Submit Info #55805

Problem Lang User Status Time Memory
Dominator Tree cpp leaf1415 AC 166 ms 82.47 MiB

ケース詳細
Name Status Time Memory
example_00 AC 1 ms 0.61 MiB
example_01 AC 1 ms 0.61 MiB
random_00 AC 102 ms 61.09 MiB
random_01 AC 166 ms 78.96 MiB
random_02 AC 40 ms 25.96 MiB
random_03 AC 145 ms 82.47 MiB
random_04 AC 8 ms 6.73 MiB

#include <iostream> #include <iomanip> #include <cstdio> #include <cmath> #include <ctime> #include <cstdlib> #include <cassert> #include <vector> #include <list> #include <stack> #include <queue> #include <deque> #include <map> #include <set> #include <bitset> #include <string> #include <algorithm> #include <utility> #include <complex> #include <unordered_set> #include <unordered_map> #define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++) #define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--) #define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++) #define chmin(x, y) (x) = min((x), (y)) #define chmax(x, y) (x) = max((x), (y)) #define sz(x) ((ll)(x).size()) #define ceil(x, y) (((x)+(y)-1) / (y)) #define all(x) (x).begin(),(x).end() #define outl(...) dump_func(__VA_ARGS__) #define outf(x) cout << fixed << setprecision(16) << (x) << endl #define inf 1e18 const double PI = 3.1415926535897932384626433; using namespace std; typedef long long llint; typedef long long ll; typedef pair<ll, ll> P; struct edge{ ll to, cost; edge(){} edge(ll a, ll b){ to = a, cost = b;} }; const ll dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1}; const ll mod = 1000000007; //const ll mod = 998244353; struct mint{ ll x = 0; mint(ll y = 0){x = y; if(x < 0 || x >= mod) x = (x%mod+mod)%mod;} mint(const mint &ope) {x = ope.x;} mint operator-(){return mint(-x);} mint operator+(const mint &ope){return mint(x) += ope;} mint operator-(const mint &ope){return mint(x) -= ope;} mint operator*(const mint &ope){return mint(x) *= ope;} mint operator/(const mint &ope){return mint(x) /= ope;} mint& operator+=(const mint &ope){ x += ope.x; if(x >= mod) x -= mod; return *this; } mint& operator-=(const mint &ope){ x += mod - ope.x; if(x >= mod) x -= mod; return *this; } mint& operator*=(const mint &ope){ x *= ope.x, x %= mod; return *this; } mint& operator/=(const mint &ope){ ll n = mod-2; mint mul = ope; while(n){ if(n & 1) *this *= mul; mul *= mul; n >>= 1; } return *this; } mint inverse(){return mint(1) / *this;} bool operator ==(const mint &ope){return x == ope.x;} bool operator !=(const mint &ope){return x != ope.x;} bool operator <(const mint &ope){return x < ope.x;} }; mint modpow(mint a, ll n){ if(n == 0) return mint(1); if(n % 2) return a * modpow(a, n-1); else return modpow(a*a, n/2); } istream& operator >>(istream &is, mint &ope){ ll t; is >> t, ope.x = t; return is; } ostream& operator <<(ostream &os, mint &ope){return os << ope.x;} ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;} vector<mint> fact, fact_inv; void make_fact(int n){ fact.resize(n+1), fact_inv.resize(n+1); fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i); fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1); } mint comb(ll n, ll k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];} mint perm(ll n, ll k){ return comb(n, k) * fact[k]; } vector<int> prime, pvec; void make_prime(int n){ prime.resize(n+1); rep(i, 2, n){ if(prime[i]) continue; for(int j = i; j <= n; j+=i) prime[j] = i; } rep(i, 2, n) if(prime[i] == i) pvec.push_back(i); } bool exceed(ll x, ll y, ll m){return x >= m / y + 1;} void mark(){ cout << "*" << endl; } void yes(){ cout << "YES" << endl; } void no(){ cout << "NO" << endl; } ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;} ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);} ll lcm(ll a, ll b){return a/gcd(a, b)*b;} ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;} ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;} string lltos(ll x){string ret; for(;x;x/=10) ret += x % 10 + '0'; reverse(ret.begin(), ret.end()); return ret;} ll stoll(string &s){ll ret = 0; for(auto c : s) ret *= 10, ret += c - '0'; return ret;} template<typename T> void uniq(T &vec){ sort(vec.begin(), vec.end()); vec.erase(unique(vec.begin(), vec.end()), vec.end());} template<class S, class T> pair<S, T>& operator+=(pair<S,T> &s, const pair<S,T> &t){ s.first += t.first, s.second += t.second; return s; } template<class S, class T> pair<S, T>& operator-=(pair<S,T> &s, const pair<S,T> &t){ s.first -= t.first, s.second -= t.second; return