bzoj 2095: [Poi2010]Bridges [混合圖歐拉回路]

2095: [Poi2010]Bridges

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二分答案，混合圖歐拉路斷定

一開始想了一個上下界網絡流模型，而後發現不用上下界網絡流也能夠

對於無向邊，強制從\(u \rightarrow v\)，計算每一個點入度出度

二者差必須是偶數，令\(x = \frac{ind_i - outd_i}{2}\)

每條無向邊v向u連容量爲1的邊

對於\(x>0\)， s向i連容量x的邊；

\(x<0\)， i向t連容量-x的邊。

這樣一條原無向邊滿流 就是 與強制方向相反

有解 當且僅當 s出邊滿流

本題l不能初始化0，貌似有什麼詭異的特殊數據...

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <set>
#include <map>
using namespace std;
typedef long long ll;
#define fir first
#define sec second
const int N = 2005, M = 1e4+5, inf = 1e9+5;
inline int read() {
    char c=getchar(); int x=0,f=1;
    while(c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9') {x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, m, s, t;
struct meow {int u, v, c, d;} a[M];

struct edge {int v, ne, c, f;} e[M];
int cnt = 1, h[N];
inline void ins(int u, int v, int c) { //printf("ins %d --> %d  %d\n", u, v, c);
    e[++cnt] = (edge) {v, h[u], c, 0}; h[u] = cnt;
    e[++cnt] = (edge) {u, h[v], 0, 0}; h[v] = cnt;
}
int d[N], q[N], head, tail, vis[N];
bool bfs() {
    memset(vis, 0, sizeof(vis));
    head = tail = 1;
    d[s] = 0; q[tail++] = s; vis[s] = 1;
    while(head != tail) {
        int u = q[head++];
        for(int i=h[u]; i; i=e[i].ne) 
            if(e[i].c > e[i].f && !vis[e[i].v]) {
                int v = e[i].v;
                vis[v] = 1;
                d[v] = d[u]+1;
                q[tail++] = v;
                if(v == t) return true;
            }
    }
    return false;
}
int cur[N];
int dfs(int u, int a) {
    if(u == t || a == 0) return a;
    int flow = 0, f;
    for(int &i=cur[u]; i; i=e[i].ne) {
        int v = e[i].v;
        if(d[v] == d[u]+1 && (f = dfs(v, min(a, e[i].c - e[i].f))) > 0) {
            flow += f;
            e[i].f += f;
            e[i^1].f -= f;
            a -= f;
            if(a == 0) break;
        }
    }
    if(a) d[u] = -1;
    return flow;
}
int dinic() {
    int flow = 0;
    while(bfs()) {
        for(int i=s; i<=t; i++) cur[i] = h[i];
        flow += dfs(s, inf);
    }
    return flow;
}

int ind[N], outd[N];
bool check(int mid) { //printf("check %d\n", mid);
    cnt = 1; memset(h, 0, sizeof(h));
    s = 0; t = n+1;
    memset(ind, 0, sizeof(ind)); 
    memset(outd, 0, sizeof(outd));
    for(int i=1; i<=m; i++) {
        int u = a[i].u, v = a[i].v;
        if(a[i].c <= mid && a[i].d <= mid) {
            outd[u]++, ind[v]++;
            ins(v, u, 1);
        } else if(a[i].c <= mid) outd[u]++, ind[v]++;
        else if(a[i].d <= mid) outd[v]++, ind[u]++;
    }
    int sum = 0;
    for(int i=1; i<=n; i++) {
        int x = abs(ind[i] - outd[i]); //printf("x %d  %d\n", i, x);
        if(x & 1) return false;
        x >>= 1;
        if(ind[i] > outd[i]) ins(s, i, x), sum += x;
        else if(ind[i] < outd[i]) ins(i, t, x);
    }
    return dinic() == sum;
}
int main() {
    freopen("in.in", "r", stdin);
    n = read(); m = read();
    int l = inf, r = 0, ans = -1;
    for(int i=1; i<=m; i++) {
        a[i].u = read(), a[i].v = read(), a[i].c = read(), a[i].d = read();
        l = min(l, min(a[i].c, a[i].d));
        r = max(r, max(a[i].c, a[i].d));
    }
    
    //printf("%d\n", check(4)); return 0;
    while(l <= r) {
        int mid = (l+r) >> 1; //printf("lrmid %d %d %d\n", l, r, mid);
        if(check(mid)) ans = mid, r = mid-1;
        else l = mid+1;
    }
    if(ans == -1) puts("NIE");
    else printf("%d\n", ans);
}