Luogu P2057 [SHOI2007]善意的投票 / [JLOI2010]冠军调查

题目描述

https://www.luogu.com.cn/problem/P2057

简要题意：$n$ 个人投票决定某件事，每个人本身有一个意见：同意或否定，现在有 $m$ 对好朋友，我们定义一次投票的冲突数为与自己意见冲突和好朋友之间发生冲突的总数，求最小冲突数

$n\le 300$

Solution

容易想到最小割，但是注意到朋友关系一定要连双向边

建图：

$s$ 连 $u$，$a[u]=1$，容量为 $1$

$v$ 连 $t$，$a[v]=1$，容量为 $1$

$u$ 连 $v$，$u$ 和 $v$ 是朋友关系，双向边，容量为 $1$

#include <iostream>
#include <cstdio>
#include <queue>
#define INF 1000000000
#define maxn 310
using namespace std;

int n, m, a[maxn];

struct Edge {
    int to, next, w;
} e[1000000]; int c1, head[maxn];
inline void add_edge(int u, int v, int w) {
    e[c1].to = v; e[c1].w = w; 
    e[c1].next = head[u]; head[u] = c1++;
}

inline void Add_edge(int u, int v, int w) {
    add_edge(u, v, w); add_edge(v, u, 0);
}

int dep[maxn], s, t; 
bool bfs() {
    fill(dep, dep + maxn, 0); dep[s] = 1;
    queue<int> Q; Q.push(s);
    while (!Q.empty()) {
        int u = Q.front(); Q.pop();
        for (int i = head[u]; ~i; i = e[i].next) {
            int v = e[i].to, w = e[i].w;
            if (w > 0 && !dep[v]) {
                dep[v] = dep[u] + 1;
                Q.push(v); if (v == t) return 1;
            }
        }
    }
    return 0; 
}

int dfs(int u, int _w) {
    if (u == t || !_w) return _w;
    int s = 0;
    for (int i = head[u]; ~i; i = e[i].next) {
        int v = e[i].to, w = e[i].w;
        if (w > 0 && dep[v] == dep[u] + 1) {
            int di = dfs(v, min(_w - s, w));
            e[i].w -= di; e[i ^ 1].w += di;
            s += di; if (s == _w) break;
        }
    }
    if (s < _w) dep[u] = 0;
    return s; 
}

int mf;
int dinic() {
    while (bfs()) mf += dfs(s, INF);
    return mf;
}

int main() { fill(head, head + maxn, -1); 
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);

    cin >> n >> m; s = 0; t = n + 1; 
    for (int i = 1; i <= n; ++i) cin >> a[i];
    for (int i = 1; i <= n; ++i)
        if (a[i]) Add_edge(s, i, 1);
        else Add_edge(i, t, 1); 
    for (int i = 1; i <= m; ++i) {
        int x, y; cin >> x >> y;
        Add_edge(x, y, 1);
        Add_edge(y, x, 1); 
    } cout << dinic() << "\n"; 
    return 0;
}