wikioi 1028 花店櫥窗佈置 最大權匹配

中文題意不描述。

連接：http://wikioi.com/problem/1028/

這題一開始很裸的最大權二分匹配。可是原來沒有接觸過，KM的這個最大權不大會。而後一開始覺得用最大費用最大流直接就能搞，後來知道單純的費用流解決的是二分最佳匹配，而不是最大權，QCMM而後看了一下這個http://hi.baidu.com/lerroy312/item/42e718ba58a1f8df85dd795f

結果改了以後不對，不知道爲何最後用的最小費用，對邊的權值取負值，結果取負值才過。。。不解。。。

  1 #include <iostream>
  2 #include <queue>
  3 #include <iostream>
  4 #include <cstdio>
  5 #include <cstring>
  6 #include <vector>
  7 using namespace std;
  8 const int maxn = 350;
  9 const int inf = 10000000;
 10 struct node
 11 {
 12     int u,v,cap,flow,cost,next;
 13 }edges[100050];
 14 int head[maxn],cnt;
 15 void init(int n)
 16 {
 17     int i;
 18     for(i = 0;i <= n;i++)
 19     head[i] = -1;
 20     cnt = 0;
 21 
 22     return ;
 23 }
 24 void addedge(int u,int v,int cap,int cost)
 25 {
 26     edges[cnt].u = u;
 27     edges[cnt].v = v;
 28     edges[cnt].cap = cap;
 29     edges[cnt].flow = 0;
 30     edges[cnt].cost = cost;
 31     edges[cnt].next = head[u];
 32     head[u] = cnt;
 33     cnt++;
 34     edges[cnt].u = v;
 35     edges[cnt].v = u;
 36     edges[cnt].cap = 0;
 37     edges[cnt].flow = 0;
 38     edges[cnt].cost = -cost;
 39     edges[cnt].next = head[v];
 40     head[v] = cnt;
 41     cnt++;
 42 }
 43 int vis[maxn],a[maxn],pre[maxn],dis[maxn];
 44 int spfa(int s,int t,int n,int &flow,int &cost)
 45 {
 46     int i;
 47     queue<int> q;
 48     for(i = 0;i <= n ;i++)
 49     dis[i] = inf,vis[i] = 0;
 50 
 51     dis[s] = 0;
 52     pre[s] = 0;
 53     vis[s] = 1;
 54     a[s] = inf;
 55 
 56     int u,v;
 57     q.push(s);
 58 
 59     while(!q.empty())
 60     {
 61         u = q.front();
 62         q.pop();
 63         vis[u] = 0;
 64 
 65         for(i = head[u];i != -1;i = edges[i].next)
 66         {
 67             struct node & e = edges[i];
 68 
 69             v = e.v;
 70             if(e.cap > e.flow &&dis[v] > dis[u]+e.cost)
 71             {
 72                 dis[v] = dis[u]+e.cost;
 73                 a[v] = min(a[u],e.cap-e.flow);
 74                 pre[v] = i;
 75                 if(!vis[v])
 76                 {
 77                     vis[v] = 1;
 78                     q.push(v);
 79                 }
 80             }
 81         }
 82     }
 83 
 84     if(dis[t] >= inf)
 85     return 0;
 86     flow+= a[t];
 87     cost += dis[t]*a[t];
 88     u = t;
 89     while(u != s)
 90     {
 91         edges[pre[u]].flow += a[t];
 92         edges[pre[u]^1].flow -= a[t];
 93         u = edges[pre[u]].u;
 94     }
 95     return 1;
 96 }
 97 int mcmf(int s,int t, int n)
 98 {
 99     int cost = 0,flow = 0;
100     while(spfa(s,t,n,flow,cost));
101 
102     return cost;
103 }
104 int main()
105 {
106     int n,m;
107     scanf("%d %d",&n,&m);
108 
109     int i,j;
110     init(n+m+4);
111     for(i =1;i <= n;i++)
112     {
113         addedge(0,i,1,0);
114         for(j = 1;j <= m;j++)
115         {
116             int w;
117             scanf("%d",&w);
118             addedge(i,j+n,1,-w);
119         }
120         addedge(i,m+n+1,1,0);
121     }
122     addedge(n+m+1,m+n+2,n,0);
123     for(j = 1;j <= m;j++)
124     addedge(j+n,m+n+2,1,0);
125     cout<<-mcmf(0,m+n+2,m+n+3)<<endl;
126     return 0;
127 }

View Code

 額，最近跟scu-frog神請教了下這個問題，scu-frog神看了下代碼，說你的最長路的初始化有問題，有負權邊爲何賦值-1.

