poj3686 The Windy's(拆点,费用流,好题)

题目链接

The Windy's

Time Limit: 5000MS Memory Limit: 65536KTotal Submissions: 5031 Accepted: 2112

Description

The Windy's is a world famous toy factory that owns M top-class workshop to make toys. This year the manager receives N orders for toys. The manager knows that every order will take different amount of hours in different workshops. More precisely, the i-th order will take Z_ij hours if the toys are making in the j-th workshop. Moreover, each order's work must be wholly completed in the same workshop. And a workshop can not switch to another order until it has finished the previous one. The switch does not cost any time.

The manager wants to minimize the average of the finishing time of the N orders. Can you help him?

Input

The first line of input is the number of test case. The first line of each test case contains two integers, N and M (1 ≤ N,M ≤ 50).
The next N lines each contain M integers, describing the matrix Z_ij (1 ≤ Z_ij ≤ 100,000) There is a blank line before each test case.

Output

For each test case output the answer on a single line. The result should be rounded to six decimal places.

Sample Input

33 4100 100 100 199 99 99 198 98 98 13 41 100 100 10099 1 99 9998 98 1 983 41 100 100 1001 99 99 9998 1 98 98

Sample Output

2.0000001.0000001.333333

Source

POJ Founder Monthly Contest – 2008.08.31, windy7926778

题解：

以前没见过的一种拆点方式,挑战程序设计上P243上的一道题。

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<vector>#include<queue>using namespace std;const int MAXN=4000;const int MAXM=MAXN*MAXN;const int INF = 0x3f3f3f3f;int g[55][55];struct Edge{    int to,next,cap,flow,cost;}edge[MAXM];int head[MAXN],tol;int pre[MAXN],dis[MAXN];bool vis[MAXN];int N;//节点总个数，节点编号从0~N-1void init(int n){    N = n;    tol = 0;    memset(head,-1,sizeof(head));}void addedge(int u,int v,int cap,int cost){    edge[tol].to = v;    edge[tol].cap = cap;    edge[tol].cost = cost;    edge[tol].flow = 0;    edge[tol].next = head[u];    head[u] = tol++;    edge[tol].to = u;    edge[tol].cap = 0;    edge[tol].cost = -cost;    edge[tol].flow = 0;    edge[tol].next = head[v];    head[v] = tol++;}bool spfa(int s,int t){    queue<int> q;    for(int i = 0;i < N;i++)    {        dis[i] = INF;        vis[i] = false;        pre[i] = -1;    }    dis[s] = 0;    vis[s] = true;    q.push(s);    while(!q.empty())    {        int u = q.front();        q.pop();        vis[u] = false;        for(int i = head[u]; i != -1;i = edge[i].next)        {            int v = edge[i].to;            if(edge[i].cap > edge[i].flow &&               dis[v] > dis[u] + edge[i].cost )            {                dis[v] = dis[u] + edge[i].cost;                pre[v] = i;                if(!vis[v])                {                    vis[v] = true;                    q.push(v);                }            }        }    }    if(pre[t] == -1)return false;    else return true;}//返回的是最大流，cost存的是最小费用int minCostMaxflow(int s,int t,int &cost){    int flow = 0;    cost = 0;    while(spfa(s,t))    {        int Min = INF;        for(int i = pre[t];i != -1;i = pre[edge[i^1].to])        {            if(Min > edge[i].cap - edge[i].flow)                Min = edge[i].cap - edge[i].flow;        }        for(int i = pre[t];i != -1;i = pre[edge[i^1].to])        {            edge[i].flow += Min;            edge[i^1].flow -= Min;            cost += edge[i].cost * Min;        }        flow += Min;    }    return flow;}int main(){int cas;scanf("%d",&cas);while(cas--){int n,m;scanf("%d%d",&n,&m);memset(g,0,sizeof(g));for(int i=1;i<=n;i++) for(int j=1;j<=m;j++)  scanf("%d",&g[i][j]);int start=0,end=n+n*m+1;init(end+1);for(int i=1;i<=n;i++) addedge(start,i,1,0);for(int i=1;i<=m;i++) for(int j=1;j<=n;j++)  addedge(n+m*(j-1)+i,end,1,0);for(int i=1;i<=n;i++)  for(int j=1;j<=m;j++)for(int k=1;k<=n;k++)addedge(i,n+m*(k-1)+j,1,g[i][j]*k);int cost=0;minCostMaxflow(start,end,cost);double ans=1.0*cost/n;printf("%.6f\n",ans);}return 0;}