#805271 (C++17) No.1326 ふたりのDominator

• 問題: No.1326 ふたりのDominator
• ユーザー: Nachia
• 提出日時: 2022-10-07 22:44:34
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 37 ms / 2,000 ms
• コード長: 19,345 bytes
• コンパイル時間: 1,314 ms
• コンパイル使用メモリ: 92,684 KB
• 最終ジャッジ日時: 2025-02-07 23:43:46
• ジャッジサーバーID （参考情報）: judge2 / judge2

ファイルパターン	結果
sample	AC * 1
other	AC * 24

ソースコード

#line 2 "nachia\\array\\csr-array.hpp"
#include <utility>
#include <vector>
#include <algorithm>

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, const std::vector<std::pair<int, Elem>>& items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = items[i].second;
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia
#line 5 "nachia\\tree\\heavy-light-decomposition.hpp"

namespace nachia{

struct HeavyLightDecomposition{
private:

    int N;
    std::vector<int> P;
    std::vector<int> PP;
    std::vector<int> PD;
    std::vector<int> D;
    std::vector<int> I;

    std::vector<int> rangeL;
    std::vector<int> rangeR;

public:

    HeavyLightDecomposition(const CsrArray<int>& E = CsrArray<int>::Construct(1, {})){
        N = E.size();
        P.assign(N, -1);
        I = {0};
        I.reserve(N);
        for(int i=0; i<(int)I.size(); i++){
            int p = I[i];
            for(int e : E[p]) if(P[p] != e){
                I.push_back(e);
                P[e] = p;
            }
        }
        std::vector<int> Z(N, 1);
        std::vector<int> nx(N, -1);
        PP.resize(N);
        for(int i=0; i<N; i++) PP[i] = i;
        for(int i=N-1; i>=1; i--){
            int p = I[i];
            Z[P[p]] += Z[p];
            if(nx[P[p]] == -1) nx[P[p]] = p;
            if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;
        }

        for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;

        PD.assign(N,N);
        PD[0] = 0;
        D.assign(N,0);
        for(int p : I) if(p != 0){
            PP[p] = PP[PP[p]];
            PD[p] = std::min(PD[PP[p]], PD[P[p]]+1);
            D[p] = D[P[p]]+1;
        }
        
        rangeL.assign(N,0);
        rangeR.assign(N,0);
        
        for(int p : I){
            rangeR[p] = rangeL[p] + Z[p];
            int ir = rangeR[p];
            for(int e : E[p]) if(P[p] != e) if(e != nx[p]){
                rangeL[e] = (ir -= Z[e]);
            }
            if(nx[p] != -1){
                rangeL[nx[p]] = rangeL[p] + 1;
            }
        }

        I.resize(N);
        for(int i=0; i<N; i++) I[rangeL[i]] = i;
    }

    int depth(int p) const { return D[p]; }
    int to_seq(int vertex) const { return rangeL[vertex]; }
    int to_vtx(int seqidx) const { return I[seqidx]; }
    int parent_of(int v) const { return P[v]; }
    int heavy_root_of(int v) const { return PP[v]; }
    int heavy_child_of(int v) const {
        if(to_seq(v) == N-1) return -1;
        int cand = to_vtx(to_seq(v) + 1);
        if(PP[v] == PP[cand]) return cand;
        return -1;
    }

    int lca(int u, int v) const {
        if(PD[u] < PD[v]) std::swap(u, v);
        while(PD[u] > PD[v]) u = P[PP[u]];
        while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }
        return (D[u] > D[v]) ? v : u;
    }

    int dist(int u, int v) const {
        return depth(u) + depth(v) - depth(lca(u,v)) * 2;
    }

    std::vector<std::pair<int,int>> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
        if(PD[c] < PD[r]) return {};
        std::vector<std::pair<int,int>> res(PD[c]-PD[r]+1);
        for(int i=0; i<(int)res.size()-1; i++){
            res[i] = std::make_pair(rangeL[PP[c]], rangeL[c]+1);
            c = P[PP[c]];
        }
        if(PP[r] != PP[c] || D[r] > D[c]) return {};
        res.back() = std::make_pair(rangeL[r]+(include_root?0:1), rangeL[c]+1);
        if(res.back().first == res.back().second) res.pop_back();
        if(!reverse_path) std::reverse(res.begin(),res.end());
        else for(auto& a : res) a = std::make_pair(N - a.second, N - a.first);
        return res;
    }

