ZOJ-2364 Data Transmission 分层图阻塞流 Dinic+贪心预流

题意：给定一个分层图，即只能够在相邻层次之间流动，给定了各个顶点的层次。要求输出一个阻塞流。

分析：该题直接Dinic求最大流TLE了，网上说采用Isap也TLE，而最大流中的最高标号预流推进（HLPP）能够直接秒掉这一题。当然还有一种挽救的方式就是首先进行一次贪心预流，然后进行dinic。也是第一次听说还有贪心预流这回事，所以找了一份代码特地学习了一番。具体步骤如下：

1.首先将所有节点按照层次进行排序，对每个节点有in[i]和out[i]两个属性，前者表示能够流入到该节点的流量，后者表示能够流出该节点的流量；
2.从层次最低的节点（即源点）开始，设in[S] = inf，表示源点能够进入无限的流量，然后按照层次的递增来推流量，维护好每个节点的in和out值；
3.从层次最高的节点（即汇点）开始，将所有节点的in都清空为0，设in[T] = inf，表示汇点能够收集无限的流量，然后从后往前计算出每条边实际能够流动的流量。

#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <queue>
using namespace std;

const int N = 1505;
const int M = 300005;
const int inf = 0x3f3f3f3f;
int n, m, L, SS, TT;
int lv[N], rank[N], in[N], out[N];

struct Edge {
    int v, c, nxt;
}e[M<<1];
int idx, head[N];
int dis[N];
char vis[N];
queue<int>q;

void insert(int a, int b, int c) {
    e[idx].v = b, e[idx].c = c;
    e[idx].nxt = head[a];
    head[a] = idx++;
}

bool bfs() {
    memset(dis, 0xff, sizeof (dis));
    memset(vis, 0, sizeof (vis));
    dis[SS] = 0, vis[SS] = 1;
    q.push(SS);
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for (int i = head[u]; ~i; i = e[i].nxt) {
            int v = e[i].v, c = e[i].c;
            if (dis[v] == -1 && c) {
                dis[v] = dis[u] + 1;
                if (!vis[v]) {
                    vis[v] = 1;
                    q.push(v);
                }
            }
        }
    }
    return dis[TT] != -1;
}

int dfs(int u, int flow) {
    if (u == TT) return flow;
    int tf = 0, f;
    for (int i = head[u]; ~i; i = e[i].nxt) {
        int v = e[i].v, c = e[i].c;
        if (dis[u]+1 == dis[v] && c && (f = dfs(v, min(flow-tf, c)))) {
            e[i].c -= f, e[i^1].c += f;
            tf += f;
            if (tf == flow) return tf;
        }
    }
    if (!tf) dis[u] = -1;
    return tf;
}

void dinic() {
    while (bfs()) {
        dfs(SS, inf);
    }
}

bool cmp(const int &a, const int &b) {
    return lv[a] < lv[b];
}

void greedy() {
    memset(in, 0, sizeof (in));
    memset(out, 0, sizeof (out));
    sort(rank+1, rank+1+n, cmp);
    in[SS] = inf;
    for (int i = 1; i <= n; ++i) {
        int u = rank[i];
        for (int j = head[u]; ~j; j = e[j].nxt) {
            int v = e[j].v, c = e[j].c;
            if (!(j & 1) && in[u] > out[u]) {
                int f = min(c, in[u]-out[u]);
                in[v] += f, out[u] += f;
            }
        }
    }
    memset(in, 0, sizeof (in));
    in[TT] = inf;
    for (int i = n; i >= 1; --i) {
        int v = rank[i];
        for (int j = head[v]; ~j; j = e[j].nxt) {
            int u = e[j].v, c = e[j^1].c;
            if (j & 1 && out[u] > in[u]) {
                int f = min(c, min(out[u]-in[u], in[v]));
                in[u] += f, in[v] -= f;
                e[j].c += f, e[j^1].c -= f;
            }
        }
    }
}

int main() {
    int T;
    scanf("%d", &T);
    while (T--) {
        idx = 0;
        memset(head, 0xff, sizeof (head));
        scanf("%d %d %d", &n, &m, &L);
        for (int i = 1; i <= n; ++i) {
            rank[i] = i;
            scanf("%d", &lv[i]);
            if (lv[i] == 1) SS = i;
            else if (lv[i] == L) TT = i;
        }
        int a, b, c;
        for (int i = 0; i < m; ++i) {
            scanf("%d %d %d", &a, &b, &c);
            insert(a, b, c), insert(b, a, 0);
        }
        greedy(), dinic();
        for (int i = 0; i < m; ++i) {
            printf("%d
", e[i<<1|1].c);
        }
    }
    return 0;
}