2019 Petrozavodsk Winter Camp, Yandex Cup C. Diverse Singing 上下界网络流
建图一共建四层 第一层为N个歌手 第二层为{pi,li} 第三层为{si,li} 第四层为M首歌
除了S和第一层与第三层与T之间的边为[1,INF] 其他边均为[0,1]
#include<bits/stdc++.h> using namespace std; typedef long long ll; typedef int JQK; const JQK INF = 1000000005; struct node { int p, s, l; bool operator <(const node &rhs) const { if (p != rhs.p) return p > rhs.p; else { if (s != rhs.s) return s > rhs.s; else return l > rhs.l; } } } nodecnt; int n, m, k, s1, t1, s2, t2; map<pair<int, int>, int> pl, sl; map<int, pair<int, int> > plb, slb; map<node, int> psl; vector<int> anser; namespace dinic { const int MAXN = 30050; const int MAXM = 100050; const JQK INF = 1000000050; int Head[MAXN], cur[MAXN], lev[MAXN], to[MAXM << 1], nxt[MAXM << 1], ed = 1; int S, T, SS, TT, MAXP; JQK f[MAXM << 1], totflow[MAXN]; inline void addedge(int u, int v, JQK cap) { to[++ed] = v; nxt[ed] = Head[u]; Head[u] = ed; f[ed] = cap; to[++ed] = u; nxt[ed] = Head[v]; Head[v] = ed; f[ed] = 0; return; } inline void add(int u, int v, JQK caplow, JQK captop) { addedge(u, v, captop - caplow); totflow[u] -= caplow, totflow[v] += caplow; return ; } inline bool BFS() { int u; for (int i = 0; i <= MAXP + 1; i++) { lev[i] = -1; } //memset(lev, -1, sizeof(lev)); queue<int>q; lev[S] = 0; q.push(S); while (q.size()) { u = q.front(); q.pop(); for (int i = Head[u]; i; i = nxt[i]) if (f[i] && lev[to[i]] == -1) { lev[to[i]] = lev[u] + 1; q.push(to[i]); /* if (to[i] == T) { return 1; } magic one way optimize */ } } for (int i = 0; i <= MAXP + 1; i++) { cur[i] = Head[i]; } //memcpy(cur, Head, sizeof Head); return lev[T] != -1; } inline JQK DFS(int u, JQK maxf) { if (u == T || !maxf) { return maxf; } JQK cnt = 0, tem; for (int &i = cur[u]; i; i = nxt[i]) if (f[i] && lev[to[i]] == lev[u] + 1) { tem = DFS(to[i], min(maxf, f[i])); maxf -= tem; f[i] -= tem; f[i ^ 1] += tem; cnt += tem; if (!maxf) { break; } } if (!cnt) { lev[u] = -1; } return cnt; } JQK Dinic() { JQK ans = 0; while (BFS()) { ans += DFS(S, INF); } return ans; } void del(int x) { for (int i = Head[x]; i; i = nxt[i]) f[i] = f[i ^ 1] = 0; } void init(int S1, int T1, int S2, int T2) { for (int i = 0; i <= MAXP + 1; i++) { totflow[i] = Head[i] = 0; } ed = 1; S = S1; T = T1; SS = S2; TT = T2; return; } inline JQK pushdownflow(int x) { JQK sum = 0; for (int i = 1; i <= x; i++) { if (totflow[i] > 0) { addedge(SS, i, totflow[i]); sum += totflow[i]; } else if (totflow[i] < 0) { addedge(i, TT, -totflow[i]); } } return sum;//sum==dinic 循环流有解 } JQK work() { //有源汇最大流 JQK ans = 0; JQK sum = pushdownflow(TT - 2); addedge(T, S, INF); swap(S, SS), swap(T, TT); if (sum != Dinic()) { //Dinic(SS,TT) 求出一个有源汇有上下界可行流.此时的流不一定最大. cout << -1 << endl; return 0; } ans = f[ed]; //可行流流量 f[ed] = f[ed ^ 1] = 0; swap(S, SS), swap(T, TT); //Dinic(S,T) ans += Dinic();//新增广出的s-t流量 cout << ans << endl; for (int i = n + m + 1; i <= n + m + k; i++) { for (int j = Head[i]; j; j = nxt[j]) { int v = to[j]; if (v >= n + m + k + 1 && v <= n + m + 2 * k && f[j] == 0) { nodecnt.p = plb[i].first; nodecnt.s = slb[v].first; nodecnt.l = slb[v].second; anser.push_back(psl[nodecnt]); } } } sort(anser.begin(), anser.end()); for (int v : anser) { cout << v << " "; } return ans; } } int main() { int u, v; JQK c; scanf("%d %d %d", &n, &m, &k); dinic::MAXP = n + m + 2 * k + 5; s1 = n + m + 2 * k + 1; t1 = s1 + 1; s2 = t1 + 1; t2 = s2 + 1; dinic::init(s1, t1, s2, t2); //S T SS TT for (int i = 1; i <= n; i++) dinic::add(s1, i, 1, INF); for (int i = n + 1; i <= n + m; i++) dinic::add(i, t1, 1, INF); for (int i = 1; i <= k; i++) { scanf("%d %d %d", &u, &v, &c); nodecnt.p = u, nodecnt.s = v, nodecnt.l = c; if (!psl[nodecnt]) psl[nodecnt] = i; if (!pl[make_pair(u, c)]) { pl[make_pair(u, c)] = n + m + i; plb[n + m + i] = make_pair(u, c); dinic::add(u, n + m + i, 0, 1); } if (!sl[make_pair(v, c)]) { sl[make_pair(v, c)] = n + m + k + i; slb[n + m + k + i] = make_pair(v, c); dinic::add(n + m + k + i, n + v, 0, 1); } dinic::add(pl[make_pair(u, c)], sl[make_pair(v, c)], 0, 1); } dinic::work(); return 0; }
