luogu4016 负载平衡问题
阅读原文时间:2023年07月09日阅读:2

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#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
int n, uu, hea[105], cnt, ss, tt, sum, minCost, pre[105], dis[105];
const int oo=0x3f3f3f3f;
bool vis[105];
queue<int> d;
struct Edge{
    int too, nxt, val, cst;
}edge[805];
void add_edge(int fro, int too, int val, int cst){
    edge[cnt].nxt = hea[fro];
    edge[cnt].too = too;
    edge[cnt].val = val;
    edge[cnt].cst = cst;
    hea[fro] = cnt++;
}
void addEdge(int fro, int too, int val, int cst){
    add_edge(fro, too, val, cst);
    add_edge(too, fro, 0, -cst);
}
bool spfa(){
    memset(dis, 0x3f, sizeof(dis));
    memset(pre, -1, sizeof(pre));
    dis[ss] = 0;
    d.push(ss);
    vis[ss] = true;
    while(!d.empty()){
        int x=d.front();
        d.pop();
        vis[x] = false;
        for(int i=hea[x]; i!=-1; i=edge[i].nxt){
            int t=edge[i].too;
            if(dis[t]>dis[x]+edge[i].cst && edge[i].val>0){
                dis[t] = dis[x] + edge[i].cst;
                pre[t] = i;
                if(!vis[t]){
                    vis[t] = true;
                    d.push(t);
                }
            }
        }
    }
    return dis[tt]!=oo;
}
void f(){
    while(spfa()){
        int tmp=oo;
        for(int i=pre[tt]; i!=-1; i=pre[edge[i^1].too])
            tmp = min(tmp, edge[i].val);
        for(int i=pre[tt]; i!=-1; i=pre[edge[i^1].too]){
            edge[i].val -= tmp;
            edge[i^1].val += tmp;
            minCost += tmp * edge[i].cst;
        }
    }
}
int main(){
    memset(hea, -1, sizeof(hea));
    cin>>n;
    ss = 0; tt = n + 1;
    for(int i=1; i<=n; i++){
        scanf("%d", &uu);
        addEdge(ss, i, uu, 0);
        sum += uu;
    }
    sum /= n;
    for(int i=1; i<=n; i++){
        addEdge(i, tt, sum, 0);
        if(i>1) addEdge(i, i-1, oo, 1);
        if(i<n) addEdge(i, i+1, oo, 1);
    }
    addEdge(1, n, oo, 1);
    addEdge(n, 1, oo, 1);
    f();
    cout<<minCost<<endl;
    return 0;
}

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