poj 2112 Optimal Milking 【最大流 简单题】 【floyd预处理最短路 + 二分 + 最大流】

Optimal Milking

Time Limit: 2000MS		Memory Limit: 30000K
Total Submissions: 13910		Accepted: 5023
Case Time Limit: 1000MS

Description

FJ has moved his K (1 <= K <= 30) milking machines out into the cow pastures among the C (1 <= C <= 200) cows. A set of paths of various lengths runs among the cows and the milking machines. The milking machine locations are named by ID numbers 1..K; the cow locations are named by ID numbers K+1..K+C. 

Each milking point can "process" at most M (1 <= M <= 15) cows each day. 

Write a program to find an assignment for each cow to some milking machine so that the distance the furthest-walking cow travels is minimized (and, of course, the milking machines are not overutilized). At least one legal assignment is possible for all input data sets. Cows can traverse several paths on the way to their milking machine. 

Input

* Line 1: A single line with three space-separated integers: K, C, and M. 

* Lines 2.. ...: Each of these K+C lines of K+C space-separated integers describes the distances between pairs of various entities. The input forms a symmetric matrix. Line 2 tells the distances from milking machine 1 to each of the other entities; line 3 tells the distances from machine 2 to each of the other entities, and so on. Distances of entities directly connected by a path are positive integers no larger than 200. Entities not directly connected by a path have a distance of 0. The distance from an entity to itself (i.e., all numbers on the diagonal) is also given as 0. To keep the input lines of reasonable length, when K+C > 15, a row is broken into successive lines of 15 numbers and a potentially shorter line to finish up a row. Each new row begins on its own line. 

Output

A single line with a single integer that is the minimum possible total distance for the furthest walking cow. 

Sample Input

2 3 2
0 3 2 1 1
3 0 3 2 0
2 3 0 1 0
1 2 1 0 2
1 0 0 2 0

Sample Output

2

题意：有C头奶牛和K台挤奶机，已知每台挤奶机只能给M头牛挤奶。奶牛编号从K+1 到 K+C，挤奶机编号从1 到 K。我们把奶牛和挤奶机看作K+C个点，现在给你一个 (K + C) * (K + C)的矩阵，矩阵第 i 行 第 j 列 的元素代表第i个点到第j个点的距离。显然的，如果要给一头奶牛挤奶，则需要这头奶牛走到挤奶机（任意一个都行）的位置。现在让你设计一种方案：安排给每头奶牛挤奶的，使得C头奶牛需要行走的路程中的最大路程最小。

简单最大流题目，我却WA了那么多次。不会再爱了。。。 以后写Floyd再不也用0来表示 两点间没有路了。

思路：1，首先Floyd预处理最短路。2，然后二分查找最优距离并以当前查找距离为限制建新图。3，接着超级源到超级汇跑一次最大流判断是否满流，若满流压缩距离，否则增大距离。4，继续二分查找 延续上面过程。

对当前查找的距离mid建图如下（不说太细了，建图思路没有违反常理。。。）

一：如果奶牛i到挤奶机j的距离不大于mid，则建边i -> j容量为1。

二：超级源点到每头奶牛建边，容量为1。

三：每台挤奶机到超级汇点建边，容量为M。

AC代码：

#include <cstdio>
#include <cstring>
#include <queue>
#include <stack>
#include <algorithm>
#define MAXN 300
#define MAXM 200000
#define INF 10000000
using namespace std;
struct Edge
{
    int from, to, cap, flow, next;
};
Edge edge[MAXM];
int head[MAXN], edgenum;
int cur[MAXN];
int dist[MAXN];
bool vis[MAXN];
int Map[300][300];
int K, C, M;
void Floyd()//预处理最短距离
{
    for(int k = 1; k <= K + C; k++)
    {
        for(int i = 1; i <= K + C; i++)
        {
            if(Map[i][k] == INF) continue;
            for(int j = 1; j <= K + C; j++)
            {
                //if(Map[k][j] == 0 || Map[i][j] == 0) continue;
                Map[i][j] = min(Map[i][j], Map[i][k] + Map[k][j]);
            }
        }
    }
}
void input()
{
    for(int i = 1; i <= K + C; i++)
    {
        for(int j = 1; j <= K + C; j++)
        {
            scanf("%d", &Map[i][j]);
            if(Map[i][j] == 0)
                Map[i][j] = INF;
        }
    }
    Floyd();
}
void init()
{
    memset(head, -1, sizeof(head));
    edgenum = 0;
}
void addEdge(int u, int v, int w)
{
    Edge E1 = {u, v, w, 0, head[u]};
    edge[edgenum] = E1;
    head[u] = edgenum++;
    Edge E2 = {v, u, 0, 0, head[v]};
    edge[edgenum] = E2;
    head[v] = edgenum++;
}
void getMap(int mid)
{
    for(int i = K + 1; i <= K + C; i++)//遍历
    {
        for(int j = 1; j <= K; j++)
        {
            if(Map[i][j] <= mid)
                addEdge(i, j, 1);//奶牛引一条容量为1的边到挤奶器
        }
    }
    for(int i = 1; i <= K + C; i++)
    {
        if(i >= K + 1)
            addEdge(0, i, 1);//超级源点引一条到 每头牛的边 容量为1
        if(i <= K)
            addEdge(i, K + C + 1, M);//挤奶器到超级汇点 建边。
    }
}
bool BFS(int start, int end)
{
    queue<int> Q;
    memset(dist, -1, sizeof(dist));
    memset(vis, false, sizeof(vis));
    dist[start] = 0;
    vis[start] = true;
    Q.push(start);
    while(!Q.empty())
    {
        int u = Q.front();
        Q.pop();
        for(int i = head[u]; i != -1; i = edge[i].next)
        {
            Edge E = edge[i];
            if(!vis[E.to] && E.cap > E.flow)
            {
                vis[E.to] = true;
                dist[E.to] = dist[u] + 1;
                if(E.to == end) return true;
                Q.push(E.to);
            }
        }
    }
    return false;
}
int DFS(int x, int a, int end)
{
    if(x == end || a == 0) return a;
    int flow = 0, f;
    for(int &i = cur[x]; i != -1; i = edge[i].next)
    {
        Edge &E = edge[i];
        if(dist[E.to] == dist[x] + 1 && (f = DFS(E.to, min(E.cap - E.flow, a), end)) > 0)
        {
            E.flow += f;
            edge[i^1].flow -= f;
            flow += f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}
int Maxflow(int start, int end)
{
    int flow = 0;
    while(BFS(start, end))
    {
        memcpy(cur, head, sizeof(head));
        flow += DFS(start, INF, end);
    }
    return flow;
}
void solve()
{
    int left = 0, right = 1000000, mid, ans;
    while(right >= left)
    {
        mid = (left + right) >> 1;//每次建图的最大距离
        init();
        getMap(mid);
        if(Maxflow(0, K + C + 1) == C)//每头奶牛都能挤上奶 满流
        {
            ans = mid;
            right = mid - 1;
        }
        else
            left = mid + 1;
    }
    printf("%d\n", ans);
}
int main()
{
    while(scanf("%d%d%d", &K, &C, &M) != EOF)
    {
        input();
        solve();
    }
    return 0;
}