POJ 1094 Sorting It All Out
题目链接：https://vjudge.net/problem/POJ-1094
题目大意
给定 N 个变量的 M 个大小关系，依次处理，判断这 N 个变量的大小关系能否确定？如能确定，在处理第几个大小关系时检测成功？如不能确定，是否有矛盾？如有矛盾，在处理第几个大小关系时检测出了矛盾？
分析
每输入一行就进行一次拓扑排序，暴力求解即可。
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< string, string > MSS; 127 typedef map< PII, string > MPIIS; 128 typedef map< PII, PII > MPIIPII; 129 typedef multimap< int, int > MMII; 130 typedef multimap< string, int > MMSI; 131 //typedef unordered_map< int, int > uMII; 132 typedef pair< LL, LL > PLL; 133 typedef vector< LL > VL; 134 typedef vector< VL > VVL; 135 typedef priority_queue< int > PQIMax; 136 typedef priority_queue< int, VI, greater< int > > PQIMin; 137 const double EPS = 1e-8; 138 const LL inf = 0x3fffffff; 139 const LL infLL = 0x3fffffffffffffffLL; 140 const LL mod = 1e9 + 7; 141 const int maxN = 1e2 + 7; 142 const LL ONE = 1; 143 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 144 const LL oddBits = 0x5555555555555555; 145 146 struct Edge{ 147 int from, to; 148 }; 149 150 istream& operator>> (istream& in, Edge &x) { 151 in >> x.from >> x.to; 152 return in; 153 } 154 155 struct Vertex{ 156 int in; 157 VI next; 158 159 void clear() { 160 in = 0; 161 next.clear(); 162 } 163 }; 164 165 int N, M, ans, type; 166 Vertex V[27]; 167 vector< Edge > E; 168 string topo; // 存拓扑序列 169 170 void addEdge(Edge &x) { 171 V[x.from].next.PB(E.size()); 172 ++V[x.to].in; 173 E.PB(x); 174 } 175 176 // 返回 1 表示能确定顺序，0 表示不能确定，-1表示矛盾 177 int TopoSort() { 178 stack< int > sk; 179 int ind[27]; 180 topo.clear(); 181 182 For(i, 1, N) { 183 if(!V[i].in) sk.push(i); 184 ind[i] = V[i].in; 185 } 186 187 bool check = true; // check大小关系是否都确定了 188 while(!sk.empty()) { 189 if(sk.size() > 1) check = false; 190 int tmp = sk.top(); sk.pop(); 191 topo.PB(tmp + 'A' - 1); 192 193 Rep(i, V[tmp].next.size()) { 194 Edge &e = E[V[tmp].next[i]]; 195 196 --ind[e.to]; 197 if(!ind[e.to]) sk.push(e.to); 198 } 199 } 200 201 if(topo.size() < N) return -1; 202 if(!check) return 0; 203 return 1; 204 } 205 206 int main(){ 207 //freopen("MyOutput.txt","w",stdout); 208 //freopen("input.txt","r",stdin); 209 //INIT(); 210 while(cin >> N >> M && N) { 211 bool flag = false; 212 type = 0; 213 E.clear(); 214 For(i, 1, N) V[i].clear(); 215 216 For(i, 1, M) { 217 string tmp; 218 Edge t; 219 220 cin >> tmp; 221 if(flag) continue; 222 223 t.from = tmp[0] - 'A' + 1; 224 t.to = tmp[2] - 'A' + 1; 225 if(tmp[1] == '>') swap(t.from, t.to); 226 addEdge(t); 227 228 int tt = TopoSort(); 229 if(tt == 1 || tt == -1) { 230 type = tt; 231 ans = i; 232 flag = true; 233 } 234 } 235 236 if(type == -1) printf("Inconsistency found after %d relations.\n", ans); 237 else if(type == 1) printf("Sorted sequence determined after %d relations: %s.\n", ans, topo.c_str()); 238 else printf("Sorted sequence cannot be determined.\n", ans); 239 } 240 return 0; 241 }
