Submission #45267

#TimeUsernameProblemLanguageResultExecution timeMemory
45267bugmenot111One-Way Streets (CEOI17_oneway)C++14
0 / 100
3065 ms262144 KiB
/* if an edge is not a bridge it can be oriented either way; the orientation of the bridges is uniquely determined; let's call the input pairs "required pairs"; for each bridge B: if there is no required pair with a node from the first component of the graph and the second component of the graph: B can be oriented either way otherwise: orient B the same way as the required pair from component A to component B obviously, there cannot be two required pairs with different orientations because there can be no solution! Algorithm: Build "bridge tree" T of G For every pair going from comp(u) to comp(v) in T: orient all edges from comp(u) to LCA(comp(u), comp(v)) upwards orient all edges from LCA(comp(u), comp(v)) to comp(v) downwards The loop can be optimized by using a version of the difference array on the tree. */ #include <cstdio> #include <vector> #include <utility> #include <algorithm> #include <numeric> #include <string> #include <functional> #define MAXN 100100 typedef std::vector< std::pair<int, int> > edge_list; typedef std::vector< std::vector<int> > graph; typedef std::vector< std::vector< std::pair<int, int> > > labeled_edge_graph; std::vector<int> label_vertices(const int n, const int m, const edge_list& el) { static int dsu[MAXN]; static bool isbridge[MAXN]; static bool vis[MAXN]; static int T; static int arr[MAXN]; std::vector<int> ans(n); graph g(MAXN); auto build_edge_graph = [&]{ size_t n = el.size(); for(size_t i = 0; i < n; i++) { g[el[i].first].push_back(el[i].second); g[el[i].second].push_back(el[i].first); } }; auto adj = [&](int u, int e) { return el[e].first ^ el[e].second ^ u; }; std::function<int(int)> f; f = [&](int x)->int { return dsu[x] == x ? x : dsu[x] = f(dsu[x]); }; auto merge = [&](int x, int y) { dsu[f(x)] = f(y); }; std::function<int(int, int)> dfs0; dfs0 = [&](int u, int edge)->int { vis[u] = true; int dbe = arr[u] = T++; for(const auto& e: g[u]) { int w = adj(u, e); if(!vis[w]) dbe = std::min(dbe, dfs0(w, e)); else if(e != edge) dbe = std::min(dbe, arr[w]); } if(dbe == arr[u] && edge != -1) isbridge[edge] = true; else if(edge != -1) merge(el[edge].first, el[edge].second); return dbe; }; build_edge_graph(); std::iota(dsu, dsu + MAXN, 0); for(int i = 0; i < n; i++) if(!vis[i]) dfs0(i, -1); for(int i = 0; i < n; i++) ans[i] = f(i); int x = *std::min_element(ans.begin(), ans.end()); for(int i = 0; i < n; i++) ans[i] -= x; return ans; } std::vector<int> get_dfs_order(const labeled_edge_graph& tree) { std::vector<int> ans; std::function<void(int, int)> dfs; dfs = [&](int v, int p) { for(const auto& c: tree[v]) if(c.first != p) dfs(c.first, v); ans.push_back(v); }; dfs(0, -1); return ans; } struct f2lk_dsu { int par[MAXN]; int rnk[MAXN]; int find(int x) { return par[x] == x ? x : par[x] = find(par[x]); } void unite(int x, int y) { x = find(x); y = find(y); if(x == y) return; if(rnk[x] > rnk[y]) par[y] = x; else if(rnk[x] < rnk[y]) par[x] = y; else if(rnk[x] == rnk[y]) rnk[par[y] = x]++; } f2lk_dsu() { std::iota(par, par + MAXN, 0); } }; std::vector<int> offline_lca(const labeled_edge_graph& tree, const std::vector<int>& dfs_order, const edge_list& queries) { static f2lk_dsu d; static int ancestor[MAXN]; static bool black[MAXN]; static bool visited[MAXN]; static