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 }