【luogu P1231 教辅的组成】题解

题目链接：https://www.luogu.org/problemnew/show/P1231

对于每本书只能用一次，所以拆点再建边

#include <queue>

#include <cstdio>

#include <cstring>

#include <iostream>

#include <algorithm>

using namespace std;

const int maxn = 50000 + 10;

const int inf = 1e9;

int n1, n2, n3, m1, m2, s, t, maxflow, deep[maxn];

struct edge{

    int flow, next, to;

}e[maxn<<3];

int head[maxn], cnt = -1;

queue<int> q;

void add(int u, int v, int w)

{

    e[++cnt].flow = w; e[cnt].next = head[u]; e[cnt].to = v; head[u] = cnt;

    e[++cnt].flow = 0; e[cnt].next = head[v]; e[cnt].to = u; head[v] = cnt;

}

bool bfs(int s, int t)

{

    memset(deep, 0x7f, sizeof(deep));

    while(!q.empty()) q.pop();

    q.push(s); deep[s] = 0;

    while(!q.empty())

    {

        int now = q.front(); q.pop();

        for(int i = head[now]; i != -1; i = e[i].next)

        {

            if(deep[e[i].to] > inf && e[i].flow)

            {

                deep[e[i].to] = deep[now] + 1;

                q.push(e[i].to);

            }

        }

    }

    if(deep[t] < inf) return true;

    else return false;

}

int dfs(int now, int t, int limit)

{

    if(!limit || now == t) return limit;

    int flow = 0, f;

    for(int i = head[now]; i != -1; i = e[i].next)

    {

        if(deep[e[i].to] == deep[now] + 1 && (f = dfs(e[i].to, t, min(e[i].flow, limit))))

        {

            flow += f;

            limit -= f;

            e[i].flow -= f;

            e[i^1].flow += f;

            if(!limit) break;

        }

    }

    return flow;

}

void Dinic(int s, int t)

{

    while(bfs(s, t))

    maxflow += dfs(s, t, inf);

}

int main()

{

    memset(head, -1, sizeof(head));

    scanf("%d%d%d", &n1, &n2, &n3);

    s = 1, t = n1*2 + n2 + n3 + 2;

    for(int i = 1; i <= n1; i++)

    {

        add(i + 1, i + n1 + n2 + n3 + 1, 1);

    }

    scanf("%d",&m1);

    for(int i = 1; i <= m1; i++)

    {

        int u, v;

        scanf("%d%d",&u,&v);

        add(v + 1 + n1, u + 1, 1);

    }

    scanf("%d",&m2);

    for(int i = 1; i <= m2; i++)

    {

        int u, v;

        scanf("%d%d",&u,&v);

        add(u + n1 + n2 + n3 + 1, v + n1 + n2 + 1, 1);

    }

    for(int i = 1; i <= n2; i++)

    add(s, i + n1 + 1, 1);

    for(int i = 1; i <= n3; i++)

    add(i + n1 + n2 + 1, t, 1);

    Dinic(s, t);

    printf("%d",maxflow);

    return 0;

}

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【luogu P1231 教辅的组成】题解