#979460 (C++23) No.650 行列木クエリ

• 問題: No.650 行列木クエリ
• ユーザー: butsurizuki
• 提出日時: 2024-05-07 02:47:33
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 247 ms / 2,000 ms
• コード長: 17,935 bytes
• コンパイル時間: 4,645 ms
• コンパイル使用メモリ: 289,732 KB
• 実行使用メモリ: 71,684 KB
• 最終ジャッジ日時: 2024-11-29 15:15:13
• 合計ジャッジ時間: 6,679 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,820 KB
testcase_01	AC	101 ms; 16,896 KB
testcase_02	AC	247 ms; 62,432 KB
testcase_03	AC	2 ms; 6,820 KB
testcase_04	AC	108 ms; 16,768 KB
testcase_05	AC	247 ms; 62,384 KB
testcase_06	AC	2 ms; 6,820 KB
testcase_07	AC	2 ms; 6,820 KB
testcase_08	AC	109 ms; 18,688 KB
testcase_09	AC	236 ms; 71,684 KB
testcase_10	AC	2 ms; 6,816 KB

ソースコード

// HLD & verify
// find "HLD starts here"

#include<bits/stdc++.h>

#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>


#ifdef _MSC_VER
#include <intrin.h>
#endif

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
}

#endif

int countr_zero(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

#if __cplusplus >= 201703L

template <class S, auto op, auto e> struct segtree {
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");

#else

template <class S, S (*op)(S, S), S (*e)()> struct segtree {

#endif

  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)internal::bit_ceil((unsigned int)(_n));
        log = internal::countr_zero((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder


#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>


namespace atcoder {

#if __cplusplus >= 201703L

template <class S,
          auto op,
          auto e,
          class F,
          auto mapping,
          auto composition,
          auto id>
struct lazy_segtree {
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");
    static_assert(
        std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
        "mapping must work as F(F, S)");
    static_assert(
        std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
        "compostiion must work as F(F, F)");
    static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
                  "id must work as F()");

#else

template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {

#endif

  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)internal::bit_ceil((unsigned int)(_n));
        log = internal::countr_zero((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder

using namespace std;
using namespace atcoder;

// HLD starts here

using Graph=vector<vector<int>>;
using pi=pair<int,int>;

struct HLD{
  vector<int> pareg;
  vector<int> backeg;
  vector<int> dep;
  int cureg;
  vector<int> topv;
  vector<int> tope;
  bool vwei; // true: vertex-weighted, false: edge-weighted

  HLD(int n,Graph &g,bool vw,int root=0){
    vwei=vw;

    dfs1(root,-1,g);

    pareg.resize(n);
    backeg.resize(n);
    dep.resize(n);
    topv.resize(n);
    tope.resize(n);

    cureg=1;
    pareg[root]=0;
    topv[0]=-1;
    tope[0]=0;

    dfs2(root,-1,0,true,g);
  }

  int dfs1(int v,int pv,Graph &g){
    int res=1;
    int uid=-1,umax=-1;
    for(int i=0;i<g[v].size();i++){
      if(g[v][i]==pv){continue;}

      int und=dfs1(g[v][i],v,g);
      res+=und;
      if(umax<und){
        umax=und;
        uid=i;
      }
    }
    if(uid>0){
      swap(g[v][uid],g[v][0]);
    }
    return res;
  }

  void dfs2(int v,int pv,int cdep,bool upheav,Graph &g){
    dep[v]=cdep;

    for(int i=0;i<g[v].size();i++){
      if(g[v][i]==pv){continue;}

      if(i==0){
        // heavy
        if(upheav){
          topv[cureg]=topv[pareg[v]];
          tope[cureg]=tope[pareg[v]];
        }
        else{
          topv[cureg]=v;
          tope[cureg]=cureg;
        }

        pareg[g[v][i]]=cureg;
        cureg++;
        dfs2(g[v][i],v,cdep+1,true,g);
      }
      else{
        // light
        topv[cureg]=v;
        tope[cureg]=cureg;

        pareg[g[v][i]]=cureg;
        cureg++;
        dfs2(g[v][i],v,cdep+1,false,g);
      }
    }

    backeg[v]=cureg;
  }

  // single vertex (for vertex-weighted)
  int single(int v){
    return pareg[v];
  }

