URAL 1099. Work Scheduling （一般图匹配带花树）

1099. Work Scheduling

Time limit: 0.5 second
Memory limit: 64 MB

There is certain amount of night guards that are available to protect the local junkyard from possible junk robberies. These guards need to scheduled in pairs, so that each pair guards at different night. The junkyard CEO ordered you to write a program which given the guards characteristics determines the maximum amount of scheduled guards (the rest will be fired). Please note that each guard can be scheduled with only one of his colleagues and no guard can work alone.

Input

The first line of the input contains one number N ≤ 222 which is the amount of night guards. Unlimited number of lines consisting of unordered pairs (i, j) follow, each such pair means that guard #i and guard #j can work together, because it is possible to find uniforms that suit both of them (The junkyard uses different parts of uniforms for different guards i.e. helmets, pants, jackets. It is impossible to put small helmet on a guard with a big head or big shoes on guard with small feet). The input ends with Eof.

Output

You should output one possible optimal assignment. On the first line of the output write the even number C, the amount of scheduled guards. Then output C/2 lines, each containing 2 integers (i, j) that denote that i and j will work together.

Sample

input	output
3 1 2 2 3 1 3	2 1 2

input

output

2
1 2

模板题！！！

以下是模板：

  1 /* ***********************************************
  2 Author        :kuangbin
  3 Created Time  :2013/8/21 22:56:05
  4 File Name     :F:\2013ACM练习\专题学习\图论\一般图匹配带花树\URAL1099.cpp
  5 ************************************************ */
  6 
  7 #include <stdio.h>
  8 #include <string.h>
  9 #include <iostream>
 10 #include <algorithm>
 11 #include <vector>
 12 #include <queue>
 13 #include <set>
 14 #include <map>
 15 #include <string>
 16 #include <math.h>
 17 #include <stdlib.h>
 18 #include <time.h>
 19 using namespace std;
 20 
 21 const int MAXN = 250;
 22 int N; //点的个数，点的编号从1到N
 23 bool Graph[MAXN][MAXN];
 24 int Match[MAXN];
 25 bool InQueue[MAXN],InPath[MAXN],InBlossom[MAXN];
 26 int Head,Tail;
 27 int Queue[MAXN];
 28 int Start,Finish;
 29 int NewBase;
 30 int Father[MAXN],Base[MAXN];
 31 int Count;//匹配数，匹配对数是Count/2
 32 void CreateGraph()
 33 {
 34     int u,v;
 35     memset(Graph,false,sizeof(Graph));
 36     scanf("%d",&N);
 37     while(scanf("%d%d",&u,&v) == 2)
 38     {
 39         Graph[u][v] = Graph[v][u] = true;
 40     }
 41 }
 42 void Push(int u)
 43 {
 44     Queue[Tail] = u;
 45     Tail++;
 46     InQueue[u] = true;
 47 }
 48 int Pop()
 49 {
 50     int res = Queue[Head];
 51     Head++;
 52     return res;
 53 }
 54 int FindCommonAncestor(int u,int v)
 55 {
 56     memset(InPath,false,sizeof(InPath));
 57     while(true)
 58     {
 59         u = Base[u];
 60         InPath[u] = true;
 61         if(u == Start) break;
 62         u = Father[Match[u]];
 63     }
 64     while(true)
 65     {
 66         v = Base[v];
 67         if(InPath[v])break;
 68         v = Father[Match[v]];
 69     }
 70     return v;
 71 }
 72 void ResetTrace(int u)
 73 {
 74     int v;
 75     while(Base[u] != NewBase)
 76     {
 77         v = Match[u];
 78         InBlossom[Base[u]] = InBlossom[Base[v]] = true;
 79         u = Father[v];
 80         if(Base[u] != NewBase) Father[u] = v;
 81     }
 82 }
 83 void BloosomContract(int u,int v)
 84 {
 85     NewBase = FindCommonAncestor(u,v);
 86     memset(InBlossom,false,sizeof(InBlossom));
 87     ResetTrace(u);
 88     ResetTrace(v);
 89     if(Base[u] != NewBase) Father[u] = v;
 90     if(Base[v] != NewBase) Father[v] = u;
 91     for(int tu = 1; tu <= N; tu++)
 92         if(InBlossom[Base[tu]])
 93         {
 94             Base[tu] = NewBase;
 95             if(!InQueue[tu]) Push(tu);
 96         }
 97 }
 98 void FindAugmentingPath()
 99 {
100     memset(InQueue,false,sizeof(InQueue));
101     memset(Father,0,sizeof(Father));
102     for(int i = 1;i <= N;i++)
103         Base[i] = i;
104     Head = Tail = 1;
105     Push(Start);
106     Finish = 0;
107     while(Head < Tail)
108     {
109         int u = Pop();
110         for(int v = 1; v <= N; v++)
111             if(Graph[u][v] && (Base[u] != Base[v]) && (Match[u] != v))
112             {
113                 if((v == Start) || ((Match[v] > 0) && Father[Match[v]] > 0))
114                     BloosomContract(u,v);
115                 else if(Father[v] == 0)
116                 {
117                     Father[v] = u;
118                     if(Match[v] > 0)
119                         Push(Match[v]);
120                     else
121                     {
122                         Finish = v;
123                         return;
124                     }
125                 }
126             }
127     }
128 }
129 void AugmentPath()
130 {
131     int u,v,w;
132     u = Finish;
133     while(u > 0)
134     {
135         v = Father[u];
136         w = Match[v];
137         Match[v] = u;
138         Match[u] = v;
139         u = w;
140     }
141 }
142 void Edmonds()
143 {
144     memset(Match,0,sizeof(Match));
145     for(int u = 1; u <= N; u++)
146         if(Match[u] == 0)
147         {
148             Start = u;
149             FindAugmentingPath();
150             if(Finish > 0)AugmentPath();
151         }
152 }
153 void PrintMatch()
154 {
155     Count = 0;
156     for(int u = 1; u <= N;u++)
157         if(Match[u] > 0)
158             Count++;
159     printf("%d\n",Count);
160     for(int u = 1; u <= N; u++)
161         if(u < Match[u])
162             printf("%d %d\n",u,Match[u]);
163 }
164 int main()
165 {
166     CreateGraph();//建图
167     Edmonds();//进行匹配
168     PrintMatch();//输出匹配数和匹配
169     return 0;
170 }

来源：https://www.cnblogs.com/kuangbin/p/3278621.html

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