Topic links: UVA-10480 Sabotage
The meaning of problems
FIG even give a side (undirected edges) and cut the cost of each edge, to cut off some of the edges so that the node 1 and the node 2 is not connected, the program seeking minimum cost cut.
Thinking
On the picture to the source node 1, node 2 is the sink node, the edge cost network flow capacity is established, the minimum is the minimum cost cut.
Provided cutting edge into the stream of the network nodes S $ $ $ T $ and two sets. Residual network after the Ford-Fulkerson method of seeking maximum flow, starting from the source dfs, each pass residual capacity is greater than $ 0 $ sides, to find all the nodes in the set $ S $. All sides $ (u, v) $, if $ u \ in S, v \ in T $, then $ (u, v) $ is cutting edge.
Code
#include <iostream> #include <cstdio> #include <cstring> #include <queue> using std::queue; const int INF = 0x3f3f3f3f, N = 60, M = 1100; int head[N], d[N]; int s, t, tot, maxflow; bool vis[N]; struct Edge { int to, cap, nex; } edge[M]; queue<int> q; void add(int x, int y, int z) { edge[++tot].to = y, edge[tot].cap = z, edge[tot].nex = head[x], head[x] = tot; } bool bfs() { memset(d, 0, sizeof(d)); while (q.size()) q.pop(); q.push(s); d[s] = 1; while (q.size()) { int x = q.front(); q.pop(); for (int i = head[x]; i; i = edge[i].nex) { int v = edge[i].to; if (edge[i].cap && !d[v]) { q.push(v); d[v] = d[x] + 1; if (v == t) return true; } } } return false; } int dinic(int x, int flow) { if (x == t) return flow; int rest = flow, k; for (int i = head[x]; i && rest; i = edge[i].nex) { int v = edge[i].to; if (edge[i].cap && d[v] == d[x] + 1) { k = dinic(v, std::min(rest, edge[i].cap)); if (!k) d[v] = 0; edge[i].cap -= k; edge[i^1].cap += k; rest -= k; } } return flow - rest; } void init() { tot = 1, maxflow = 0; s = 1, t = 2; memset(head, 0, sizeof(head)); memset(vis, false, sizeof(vis)); } void dfs(int u) { vis[u] = true; for (int i = head[u]; i; i = edge[i].nex) { int v = edge[i].to; if (!vis[v] && edge[i].cap) dfs(v); } } int main() { int n, m; while (~scanf("%d %d", &n, &m) && (n || m)) { init(); for (int i = 0, u, v, z; i < m; i++) { scanf("%d %d %d", &u, &v, &z); add(u, v, z); add(v, u, z); } while (bfs()) maxflow += dinic(s, INF); dfs(s); for (int i = 1; i <= n; i++) { if (vis[i]) { for (int j = head[i]; j; j = edge[j].nex) { if (!vis[edge[j].to]) printf("%d %d\n", i, edge[j].to); } } } puts(""); } return 0; }