109 lines
3.9 KiB
C++
109 lines
3.9 KiB
C++
namespace tarjan {
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struct mutex_cond {
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int v1; bool cond1;
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int v2; bool cond2;
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mutex_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
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};
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struct inclusive_cond {
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int v1; bool cond1;
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int v2; bool cond2;
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inclusive_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
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};
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// Returns the mapping between vertices and their affiliated sccs.
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vector<int> scc(const vector<vector<int>>& ch) {
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int n = ch.size();
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int cnt = 0, scn = 0;
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vector<int> dfn(n), low(n), vis(n), st;
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vector<int> br(n);
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auto tarjan = [&] (auto tarjan, int v) -> void {
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dfn[v]=low[v]=++cnt;
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st.push_back(v);
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vis[v]=1;
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for(const auto&u:ch[v])
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if(!dfn[u]) tarjan(tarjan, u),low[v]=min(low[v],low[u]);
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else if(vis[u])low[v]=min(low[v],dfn[u]);
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if(dfn[v]==low[v]){
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++scn;
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int u;
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do u=st.back(), st.pop_back(),vis[u]=0,br[u]=scn; while(u!=v);
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}
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};
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for (int i = 0; i < n; ++i) {
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if (!dfn[i]) {
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tarjan(tarjan, i);
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}
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}
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return br;
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}
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// This method can eliminate redundant edges or self-loops
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vector<vector<int>> build_scc(const vector<vector<int>>& ch) {
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int n = ch.size();
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auto br = scc(ch);
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int cnt = *max_element(br.begin(), br.end());
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vector<unordered_set<int, safe_hash>> rb(cnt + 1);
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for (int i = 0; i < n; ++i) {
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for (auto&& u : ch[i]) {
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if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
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}
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}
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vector<vector<int>> res(cnt + 1);
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for (int i = 1; i <= cnt; ++i) {
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res[i] = vector<int>(rb[i].begin(), rb[i].end());
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}
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return res;
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}
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// This method can eliminate redundant edges or self-loops
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// return form: (scc size, children of scc)
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vector<pair<size_t, vector<int>>> build_scc_with_size(const vector<vector<int>>& ch) {
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int n = ch.size();
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auto br = scc(ch);
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int cnt = *max_element(br.begin(), br.end());
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vector<unordered_set<int, safe_hash>> rb(cnt + 1);
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for (int i = 0; i < n; ++i) {
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for (auto&& u : ch[i]) {
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if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
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}
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}
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vector<pair<size_t, vector<int>>> res(cnt + 1);
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for (int i = 1; i <= cnt; ++i) {
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res[i].second = vector<int>(rb[i].begin(), rb[i].end());
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}
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for (int i = 1; i <= n; ++i) {
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res[br[i]].first += 1;
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}
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return res;
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}
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// indices start from 1, result has `n` items
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optional<vector<bool>> solve_twosat(int n, const vector<mutex_cond>& conditions) {
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vector<vector<int>> ch(2 * n + 1);
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for (auto&& [v1, cond1, v2, cond2] : conditions) {
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ch[(1 ^ cond1) * n + v1].emplace_back(cond2 * n + v2);
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ch[(1 ^ cond2) * n + v2].emplace_back(cond1 * n + v1);
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}
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auto sccno = scc(ch);
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for (int i = 1; i <= n; ++i) {
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if (sccno[i] == sccno[i + n]) {
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return nullopt;
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}
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}
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vector<bool> res;
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for (int i = 1; i <= n; ++i) {
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if (sccno[i] < sccno[i + n]) {
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res.emplace_back(false);
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} else {
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res.emplace_back(true);
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}
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}
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return res;
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};
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// indices start from 1, result has `n` items
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optional<vector<bool>> solve_twosat(int n, const vector<inclusive_cond>& conditions) {
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vector<mutex_cond> trans_conds;
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for (auto&& [v1, cond1, v2, cond2] : conditions) {
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trans_conds.emplace_back(v1, cond1, v2, not cond2);
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}
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return solve_twosat(n, trans_conds);
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}
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}
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