edge_list qr[MAXN]; std::vector<int> lc(queries.size()); for(int i = 0; i < queries.size(); i++) { auto p = queries[i]; qr[p.first].push_back({p.second, i}); qr[p.second].push_back({p.first, i}); } for(const int u: dfs_order) { visited[u] = true; for(const auto& p: tree[u]) if(visited[p.first]) { int v = p.first; d.unite(u, v); ancestor[d.find(u)] = u; } black[u] = true; for(const auto& p: qr[u]) if(black[p.first]) lc[p.second] = ancestor[d.find(p.first)]; } return lc; } std::string solve(const int n, const int m, const int p, const edge_list& el, const edge_list& pairs) { static int up_edges[MAXN]; static int down_edges[MAXN]; static bool visited[MAXN]; static std::string ans(m, 'B'); labeled_edge_graph tree(MAXN); edge_list p2(pairs); auto lab = label_vertices(n, m, el); // build bridge-block tree for(int i = 0; i < m; i++) { int x = lab[el[i].first]; int y = lab[el[i].second]; if(x != y) { tree[x].push_back({y, i}); tree[y].push_back({x, i}); } } for(auto& p: p2) p = {lab[p.first], lab[p.second]}; std::sort(p2.begin(), p2.end()); p2.erase(std::unique(p2.begin(), p2.end()), p2.end()); auto dfs_order = get_dfs_order(tree); auto lc = offline_lca(tree, dfs_order, p2); for(int i = 0; i < p2.size(); i++) { int x = p2[i].first; int y = p2[i].second; int l = lc[i]; up_edges[x]++; up_edges[l]--; down_edges[y]++; down_edges[l]--; } for(int i: dfs_order) { visited[i] = true; int pedge = -1; for(const auto& p: tree[i]) { if(!visited[p.first]) pedge = p.second; else { up_edges[i] += up_edges[p.first]; down_edges[i] += down_edges[p.first]; } } if(pedge == -1) continue; if(up_edges[i] == 0 && down_edges[i] != 0) ans[pedge] = el[pedge].first == i ? 'R' : 'L'; else if(up_edges[i] != 0 && down_edges[i] == 0) ans[pedge] = el[pedge].first == i ? 'L' : 'R'; } return ans; } int main(void) { int n, m, p; scanf("%d%d", &n, &m); edge_list edges(m); for(int i = 0; i < m; i++) { int x; int y; scanf("%d%d", &x, &y); edges[i] = {x - 1, y - 1}; } scanf("%d", &p); edge_list pairs(p); for(int i = 0; i < p; i++) { int x; int y; scanf("%d%d", &x, &y); pairs[i] = {x - 1, y - 1}; } puts(solve(n, m, p, edges, pairs).c_str()); return 0; }

Compilation message (stderr)

oneway.cpp: In function 'std::vector<int> label_vertices(int, int, const edge_list&)':
oneway.cpp:30:14: warning: variable 'isbridge' set but not used [-Wunused-but-set-variable]
  static bool isbridge[MAXN];
              ^~~~~~~~
oneway.cpp: In function 'std::vector<int> offline_lca(const labeled_edge_graph&, const std::vector<int>&, const edge_list&)':
oneway.cpp:111:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i = 0; i < queries.size(); i++) {
                 ~~^~~~~~~~~~~~~~~~
oneway.cpp: In function 'std::__cxx11::string solve(int, int, int, const edge_list&, const edge_list&)':
oneway.cpp:151:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i = 0; i < p2.size(); i++) {
                 ~~^~~~~~~~~~~
oneway.cpp: In function 'int main()':
oneway.cpp:178:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &n, &m);
  ~~~~~^~~~~~~~~~~~~~~~
oneway.cpp:183:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d%d", &x, &y);
   ~~~~~^~~~~~~~~~~~~~~~
oneway.cpp:186:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &p);
  ~~~~~^~~~~~~~~~
oneway.cpp:191:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d%d", &x, &y);
   ~~~~~^~~~~~~~~~~~~~~~
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