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 }
原文地址：https://www.cnblogs.com/zaq19970105/p/11311284.html
时间： 2024-10-05 00:34:31