    std::pair<int,int> subtree(int p){
        return std::make_pair(rangeL[p], rangeR[p]);
    }

    int median(int x, int y, int z) const {
        return lca(x,y) ^ lca(y,z) ^ lca(x,z);
    }

    int la(int from, int to, int d) const {
        if(d < 0) return -1;
        int g = lca(from,to);
        int dist0 = D[from] - D[g] * 2 + D[to];
        if(dist0 < d) return -1;
        int p = from;
        if(D[from] - D[g] < d){ p = to; d = dist0 - d; }
        while(D[p] - D[PP[p]] < d){
            d -= D[p] - D[PP[p]] + 1;
            p = P[PP[p]];
        }
        return I[rangeL[p] - d];
    }
};

} // namespace nachia
#line 4 "nachia\\graph\\graph.hpp"
#include <cassert>
#line 6 "nachia\\graph\\graph.hpp"

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
    };
    using Base = std::vector<std::pair<int, int>>;
    Graph(int n = 0, bool undirected = false) : m_n(n), m_e(), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    Graph(int n, const std::vector<Edge>& edges, bool undirected = false) : m_n(n), m_e(edges), m_isUndir(undirected) {}
    Graph(int n, std::vector<Edge>&& edges, bool undirected = false) : m_n(n), m_e(edges), m_isUndir(undirected) {}
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = ++newV[mapping[i]];
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia
#line 3 "nachia\\graph\\dfs-tree.hpp"

namespace nachia{

struct DfsTree{
    std::vector<int> dfsOrd;
    std::vector<int> parent;

    template<bool OutOrd>
    static DfsTree Construct(const CsrArray<int>& adj){
        DfsTree res;
        int n = adj.size();
        res.dfsOrd.resize(n);
        int Oi = 0;
        std::vector<int> eid(n, 0), parent(n, -2);
        for(int s=0; s<n; s++) if(parent[s] == -2){
            int p = s;
            if(p >= n) p -= n;
            parent[p] = -1;
            while(0 <= p){
                if(eid[p] == (OutOrd ? (int)adj[p].size() : 0)) res.dfsOrd[Oi++] = p;
                if(eid[p] == (int)adj[p].size()){ p = parent[p]; continue; }
                int nx = adj[p][eid[p]++];
                if(parent[nx] != -2) continue;
                parent[nx] = p;
                p = nx;
            }
        }
        res.parent = std::move(parent);
        return res;
    }
    template<bool OutOrd>
    static DfsTree Construct(const Graph& g){ return Construct<OutOrd>(g.getAdjacencyArray()); }
};

} // namespace nachia
#line 6 "nachia\\graph\\biconnected-components.hpp"

namespace nachia{

class BiconnectedComponents{
private:
    int mn;
    int mm;
    int mnum_bcs;
    Graph mG;
    std::vector<std::pair<int,int>> m_bcVtxPair;
public:
    BiconnectedComponents(Graph G = Graph(0, true)){
        int n = mn = G.numVertices();
        int m = mm = G.numEdges();
        mG = std::move(G);
        if(n == 0){ mnum_bcs = 0; return; }
        auto adj = mG.getAdjacencyArray();

        auto dfstree = DfsTree::Construct<false>(adj);
        std::vector<int> vtxToDfsi(n), parent, low;
        for(int i=0; i<n; i++) vtxToDfsi[dfstree.dfsOrd[i]] = i;
        parent = std::move(dfstree.parent);
        low = vtxToDfsi;
        
        for(int p=0; p<n; p++) for(int e : adj[p]) low[p] = std::min(low[p], vtxToDfsi[e]);

        for(int i=n-1; i>=0; i--){
            int p = dfstree.dfsOrd[i];
            int pp = parent[p];
            if(pp >= 0) low[pp] = std::min(low[pp], low[p]);
        }
        
