
146 
147 struct Edge
148     int from, to;
149 ;
150 
151 istream& operator>> (istream& in, Edge &x) 
152     in >> x.from >> x.to;
153     return in;
154 
155 
156 struct Vertex
157     int in;
158     VI next;
159     
160     void clear() 
161         in = 0;
162         next.clear();
163     
164 ;
165 
166 int N, M, T;
167 Vertex V[maxN];
168 vector< Edge > E;
169 int topo[maxN], cnt; // 存拓扑序列 
170 
171 void addEdge(Edge &x) 
172     V[x.from].next.PB(E.size());
173     ++V[x.to].in;
174     E.PB(x);
175 
176 
177 bool TopoSort() 
178     PQIMax Q;
179     
180     For(i, 1, N) if(!V[i].in) Q.push(i);
181     
182     while(!Q.empty()) 
183         int tmp = Q.top(); Q.pop();
184         
185         topo[tmp] = cnt--;
186         Rep(i, V[tmp].next.size()) 
187             Edge &e = E[V[tmp].next[i]];
188             if(!--V[e.to].in) Q.push(e.to);
189         
190     
191     return cnt == 0;
192 
193 
194 void init() 
195     For(i, 1, N) V[i].clear();
196     E.clear();
197     cnt = N;
198 
199 
200 int main()
201     //freopen("MyOutput.txt","w",stdout);
202     //freopen("input.txt","r",stdin);
203     INIT();
204     cin >> T;
205     while(T--) 
206         cin >> N >> M;
207         init();
208         
209         For(i, 1, M) 
210             Edge t;
211             cin >> t.to >> t.from; // 存反向拓扑图 
212             addEdge(t);
213         
214         
215         if(TopoSort()) For(i, 1, N) cout << topo[i] << " \n"[i == N];
216         else cout << "-1\n";
217     
218     return 0;
219 

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