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今晚ABC的G题的最小割问题

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@lo9a8td2
此快照首次捕获于
2023/10/28 08:07
2 年前
此快照最后确认于
2023/10/28 08:07
2 年前
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ABC239G 在跑完Dinic算法之后,怎么判断哪些边属于割边呢? 为什么下面的代码里用分层图的d数组可以判断出来那些点被用到了呢?
CPP
#include<iostream>
#include<cstring>
#include<vector>
using namespace std;
typedef long long LL;
const int maxn = 205, maxm = 100 * maxn * maxn;
const LL INF = 0x3f3f3f3f3f3f3f3f;
int h[maxn], cur[maxn], e[maxm], ne[maxm], idx;
LL f[maxm];
int d[maxn], q[maxn];
int n, m, S, T;

void add(int a, int b, LL c){
    e[idx] = b, f[idx] = c, ne[idx] = h[a], h[a] = idx++;
    e[idx] = a, f[idx] = 0, ne[idx] = h[b], h[b] = idx++;
}

bool bfs(){
    int hh = 0, tt = -1;
    memset(d, -1, sizeof(d));
    q[++tt] = S, d[S] = 0, cur[S] = h[S];
    while(hh <= tt){
        int t = q[hh++];
        for(int i = h[t]; ~i; i = ne[i]){
            int j = e[i];
            if (d[j] == -1 && f[i]){
                d[j] = d[t] + 1;
                cur[j] = h[j];
                if (j == T) return true;
                q[++tt] = j;
            }
        }
    }
    return false;
}

LL find(int u, LL limit){
    if (u == T) return limit;
    LL flow = 0;
    // start from cur[u] instead of h[u] <- important
    for(int i = cur[u]; ~i && flow < limit; i = ne[i]){
        int j = e[i];
        cur[u] = i;
        if (d[j] == d[u] + 1 && f[i]){
            LL t = find(j, min(f[i], limit - flow));
            if (!t) d[j] = -1;
            else f[i] -= t, f[i ^ 1] += t, flow += t; 
        }
    }
    return flow;
}

LL dinic(){
    LL res = 0, flow;
    while(bfs()) while(flow = find(S, INF)) res += flow;
    return res;
}

int main(){

#ifdef LOCAL
    freopen("data.in","r",stdin);
    freopen("data.out","w",stdout);
#endif

    memset(h, -1, sizeof h);
    scanf("%d%d", &n, &m);
    S = n + 1, T = n;
    while(m--){
        int a, b;
        scanf("%d%d", &a, &b);
        add(a + n, b, INF), add(b + n, a, INF);
    }
    int t = idx;
    for(int i = 1; i <= n; i++){
        int x;
        scanf("%d", &x);
        if (i != 1 && i != n) add(i, i + n, x);
        else add(i, i + n, INF);
    }
    cout << dinic() << '\n';
    vector<int> ans;
    for(int i = 1; i <= n; i++)
        if (d[i] != -1 && d[i + n] == -1) ans.push_back(i);
    cout << ans.size() << '\n';
    for(auto u : ans) printf("%d ", u);
    putchar('\n');

}

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