s; } template<class S, class T> pair<S, T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second); } template<class S, class T> pair<S, T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second); } template<typename T> ostream& operator << (ostream& os, vector<T>& vec) { for(int i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template<typename T> ostream& operator << (ostream& os, deque<T>& deq) { for(int i = 0; i < deq.size(); i++) os << deq[i] << (i + 1 == deq.size() ? "" : " "); return os; } template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } template<typename T, typename U> ostream& operator << (ostream& os, const pair<T, U>& pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) { for(typename map<T, U>::iterator itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if(itr != map_var.end()) os << ","; itr--; } return os; } template<typename T> ostream& operator << (ostream& os, set<T>& set_var) { for(typename set<T>::iterator itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if(itr != set_var.end()) os << " "; itr--; } return os; } template<typename T> ostream& operator << (ostream& os, multiset<T>& set_var) { for(typename multiset<T>::iterator itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if(itr != set_var.end()) os << " "; itr--; } return os; } template<typename T> void outa(T a[], ll s, ll t){for(ll i = s; i <= t; i++){ cout << a[i]; if(i < t) cout << " ";}cout << endl;} void dump_func(){cout << endl;} template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) { cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...); } struct DominatorTree{ int n, logn, id; vector<vector<int> > G, revG; vector<vector<int> > prev; vector<vector<P> > table; vector<int> vec, order, depth; vector<int> idom, sdom; vector<int> ans; DominatorTree(){} DominatorTree(int n){this->n = n, init();} void init(){ G.resize(n+1), revG.resize(n+1); for(int i = 1; i <= n; i++) G[i].clear(), revG[i].clear(); } void add_edge(int u, int v){ G[u].push_back(v); revG[v].push_back(u); } void predfs(int v, int p, int d) { vec.push_back(v); order[v] = ++id, depth[v] = d, prev[v][0] = p; for(auto u : G[v]){ if(order[u]) continue; predfs(u, v, d+1); } } int getLCA(int u, int v){ int x = u, y = v; if(depth[y] > depth[x]) swap(x, y); for(int i = logn-1; i >= 0; i--){ if(depth[x] - (1<<i) >= depth[y]) x = prev[x][i]; } if(x == y) return x; for(int i = logn-1; i >= 0; i--){ if(prev[x][i] != prev[y][i]){ x = prev[x][i]; y = prev[y][i]; } } x = prev[x][0]; return x; } void calc(int root) { for(int i = 0; ; i++) if(n <= (1<<i)){ logn = i; break; } vec.clear(), order.resize(n+1), prev.resize(n+1), depth.resize(n+1); for(int i = 1; i <= n; i++) order[i] = 0; for(int i = 0; i < prev.size(); i++) prev[i].resize(logn); id = 0, vec.push_back(0); predfs(root, 0, 0); prev[0][0] = 0; for(int i = 1; i < logn; i++) for(int j = 0; j <= n; j++) prev[j][i] = prev[prev[j][i-1]][i-1]; //rep(i, 1, n) cout << order[i] << " "; cout << endl; sdom.resize(n+1); for(int i = id; i >= 2; i--){ //sdom計算 int v = vec[i]; sdom[v] = i; for(auto u : revG[v]){ if(order[u] == 0) continue; if(order[u] < i) chmin(sdom[v], order[u]); if(order[u] > i) chmin(sdom[v], order[getLCA(u, v)]); } } //rep(i, 1, n) cout << sdom[i] << " "; cout << endl; table.resize(n+1); //sdomのパスminを求めるためのテーブル準備 for(int i = 0; i < table.size(); i++) table[i].resize(logn); table[0][0] = table[1][0] = P(inf, inf); for(int i = 2; i <= n; i++) table[i][0] = P(sdom[i], i); for(int i = 1; i < logn; i++) for(int j = 0; j <= n; j++){ ll u = prev[j][i-1]; table[j][i] = min(table[j][i-1], table[u][i-1]); } idom.resize(n+1); idom[vec[1]] = 1; //idom計算 for(int i = 2; i <= id; i++){ int v = vec[i], w = vec[sdom[v]], dif = depth[v] - depth[w]; int p = v; P mn = P(inf, inf); for(int i = 0; i < logn; i++){ if(dif & (1<<i)) chmin(mn, table[p][i]), p = prev[p][i]; } //outl(i, mn); if(mn.first == sdom[v]) idom[v] = sdom[v]; else idom[v] = idom[mn.second]; } //rep(i, 1, n) cout << idom[i] << " "; cout << endl; ans.resize(n+1); for(int i = 1; i <= n; i++) ans[i] = -1; for(int i = 1; i <= id; i++) ans[vec[i]] = vec[idom[vec[i]]]; } }; ll n, m, s; int main(void) { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> m >> s, s++; DominatorTree dt(n); ll u, v; rep(i, 1, m){ cin >> u >> v; u++, v++; dt.add_edge(u, v); } dt.calc(s); rep(i, 1, n){ if(dt.ans[i] == -1) cout << -1 << " "; else cout << dt.ans[i]-1 << " "; } cout << endl; return 0; }