SGU194 Reactor Cooling 有下界最大流

学习别人的方法。大致是：

无源汇的最大流 ： 新建源点，汇点，sum[i]为每个点进来的下界流之和减去出去的下界流之和，如果sum[i] > 0，由源点向该点建一条边，上界为sum[i]，下界为0

如果sum[i] < 0, 由该点向汇点建边，上界为-sum[i]，下界为0。跑一遍源点到汇点的最大流即为答案

#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
#include <bitset>
#include <fstream>
using namespace std;
//LOOP
#define FF(i, a, b) for(int i = (a); i < (b); ++i)
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FED(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)
//OTHER
#define SZ(V) (int)V.size()
#define PB push_back
#define MP make_pair
#define all(x) (x).begin(),(x).end()
//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)
#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)
#define RS(s) scanf("%s", s)
//OUTPUT
#define WI(n) printf("%d\n", n)
#define WS(n) printf("%s\n", n)
//debug
//#define online_judge
#ifndef online_judge
#define dt(a)  << (#a) << "=" << a << " "
#define debugI(a) cout dt(a) << endl
#define debugII(a, b) cout dt(a) dt(b) << endl
#define debugIII(a, b, c) cout dt(a) dt(b) dt(c) << endl
#define debugIV(a, b, c, d) cout dt(a) dt(b) dt(c) dt(d) << endl
#define debugV(a, b, c, d, e) cout dt(a) dt(b) dt(c) dt(d) dt(e) << endl
#else
#define debugI(v)
#define debugII(a, b)
#define debugIII(a, b, c)
#define debugIV(a, b, c, d)
#endif

#define sqr(x) (x) * (x)
typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> VI;
const double eps = 1e-9;
const int MOD = 1000000007;
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const int maxn = 100010;

struct Edge{
    int from, to, cap, flow, lcap;
};

int n, m, s, t;
vector<Edge> edges;
VI G[maxn];
bool vis[maxn];
int d[maxn], cur[maxn];

void init()
{
    REP(i, n + 1)   G[i].clear();
    edges.clear();
}

void addEdge(int from, int to, int cap, int lcap)
{
    edges.PB((Edge){from, to, cap, 0, lcap});
    edges.PB((Edge){to, from, 0, 0, -lcap});
    m = edges.size();
    G[from].PB(m - 2);
    G[to].PB(m - 1);
}

bool bfs()
{
    CLR(vis, 0);
    queue<int> Q;
    Q.push(s);
    d[s] = 0, vis[s] = 1;
    while (!Q.empty())
    {
        int u = Q.front(); Q.pop();
        REP(i, G[u].size())
        {
            Edge& e = edges[G[u][i]];
            if (!vis[e.to] && e.cap > e.flow)
            {
                vis[e.to] = 1;
                d[e.to] = d[u] + 1;
                Q.push(e.to);
            }
        }
    }
    return vis[t];
}

int dfs(int x, int a)
{
    if (x == t || a == 0)
        return a;
    int flow = 0, f;
    for (int& i = cur[x];i < G[x].size(); i++)
    {
        Edge& e = edges[G[x][i]];
        if (d[x] + 1 == d[e.to] && (f = dfs(e.to, min(a, e.cap - e.flow))) > 0)
        {
            e.flow += f;
            edges[G[x][i] ^ 1].flow -= f;
            flow += f;
            a -= f;
            if (a == 0) break;
        }
    }
    return flow;
}

int maxflow(int ss, int tt)
{
    s = ss, t = tt;
    int flow = 0;
    while (bfs())
    {
        CLR(cur, 0);
        flow += dfs(s, INF);
    }
    return flow;
}

int sum[maxn];

int main()
{
    //freopen("0.txt", "r", stdin);
    int nodenum, edgenum;
    int u, v, l, c;
    int se, te;
    while (~RII(nodenum, edgenum))
    {
        CLR(sum, 0);
        n = nodenum + 2;
        init();
        REP(i, edgenum)
        {
            RIV(u, v, l, c);
            addEdge(u, v, c - l, l);
            sum[u] -= l;
            sum[v] += l;
        }
        se = edges.size(), te = se;
        FE(i, 1, nodenum)
            if (sum[i] > 0)
                addEdge(0, i, sum[i], 0), te = edges.size();
        FE(i, 1, nodenum)
            if (sum[i] < 0)
                addEdge(i, nodenum + 1, -sum[i], 0);
        int maxf = maxflow(0, nodenum + 1);
//        debugI(maxf);
//        debugII(se, te);
        bool f = 0;
        for (int i = se; i < te; i += 2)
            if (edges[i].flow < edges[i].cap)
            {
                f = 1;
                break;
            }
        if (f)
            puts("NO");
        else
        {
            puts("YES");
//            REP(i, edges.size())
            for (int i = 0; i < se; i += 2)
                printf("%d\n", edges[i].flow + edges[i].lcap);
        }
    }
    return 0;
}

SGU194 Reactor Cooling 有下界最大流