        int num_bcs = 0;
        std::vector<int> res(m);
        for(int p : dfstree.dfsOrd) if(parent[p] >= 0){
            int pp = parent[p];
            if(low[p] < vtxToDfsi[pp]){
                low[p] = low[pp];
                m_bcVtxPair.push_back(std::make_pair(low[p], p));
            }
            else{
                low[p] = num_bcs++;
                m_bcVtxPair.push_back(std::make_pair(low[p], pp));
                m_bcVtxPair.push_back(std::make_pair(low[p], p));
            }
        }
        for(int s=0; s<mn; s++) if(adj[s].size() == 0) m_bcVtxPair.push_back(std::make_pair(num_bcs++, s));
        mnum_bcs = num_bcs;
    }

    int numComponents() const { return mnum_bcs; }

    CsrArray<int> getBcVertices() const {
        return CsrArray<int>::Construct(numComponents(), m_bcVtxPair);
    }

    Graph getBcTree() const {
        int bct_n = mn + mnum_bcs;
        std::vector<std::pair<int, int>> res = m_bcVtxPair;
        for(auto& e : res) e.first += mn;
        return Graph(bct_n, std::move(res), true);
    }

    CsrArray<int> getBcEdges() const {
        auto bct = getBcTree().getAdjacencyArray();
        std::vector<int> bfsP(bct.size(), -1);
        std::vector<int> bfsD(bct.size(), 0);
        std::vector<int> bfs(bct.size());
        int p0 = 0, p1 = 0;
        for(int s=0; s<bct.size(); s++) if(bfsP[s] < 0){
            for(bfs[p1++]=s; p0<p1; p0++){
                int p = bfs[p0];
                for(auto e : bct[p]) if(bfsP[p] != e){
                    bfsP[e] = p;
                    bfsD[e] = bfsD[p] + 1;
                    bfs[p1++] = e;
                }
            }
        }
        std::vector<std::pair<int,int>> res(mm);
        for(int i=0; i<mm; i++){
            int u = mG[i].from, v = mG[i].to;
            res[i].first = bfsP[(bfsD[u] <= bfsD[v]) ? v : u] - mn;
            res[i].second = i;
        }
        return CsrArray<int>::Construct(mnum_bcs, res);
    }
};

} // namespace nachia
#line 2 "nachia\\misc\\fastio.hpp"
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <string>

namespace nachia{

struct CInStream{
private:
	static const unsigned int INPUT_BUF_SIZE = 1 << 17;
	unsigned int p = INPUT_BUF_SIZE;
	static char Q[INPUT_BUF_SIZE];
public:
	using MyType = CInStream;
	char seekChar(){
		if(p == INPUT_BUF_SIZE){
			size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);
			if(len != INPUT_BUF_SIZE) Q[len] = '\0';
			p = 0;
		}
		return Q[p];
	}
	void skipSpace(){ while(isspace(seekChar())) p++; }
	uint32_t nextU32(){
		skipSpace();
		uint32_t buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
	int32_t nextI32(){
		skipSpace();
		if(seekChar() == '-'){ p++; return (int32_t)(-nextU32()); }
		return (int32_t)nextU32();
	}
	uint64_t nextU64(){
		skipSpace();
		uint64_t buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
	int64_t nextI64(){
		skipSpace();
		if(seekChar() == '-'){ p++; return (int64_t)(-nextU64()); }
		return (int64_t)nextU64();
	}
	char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }
	std::string nextToken(){
		skipSpace();
		std::string buf;
		while(true){
			char ch = seekChar();
			if(isspace(ch) || ch == '\0') break;
			buf.push_back(ch);
			p++;
		}
		return buf;
	}
	MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }
	MyType& operator>>(int& dest){ dest = nextI32(); return *this; }
	MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
	MyType& operator>>(char& dest){ dest = nextChar(); return *this; }
} cin;