而後默默對本身說了一句sb。。。默默改了交了一下，ac= =。

  1 #include <iostream>
  2 #include <queue>
  3 #include <iostream>
  4 #include <cstdio>
  5 #include <cstring>
  6 #include <vector>
  7 using namespace std;
  8 const int maxn = 350;
  9 const int inf = 10000000;
 10 struct node
 11 {
 12     int u,v,cap,flow,cost,next;
 13 }edges[100050];
 14 int head[maxn],cnt;
 15 void init(int n)
 16 {
 17     int i;
 18     for(i = 0;i <= n;i++)
 19     head[i] = -1;
 20     cnt = 0;
 21 
 22     return ;
 23 }
 24 void addedge(int u,int v,int cap,int cost)
 25 {
 26     edges[cnt].u = u;
 27     edges[cnt].v = v;
 28     edges[cnt].cap = cap;
 29     edges[cnt].flow = 0;
 30     edges[cnt].cost = cost;
 31     edges[cnt].next = head[u];
 32     head[u] = cnt;
 33     cnt++;
 34     edges[cnt].u = v;
 35     edges[cnt].v = u;
 36     edges[cnt].cap = 0;
 37     edges[cnt].flow = 0;
 38     edges[cnt].cost = -cost;
 39     edges[cnt].next = head[v];
 40     head[v] = cnt;
 41     cnt++;
 42 }
 43 int vis[maxn],a[maxn],pre[maxn],dis[maxn];
 44 int spfa(int s,int t,int n,int &flow,int &cost)
 45 {
 46     int i;
 47     queue<int> q;
 48     for(i = 0;i <= n ;i++)
 49     dis[i] = -inf,vis[i] = 0;
 50 
 51     dis[s] = 0;
 52     pre[s] = 0;
 53     vis[s] = 1;
 54     a[s] = inf;
 55 
 56     int u,v;
 57     q.push(s);
 58 
 59     while(!q.empty())
 60     {
 61         u = q.front();
 62         q.pop();
 63         vis[u] = 0;
 64 
 65         for(i = head[u];i != -1;i = edges[i].next)
 66         {
 67             struct node & e = edges[i];
 68 
 69             v = e.v;
 70             if(e.cap > e.flow &&dis[v] < dis[u]+e.cost)
 71             {
 72                 dis[v] = dis[u]+e.cost;
 73                 a[v] = min(a[u],e.cap-e.flow);
 74                 pre[v] = i;
 75                 if(!vis[v])
 76                 {
 77                     vis[v] = 1;
 78                     q.push(v);
 79                 }
 80             }
 81         }
 82     }
 83 
 84     if(dis[t] <= -inf)
 85     return 0;
 86     flow+= a[t];
 87     cost += dis[t]*a[t];
 88     u = t;
 89     while(u != s)
 90     {
 91         edges[pre[u]].flow += a[t];
 92         edges[pre[u]^1].flow -= a[t];
 93         u = edges[pre[u]].u;
 94     }
 95     return 1;
 96 }
 97 int mcmf(int s,int t, int n)
 98 {
 99     int cost = 0,flow = 0;
100     while(spfa(s,t,n,flow,cost));
101 
102     return cost;
103 }
104 int main()
105 {
106     int n,m;
107     scanf("%d %d",&n,&m);
108 
109     int i,j;
110     init(n+m+4);
111     for(i =1;i <= n;i++)
112     {
113         addedge(0,i,1,0);
114         for(j = 1;j <= m;j++)
115         {
116             int w;
117             scanf("%d",&w);
118             addedge(i,j+n,1,w);
119         }
120         addedge(i,m+n+1,1,0);
121     }
122     addedge(n+m+1,m+n+2,n,0);
123     for(j = 1;j <= m;j++)
124     addedge(j+n,m+n+2,1,0);
125     cout<<mcmf(0,m+n+2,m+n+3)<<endl;
126     return 0;
127 }

View Code