Ultraviolet A 11248-Frequency Hopping (Network Stream)

Ultraviolet A 11248-frequency hopping

Question Link

Given a network, we need to transport traffic from 1 to n C and ask if it is possible. If it is possible to output data, if it is not possible, ask if it is possible to expand the capacity of an edge, if you can output these edges (first by u and then by V), if not, the output is impossible.

Idea: first perform a network flow, and then increase the capacity on the minimum cut each time. Two optimizations are required. You can find the traffic> = C each time, and then modify the capacity each time, you can continue with the previous network flow.

Code:

#include <cstdio>#include <cstring>#include <queue>#include <algorithm>using namespace std;const int MAXNODE = 105 * 2;const int MAXEDGE = 100005;typedef int Type;const Type INF = 0x3f3f3f3f;int n, m, c;struct Edge {int u, v;Type cap, flow;Edge() {}Edge(int u, int v, Type cap, Type flow) {this->u = u;this->v = v;this->cap = cap;this->flow = flow;}};bool cmp(Edge a, Edge b) {if (a.u != b.u) return a.u < b.u;return a.v < b.v;}struct Dinic {int n, m, s, t;Edge edges[MAXEDGE], etmp[MAXEDGE];int first[MAXNODE];int next[MAXEDGE];bool vis[MAXNODE];Type d[MAXNODE];int cur[MAXNODE];vector<int> cut;vector<Edge> ans;Type flow;void init(int n) {this->n = n;memset(first, -1, sizeof(first));m = 0;flow = 0;}void add_Edge(int u, int v, Type cap) {edges[m] = Edge(u, v, cap, 0);next[m] = first[u];first[u] = m++;edges[m] = Edge(v, u, 0, 0);next[m] = first[v];first[v] = m++;}bool bfs() {memset(vis, false, sizeof(vis));queue<int> Q;Q.push(s);d[s] = 0;vis[s] = true;while (!Q.empty()) {int u = Q.front(); Q.pop();for (int i = first[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (!vis[e.v] && e.cap > e.flow) {vis[e.v] = true;d[e.v] = d[u] + 1;Q.push(e.v);}}}return vis[t];}Type dfs(int u, Type a) {if (u == t || a == 0) return a;Type flow = 0, f;for (int &i = cur[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {e.flow += f;edges[i^1].flow -= f;flow += f;a -= f;if (a == 0) break;}}return flow;}void MinCut() {cut.clear();for (int i = 0; i < m; i += 2) {if (vis[edges[i].u] && !vis[edges[i].v])cut.push_back(i);}}bool Maxflow(int s, int t) {this->s = s; this->t = t;while (bfs()) {for (int i = 0; i < n; i++)cur[i] = first[i];flow += dfs(s, INF);if (flow >= c) return true;}return false;}void solve() {if (Maxflow(0, n - 1) || c == 0) printf("possible\n");else {MinCut();ans.clear();for (int i = 0; i < m; i++)etmp[i] = edges[i];int tmpf = flow;for (int i = 0; i < cut.size(); i++) {edges[cut[i]].cap = edges[cut[i]].flow + c;if (Maxflow(0, n - 1)) ans.push_back(edges[cut[i]]);flow = tmpf;for (int i = 0; i < m; i++)edges[i] = etmp[i];}if (ans.size() == 0) printf("not possible\n");else {sort(ans.begin(), ans.end(), cmp);printf("possible option:");for (int i = 0; i < ans.size(); i++)printf("(%d,%d)%c", ans[i].u + 1, ans[i].v + 1, i == ans.size() - 1 ? '\n' : ',');}}}} gao;int main() {int cas = 0;while (~scanf("%d%d%d", &n, &m, &c) && n) {gao.init(n);int u, v, cap;while (m--) {scanf("%d%d%d", &u, &v, &cap);u--; v--;gao.add_Edge(u, v, cap);}printf("Case %d: ", ++cas);gao.solve();}return 0;}

Ultraviolet A 11248-Frequency Hopping (Network Stream)