struct FastOutputTable{
	char LZ[1000][4] = {};
	char NLZ[1000][4] = {};
	constexpr FastOutputTable(){
		using u32 = uint_fast32_t;
		for(u32 d=0; d<1000; d++){
			LZ[d][0] = ('0' + d / 100 % 10);
			LZ[d][1] = ('0' + d /  10 % 10);
			LZ[d][2] = ('0' + d /   1 % 10);
			LZ[d][3] = '\0';
		}
		for(u32 d=0; d<1000; d++){
			u32 i = 0;
			if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);
			if(d >=  10) NLZ[d][i++] = ('0' + d /  10 % 10);
			if(d >=   1) NLZ[d][i++] = ('0' + d /   1 % 10);
			NLZ[d][i++] = '\0';
		}
	}
};

struct COutStream{
private:
	using u32 = uint32_t;
	using u64 = uint64_t;
	using MyType = COutStream;
	static const u32 OUTPUT_BUF_SIZE = 1 << 17;
	static char Q[OUTPUT_BUF_SIZE];
	static constexpr FastOutputTable TB = FastOutputTable();
	u32 p = 0;
	static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }
	static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }
	template<class T, class U> static void Fil(T& m, U& l, U x) noexcept { m = l/x; l -= m*x; }
	void next_dig9(u32 x){
		u32 y;
		Fil(y, x, P10(6));
		nextCstr(TB.LZ[y]);
		Fil(y, x, P10(3));
		nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
	}
public:
	void nextChar(char c){
		Q[p++] = c;
		if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }
	}
	void nextEoln(){ nextChar('\n'); }
	void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }
	void nextU32(uint32_t x){
		u32 y = 0;
		if(x >= P10(9)){
			Fil(y, x, P10(9));
			nextCstr(TB.NLZ[y]); next_dig9(x);
		}
		else if(x >= P10(6)){
			Fil(y, x, P10(6));
			nextCstr(TB.NLZ[y]);
			Fil(y, x, P10(3));
			nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= P10(3)){
			Fil(y, x, P10(3));
			nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= 1) nextCstr(TB.NLZ[x]);
		else nextChar('0');
	}
	void nextI32(int32_t x){
		if(x >= 0) nextU32(x);
		else{ nextChar('-'); nextU32((u32)-x); }
	}
	void nextU64(uint64_t x){
		u32 y = 0;
		if(x >= P10L(18)){
			Fil(y, x, P10L(18));
			nextU32(y);
			Fil(y, x, P10L(9));
			next_dig9(y); next_dig9(x);
		}
		else if(x >= P10L(9)){
			Fil(y, x, P10L(9));
			nextU32(y); next_dig9(x);
		}
		else nextU32(x);
	}
	void nextI64(int64_t x){
		if(x >= 0) nextU64(x);
		else{ nextChar('-'); nextU64((u64)-x); }
	}
	void writeToFile(bool flush = false){
		fwrite(Q, p, 1, stdout);
		if(flush) fflush(stdout);
		p = 0;
	}
	COutStream(){ Q[0] = 0; }
	~COutStream(){ writeToFile(); }
	MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }
	MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }
	MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }
	MyType& operator<<(int tg){ nextI32(tg); return *this; }
	MyType& operator<<(long tg){ nextI64(tg); return *this; }
	MyType& operator<<(long long tg){ nextI64(tg); return *this; }
	MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }
	MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }
	MyType& operator<<(char tg){ nextChar(tg); return *this; }
} cout;

char CInStream::Q[INPUT_BUF_SIZE];
char COutStream::Q[OUTPUT_BUF_SIZE];

} // namespace nachia
#line 6 "Main.cpp"
#define rep(i,n) for(int i=0; i<(int)(n); i++)

int main() {
    using nachia::cin, nachia::cout;
    int n; cin >> n;
    int m; cin >> m;
    nachia::Graph G(n, true);
    for(int i=0; i<m; i++){ int u,v; cin >> u >> v; G.addEdge(u-1, v-1); }
    auto hld_bct = nachia::HeavyLightDecomposition(nachia::BiconnectedComponents(G).getBcTree().getAdjacencyArray());
    int q; cin >> q;
    for(int queryi=0; queryi<q; queryi++){
        int u,v; cin >> u >> v; u--; v--;
        int d = hld_bct.dist(u,v);
        int ans = std::max(0, d/2-1);
        cout << ans << '\n';
    }
    return 0;
}