  // subtree is [l,r]
  pi subtree(int v){
    if(vwei){
      return {pareg[v],backeg[v]-1};
    }
    else{
      return {pareg[v]+1,backeg[v]-1};
    }
  }

  // u->v path is {[l0,r0], [l1,r1], ...}
  // each segments may reversed (so li<=ri may NOT be satisfied)
  vector<pi> path(int u,int v){
    vector<pi> uu;
    vector<pi> vv;
    while(u!=v){
      if(tope[pareg[u]]==tope[pareg[v]]){ // same path
        if(dep[u]>dep[v]){
          // u goes up
          uu.push_back({pareg[u],pareg[u]-(dep[u]-dep[v]-1)});
          u=v;
        }
        else{
          // v goes up
          vv.push_back({pareg[v],pareg[v]-(dep[v]-dep[u]-1)});
          v=u;
        }
        break;
      }

      int du=-1;
      int dv=-1;
      if(topv[pareg[u]]>=0){du=dep[topv[pareg[u]]];}
      if(topv[pareg[v]]>=0){dv=dep[topv[pareg[v]]];}

      if(du>dv){
        // u goes up
        uu.push_back({pareg[u],tope[pareg[u]]});
        u=topv[pareg[u]];
      }
      else{
        // v goes up
        vv.push_back({pareg[v],tope[pareg[v]]});
        v=topv[pareg[v]];
      }
    }

    vector<pi> res;
    for(auto &nx : uu){
      res.push_back(nx);
    }
    if(vwei){
      res.push_back({pareg[u],pareg[u]});
    }
    reverse(vv.begin(),vv.end());
    for(auto &nx : vv){
      swap(nx.first,nx.second);
      res.push_back(nx);
    }
    return res;
  }
};

long long op_sum(long long a,long long b){
  return (a+b);
}
long long e_sum(){
  return 0;
}

// https://judge.yosupo.jp/problem/vertex_add_path_sum
void val_yosupo_VAPS(){
  int n,q;
  cin >> n >> q;
  vector<int> a(n);
  for(auto &nx : a){cin >> nx;}
  Graph g(n);
  for(int i=0;i<n-1;i++){
    int u,v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  HLD hld(n,g,true); // vertex-weighted

  vector<long long> ini(n,0);
  for(int i=0;i<n;i++){
    ini[hld.single(i)]=a[i];
  }
  segtree<long long,op_sum,e_sum> seg(ini);
  while(q>0){
    q--;
    int typ;
    cin >> typ;
    if(typ==0){
      int u;
      long long x;
      cin >> u >> x;
      int pos=hld.single(u);
      seg.set(pos,seg.get(pos)+x);
    }
    else{
      int u,v;
      cin >> u >> v;
      vector<pi> ss=hld.path(u,v);
      long long res=0;
      for(auto &nx : ss){
        res+=seg.prod(min(nx.first,nx.second),max(nx.first,nx.second)+1);
      }
      cout << res << "\n";
    }
  }
}

#define mod 998244353

using pl=pair<long long,long long>;

pl op_aff(pl l,pl r){
  return {
    (l.first*r.first)%mod,
    (l.second*r.first+r.second)%mod
  };
}
pl e_aff(){return {1,0};}

// https://judge.yosupo.jp/problem/vertex_set_path_composite
void val_yosupo_VSPC(){
  int n,q;
  cin >> n >> q;
  vector<pl> a(n);
  for(auto &nx : a){
    cin >> nx.first >> nx.second;
  }
  Graph g(n);
  for(int i=0;i<n-1;i++){
    int u,v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  HLD hld(n,g,true); // vertex-weighted

  vector<pl> ini(2*n);
  for(int i=0;i<n;i++){
    ini[hld.single(i)]=a[i];
    ini[2*n-1-hld.single(i)]=a[i];
  }

  segtree<pl,op_aff,e_aff> seg(ini);

  while(q>0){
    q--;
    int typ;
    cin >> typ;
    if(typ==0){
      int p;
      pl x;
      cin >> p >> x.first >> x.second;

