SGU 194. Reactor Cooling(无源汇有上下界的网络流)

时间限制：0.5s

空间限制：6M

题意：

       显然就是求一个无源汇有上下界的网络流的可行流的问题

 

 

Solution：

没什么好说的，直接判定可行流，输出就好了

code

/*

       无汇源有上下界的网络流

*/

#include <iostream>

#include <cstring>

#define ms(a,b) memset(a,b,sizeof a)

using namespace std;

const int MAXN = 209;



struct node {

    int u, v, c, ne;

} edge[MAXN * MAXN << 2];

int pHead[MAXN*MAXN], SS, ST, T, ncnt, ans;

int Gup[MAXN][MAXN], Glow[MAXN][MAXN], st[MAXN], ed[MAXN], cap[MAXN][MAXN], tflow;



void addEdge (int u, int v, int c) {

    edge[++ncnt].v = v, edge[ncnt].c = c, edge[ncnt].u = u;

    edge[ncnt].ne = pHead[u], pHead[u] = ncnt;

    edge[++ncnt].v = u, edge[ncnt].c = 0, edge[ncnt].u = v;

    edge[ncnt].ne = pHead[v], pHead[v] = ncnt;

}



int SAP (int pStart, int pEnd, int N) {

    int numh[MAXN], h[MAXN], curEdge[MAXN], pre[MAXN];

    int cur_flow, flow_ans = 0, u, neck, i, tmp;

    ms (h, 0); ms (numh, 0); ms (pre, -1);

    for (i = 0; i <= N; i++) curEdge[i] = pHead[i];

    numh[0] = N;

    u = pStart;

    while (h[pStart] <= N) {

        if (u == pEnd) {

            cur_flow = 1e9;

            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v)

                if (cur_flow > edge[curEdge[i]].c) neck = i, cur_flow = edge[curEdge[i]].c;

            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v) {

                tmp = curEdge[i];

                edge[tmp].c -= cur_flow, edge[tmp ^ 1].c += cur_flow;

            }

            flow_ans += cur_flow;

            u = neck;

        }

        for ( i = curEdge[u]; i != 0; i = edge[i].ne) {

            if (edge[i].v > N) continue; //重要!!!

            if (edge[i].c && h[u] == h[edge[i].v] + 1)     break;

        }

        if (i != 0) {

            curEdge[u] = i, pre[edge[i].v] = u;

            u = edge[i].v;

        }

        else {

            if (0 == --numh[h[u]]) continue;

            curEdge[u] = pHead[u];

            for (tmp = N, i = pHead[u]; i != 0; i = edge[i].ne) {

                if (edge[i].v > N) continue; //重要!!!

                if (edge[i].c)  tmp = min (tmp, h[edge[i].v]);

            }

            h[u] = tmp + 1;

            ++numh[h[u]];

            if (u != pStart) u = pre[u];

        }

    }

    return flow_ans;

}

int solve (int n) {

    SS = n + 1, ST = n + 2;

    for (int i = 1; i <= n; i++) {

        if (ed[i]) addEdge (SS, i, ed[i]);

        if (st[i]) addEdge (i, ST, st[i]);

    }

    int tem = SAP (SS, ST, ST);

    if (tem != tflow) return 0;

    else

              return 1;

}

int n, m;

int main() {

    ios::sync_with_stdio (0);

    ncnt = 1;

    cin >> n >> m;

    for (int i = 1, u, v, x, y; i <= m; i++) {

        cin >> u >> v >> x >> y;

        Gup[u][v] = y, Glow[u][v] = x;

        st[u] += x, ed[v] += x;

        tflow += x;

        addEdge (u, v, y - x);

    }

    if (solve (n) ) {

        cout << "YES\n";

        for (int i = 2, x, y; i <= m * 2; i += 2) {

            x = edge[i].u, y = edge[i].v;

            cout << Gup[x][y]-edge[i].c << '\n';

        }

    }

    else

        cout << "NO\n";

    return 0;

}

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