POJ 2516 Minimum Cost 最小费用流

题目: 

给出n*kk的矩阵,格子a[i][k]表示第i个客户需要第k种货物a[i][k]单位。

给出m*kk的矩阵,格子b[j][k]表示第j个供应商可以提供第k种货物b[j][k]单位。

再给出k个n*m的矩阵,格子c[k][i][j]表示第k种货物由j供应商提供给客户i的话,每单位运费为c[k][i][j]。

问最小费用。

分析:

  刚开始时,虽然考虑到每种货物其实是不相关的,但是想到在跑费用流时应该没多大影响,所以直接建图,跑最小费用流,TLE了。。。

  后来对于每种货物单独来考虑,即建图之后跑一次最小费用流,进行k次求费用流之后,判断总流是否等于需求的货物数量。这样建图,节点数明显减少了很多,实际效果非常明显。

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

#define debug puts("here")
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,b) for(int i=a;i<=b;i++)
#define foreach(i,vec) for(unsigned i=0;i<vec.size();i++)
#define pb push_back
#define RD(n) scanf("%d",&n)
#define RD2(x,y) scanf("%d%d",&x,&y)
#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define RD4(x,y,z,w) scanf("%d%d%d%d",&x,&y,&z,&w)
#define All(vec) vec.begin(),vec.end()
#define MP make_pair
#define PII pair<int,int>
#define PQ priority_queue
#define cmax(x,y) x = max(x,y)
#define cmin(x,y) x = min(x,y)
#define Clear(x) memset(x,0,sizeof(x))
/*

#pragma comment(linker, "/STACK:1024000000,1024000000")

int size = 256 << 20; // 256MB
char *p = (char*)malloc(size) + size;
__asm__("movl %0, %%esp
" :: "r"(p) );

*/

char IN;
inline void Int(int &x){
    while(!isdigit(IN=getchar()));
    x = IN-'0';
    while(isdigit(IN=getchar()))
        x = x*10+IN-'0';
}

/******** program ********************/


const int MAXN = 205;
const int MAXM = 100005;
const int INF = 1e9;
const int X = 52;

int pre[MAXN],dis[MAXN];
int po[MAXN],tol;
bool use[MAXN];
int q[MAXM],head,tail;
int n,m,vs,vt,ans;

int a[X][X],b[X][X],c[X][X][X];
int kk,flow;

struct node{
    int y,f,cost,next;
}edge[MAXM];

void Add(int x,int y,int f,int cost){
    edge[++tol].y = y;
    edge[tol].f = f;
    edge[tol].cost = cost;
    edge[tol].next = po[x];
    po[x] = tol;
}

void add(int x,int y,int f,int cost){
    Add(x,y,f,cost);
    Add(y,x,0,-cost);
}

bool spfa(){
    memset(use,false,sizeof(use));
    rep1(i,vt)
        dis[i] = INF;
    dis[vs] = 0;
    head = tail = 0;
    q[tail++] = vs;
    pre[vs] = 0;
    while(head<tail){
        int x = q[head++];
        use[x] = false;
        for(int i=po[x];i;i=edge[i].next){
            int y = edge[i].y;
            if(edge[i].f>0&&edge[i].cost+dis[x]<dis[y]){
                dis[y] = dis[x]+edge[i].cost;
                pre[y] = i;
                if(!use[y]){
                    use[y] = true;
                    q[tail++] = y;
                }
            }
        }
    }
    if(dis[vt]==INF)
        return false;

    int aug = INF;
    for(int i=pre[vt];i;i=pre[edge[i^1].y])
        aug = min(aug,edge[i].f);
    for(int i=pre[vt];i;i=pre[edge[i^1].y]){
        edge[i].f -= aug;
        edge[i^1].f += aug;
    }
    ans += dis[vt]*aug;
    return true;
}

inline void fareFlow(int k){
    Clear(po);
    tol = 1;
    vs = MAXN-3;
    vt = vs+1;
    rep1(i,n)if(a[i][k])
        add( vs,i,a[i][k],0 );
    rep1(j,m)if(b[j][k]){
        add( j+n,vt,b[j][k],0 );
        rep1(i,n)
            add(i,j+n,b[j][k],c[k][i][j]);
    }
    while(spfa())
        ;
    for(int i=po[vt];i;i=edge[i].next)
        if(edge[i].f>0)
            flow += edge[i].f;
}

int main(){

#ifndef ONLINE_JUDGE
    freopen("sum.in","r",stdin);
    //freopen("sum.out","w",stdout);
#endif

    while(true){
        Int(n);Int(m);Int(kk);
        if(!n&&!m&&!kk)return 0;

        int tot = 0;
        rep1(i,n)
            rep1(k,kk){
                Int(a[i][k]);
                tot += a[i][k];
            }
        rep1(j,m)
            rep1(k,kk)
                Int(b[j][k]);
        rep1(k,kk)
            rep1(i,n)
                rep1(j,m)
                    Int(c[k][i][j]);

        flow = 0;
        ans = 0;
        rep1(k,kk)
            fareFlow(k);

        printf("%d
",tot==flow?ans:-1);
    }

    return 0;
}

  

原文地址:https://www.cnblogs.com/yejinru/p/3304233.html