#include #include #include #include #include using namespace std; const int INF = (int)1e9, lgmax = 20; int N, M, Q; vector> adj, block_adj; // Start of bridge-finding code. int timer, nblocks; vector visit; vector lowlink, tin, stack, block; vector> blocks; set> bridges; void dfs(int u, int p) { visit[u] = true; lowlink[u] = tin[u] = timer++; stack.push_back(u); int children = 0; for (int v : adj[u]) { if (v == p) { continue; } if (visit[v]) { lowlink[u] = min(lowlink[u], tin[v]); } else { dfs(v, u); lowlink[u] = min(lowlink[u], lowlink[v]); if (lowlink[v] > tin[u]) { bridges.insert({u, v}); } children++; } } if (lowlink[u] == tin[u]) { vector tmp; int v; do { v = stack.back(); stack.pop_back(); tmp.push_back(v); } while (u != v); blocks.push_back(tmp); } } void tarjan(int nodes) { visit.assign(nodes, false); lowlink.assign(nodes, 0); tin.assign(nodes, 0); bridges.clear(); stack.clear(); blocks.clear(); timer = 0; for (int i = 0; i < nodes; i++) { if (!visit[i]) { dfs(i, -1); } } // Get node to block mapping. block.assign(nodes, 0); nblocks = blocks.size(); for (int i = 0; i < nblocks; i++) { for (int j : blocks[i]) { block[j] = i; } } // Get bridge-block forest adjacencies. block_adj.assign(nblocks, {}); for (int i = 0; i < nodes; i++) { for (int j : adj[i]) { if (block[i] != block[j]) { block_adj[block[i]].push_back(block[j]); } } } } // Start of code to find odd cycles/distances to odd cycle blocks. bool no_odd_cycles; vector color; vector has_odd_cycle; vector dist_to_odd; bool dfs_color(int u, int c = 1) { // Color edges in search of an odd cycle. color[u] = c; int nextc = 3 - c; for (int v : adj[u]) { if (bridges.count({u, v}) || bridges.count({v, u})) { continue; } if (color[v]) { if (color[v] != nextc) { return true; } } else if (dfs_color(v, nextc)) { return true; } } return false; } void find_odd_cycles_and_distances() { color.assign(N, 0); has_odd_cycle.assign(nblocks, false); dist_to_odd.assign(nblocks, INF); queue q; for (int i = 0; i < nblocks; i++) { has_odd_cycle[i] = dfs_color(blocks[i].front()); if (has_odd_cycle[i]) { dist_to_odd[i] = 0; q.push(i); } } no_odd_cycles = q.empty(); while (!q.empty()) { int v = q.front(); q.pop(); for (int u : block_adj[v]) { if (dist_to_odd[u] == INF) { dist_to_odd[u] = dist_to_odd[v] + 1; q.push(u); } } } } // Start of binary lifting code for path-min queries. vector depth; vector> lift, liftval; void dfs_lift(int u, int p, int d) { depth[u] = d; lift[u][0] = p; liftval[u][0] = dist_to_odd[u]; for (int v : block_adj[u]) { if (v != p) { dfs_lift(v, u, d + 1); } } } void init_binary_lifting() { depth.assign(nblocks, -1); lift.assign(nblocks, vector(lgmax, -1)); liftval.assign(nblocks, vector(lgmax)); dfs_lift(0, -1, 0); for (int e = 1; e < lgmax; e++) { for (int u = 0; u < nblocks; u++) { if (lift[u][e - 1] != -1) { lift[u][e] = lift[lift[u][e - 1]][e - 1]; liftval[u][e] = min(liftval[u][e - 1], liftval[lift[u][e - 1]][e - 1]); } } } } int go_up(int u, int to_depth) { if (depth[u] == to_depth) { return u; } return go_up(lift[u][__builtin_ctz(depth[u] - to_depth)], to_depth); } int get_lca(int u, int v, int maxlift) { if (depth[u] != depth[v]) { if (depth[u] > depth[v]) { return get_lca(go_up(u, depth[v]), v, lgmax - 1); } return get_lca(u, go_up(v, depth[u]), lgmax - 1); } if (u == v) { return u; } if (lift[u][0] == lift[v][0]) { return lift[u][0]; } while (lift[u][maxlift] == lift[v][maxlift]) { --maxlift; } return get_lca(lift[u][maxlift], lift[v][maxlift], maxlift); } int path_min_go_up(int u, int to_depth) { if (depth[u] == to_depth) { return dist_to_odd[u]; } int e = __builtin_ctz(depth[u] - to_depth); return min(path_min_go_up(lift[u][e], to_depth), liftval[u][e]); } int path_min(int u, int v) { int lca = get_lca(u, v, lgmax - 1); return min(path_min_go_up(u, depth[lca]), path_min_go_up(v, depth[lca])); } // Main Solution. long long solve() { cin >> N >> M; adj.assign(N, {}); for (int i = 0, u, v; i < M; i++) { cin >> u >> v; --u, --v; adj[u].push_back(v); adj[v].push_back(u); } // Find bridges and bridge block tree. tarjan(N); // Find odd cycle blocks, and min-distance to odd cycles from each block. find_odd_cycles_and_distances(); // Initialize binary lifting for path mins. init_binary_lifting(); // Process queries. long long ans = 0; cin >> Q; for (int i = 0, a, b; i < Q; i++) { cin >> a >> b; --a, --b; ans += no_odd_cycles ? -1 : path_min(block[a], block[b]); } return ans; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }