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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; }
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