牛客网暑期ACM多校训练营（第五场） E room（最小费用最大流 ， 最小权二分图匹配模板）

链接：

https://www.nowcoder.com/acm/contest/143/E

题意:

给定n个宿舍的新安排， 每个宿舍都有4个人， 问要至少有多少个人换位才能变成新安排。

可以建一个二分图， 左边n个点为原来的安排， 右边n个点为新安排，  每条边花费设为（ 4 - 交集）， 然后跑费用流。

#include<bits/stdc++.h>
using namespace std;
const int maxN = ;
const int maxM = 1e5 + ;
const int INF = 1e9 + ;
int n, ecnt, S, T;
struct {
    int to, w, cost, nxt;
} edge[maxM];

struct Node{
    int v, id;
}pre[maxN];
int head[maxN];
int bef[maxN][], after[maxN][];

void init() {
    memset(head, -, sizeof(head));
    ecnt = ;
}
void addEdge(int u, int v, int w, int c) {
    edge[ecnt].to = v;
    edge[ecnt].w = w;
    edge[ecnt].cost = c;
    edge[ecnt].nxt = head[u];
    head[u] = ecnt++;
}
inline int dif(int a, int b) {
    int res = ;
    for(int i = ; i < ; i++) {
        for(int j = ; j < ; j++) {
            if(bef[a][i] == after[b][j]) {
                res--;
                break;
            }
        }
    }
    return res;
}
void build() {
    S = , T =  * n + ;

    for(int i = ; i <= n; i++) {
        addEdge(S, i, , );
        addEdge(i, S, , );
        addEdge(i + n, T, , );
        addEdge(T, i + n, , );
    }

    for(int i = ; i <= n; i++) {
        for(int j = ; j <= n; j++) {
            int c = dif(i, j);
            addEdge(i, j + n, , c);
            addEdge(j + n, i, , -c); //建反向边的时候注意花费要为负
        }
    }
}
int vis[maxN], cost[maxN];
bool spfa(){
    queue<int> q;
    memset(vis, , sizeof(vis));
    fill(cost ,cost + maxN, INF);
    vis[S] = ;
    cost[S] = ;
    q.push(S);
    while(!q.empty()){
        int u = q.front();
        for(int i = head[u]; i != -; i = edge[i].nxt){
            int v = edge[i].to, f = edge[i].w , c = edge[i].cost;
            if(f ==  || cost[v] <= cost[u] + c) continue;
            cost[v] = cost[u] + c;
            pre[v].v = u;
            pre[v].id = i;
            if(!vis[v]){
                q.push(v);
                vis[v] = true;
            }
        }
        vis[u] = ;
        q.pop();
    }
    return cost[T] != INF;
}
int MCMF(){
    int flow = ;
    int minCost = ;
    while(spfa()){
        int minFlow = INF;
        for(int i = T; i != S; i = pre[i].v){
            minFlow = min(minFlow, edge[pre[i].id].w);
        }
        for(int i = T; i != S; i = pre[i].v){
            edge[pre[i].id].w -= minFlow;
            edge[pre[i].id ^ ].w += minFlow;
        }
        minCost += cost[T];
    }
    return minCost;
}
int main() {
//    freopen("1.txt","r", stdin);
    ios::sync_with_stdio(false);

    cin >> n;
    init();
    for(int i = ; i <= n; i++)
        for(int j = ; j < ; j++)
            cin >> bef[i][j];

    for(int i = ; i <= n; i++)
        for(int j = ; j < ; j++)
            cin >> after[i][j];

    build();
    cout << MCMF() << "\n";
}