      seg.set(hld.single(p),x);
      seg.set(2*n-1-hld.single(p),x);
    }
    else{
      int u,v;
      long long x;
      cin >> u >> v >> x;

      vector<pi> ss=hld.path(u,v);
      pl cf=e_aff();

      for(auto &nx : ss){
        if(nx.first<=nx.second){
          cf=op_aff(cf,seg.prod(nx.first,nx.second+1));
        }
        else{
          cf=op_aff(cf,seg.prod((2*n-1-nx.first),(2*n-1-nx.second)+1));
        }
      }

      cout << (x*cf.first+cf.second)%mod << "\n";
    }
  }
}

#define mod107 1000000007

using vl=vector<long long>;
vl op_mat2(vl l,vl r){
  return {
    (l[0]*r[0]+l[1]*r[2])%mod107,
    (l[0]*r[1]+l[1]*r[3])%mod107,
    (l[2]*r[0]+l[3]*r[2])%mod107,
    (l[2]*r[1]+l[3]*r[3])%mod107
  };
}
vl e_mat2(){
  return {1,0,0,1};
}

// https://yukicoder.me/problems/no/650
void val_ykc_650(){
  int n;
  cin >> n;
  Graph g(n);
  vector<int> uu(n-1),vv(n-1);
  for(int i=0;i<n-1;i++){
    int u,v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
    uu[i]=u;
    vv[i]=v;
  }

  HLD hld(n,g,false);
  segtree<vl,op_mat2,e_mat2> seg(2*n);

  int q;
  cin >> q;
  while(q>0){
    q--;
    string typ;
    cin >> typ;
    if(typ[0]=='x'){
      int i;
      cin >> i;
      if(hld.dep[uu[i]]<hld.dep[vv[i]]){
        swap(uu[i],vv[i]);
      }
      int eid=hld.pareg[uu[i]];

      vl x=e_mat2();
      for(auto &nx : x){cin >> nx;}
      seg.set(eid,x);
      seg.set(2*n-1-eid,x);
    }
    else{
      int u,v;
      cin >> u >> v;
      vector<pi> pt=hld.path(u,v);
      vl x=e_mat2();
      for(auto &nx : pt){
        if(nx.first<=nx.second){
          x=op_mat2(x,seg.prod(nx.first,nx.second+1));
        }
        else{
          x=op_mat2(x,seg.prod(2*n-1-nx.first,(2*n-1-nx.second)+1));
        }
      }
      cout << x[0] << " ";
      cout << x[1] << " ";
      cout << x[2] << " ";
      cout << x[3] << "\n";
    }
  }
}

// https://betrue12.hateblo.jp/entry/2020/09/23/005940#%E5%8C%BA%E9%96%93%E5%8A%A0%E7%AE%97%E5%8C%BA%E9%96%93%E5%92%8C%E5%8F%96%E5%BE%97
struct S{
    long long value;
    int size;
};
using F = long long;

S op_S(S a, S b){ return {a.value+b.value, a.size+b.size}; }
S e_S(){ return {0, 0}; }
S mapping(F f, S x){ return {x.value + f*x.size, x.size}; }
F composition(F f, F g){ return f+g; }
F id(){ return 0; }

// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667
void val_AOJ_2667(){
  int n,q;
  cin >> n >> q;
  Graph g(n);
  for(int i=0;i<(n-1);i++){
    int u,v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  std::vector<S> v(n, {0, 1});
  atcoder::lazy_segtree<S, op_S, e_S, F, mapping, composition, id> seg(v);
  HLD hld(n,g,false);

  while(q>0){
    q--;
    int typ;
    cin >> typ;
    if(typ==0){
      long long res=0;
      int u,v;
      cin >> u >> v;
      vector<pi> pt=hld.path(u,v);
      for(auto &nx : pt){
        res+=seg.prod(min(nx.first,nx.second),max(nx.first,nx.second)+1).value;
      }
      cout << res << "\n";
    }
    else{
      int v;
      long long x;
      cin >> v >> x;
      pi st=hld.subtree(v);
      seg.apply(st.first,st.second+1,x);
    }
  }
}

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  // val_yosupo_VAPS();
  // val_yosupo_VSPC();
  val_ykc_650();
  // val_AOJ_2667();
  return 0;
}