test/verify/yukicoder-465.test.cpp

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Last update: 2024-04-24 02:34:04+09:00
Problem: https://yukicoder.me/problems/no/465

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Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/465

#include "../../template/template.hpp"

#include "../../string/palindromic-tree.hpp"

int main() {
  string S;
  cin >> S;
  int N = (int) S.size();
  vector< int64 > dp1(N + 1), dp2(N + 1);
  vector< int64 > buf(N + 3);
  PalindromicTree t;
  for(int i = 0; i < N; i++) {
    int id = t.add(S[i]);
    if(t[id].len == i + 1) dp1[i + 1] = 1;
    auto ret = t.update_dp([&](int id, int pos) {
                             buf[id] = dp1[pos];
                           },
                           [&](int id, int par) {
                             buf[id] += buf[par];
                           });
    for(auto &p: ret) dp2[i + 1] += buf[p];
  }
  PalindromicTree ts;
  int64 ret = 0, sum = 0;
  for(int i = N - 1; i >= 0; i--) {
    ret += 1LL * dp2[i] * sum;
    int id = ts.add(S[i]);
    if(ts[id].len == N - i) {
      sum++;
    }
  }
  cout << ret << "\n";
}

#line 1 "test/verify/yukicoder-465.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/465

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yukicoder-465.test.cpp"

#line 1 "string/palindromic-tree.hpp"
/**
 * @brief Palindromic Tree(回文木)
 * @see https://math314.hateblo.jp/entry/2016/12/19/005919
 * 
 */
template< typename T = char >
struct PalindromicTree {
public:
  struct Node {
    map< T, int > link; // 子のidx
    int suffix_link; // 最長回文接尾辞のidx
    int len; // 対応する回文の長さ
    vector< int > idx; // 対応する回文を最長回文接尾辞とするidx
    int delta_link; // 差分が異なる最長回文接尾辞のidx

    Node() = default;

    Node(int suf, int len) : suffix_link(suf), len(len), delta_link(-1) {}
  };

  vector< Node > ns;
  int ptr;
  vector< T > vs;

private:
  int find_prev_palindrome(int cur) const {
    int pos = (int) vs.size() - 1;
    for(;;) {
      int rev = pos - 1 - ns[cur].len;
      if(rev >= 0 and vs[rev] == vs.back()) break;
      cur = ns[cur].suffix_link;
    }
    return cur;
  }

  bool output_dfs(int v, int id, vector< T > &ret) const {
    if(v == id) return true;
    for(auto &nxt: ns[v].link) {
      if(output_dfs(nxt.second, id, ret)) {
        ret.emplace_back(nxt.first);
        return true;
      }
    }
    return false;
  }

public:
  PalindromicTree() : ptr(0) {
    ns.emplace_back(0, -1); // 長さ -1
    ns.emplace_back(0, 0); // 長さ 0
  }

  PalindromicTree(const string &S) : PalindromicTree() {
    add(S);
  }

  int diff(int t) const {
    if(ns[t].suffix_link <= 0) return -1;
    return ns[t].len - ns[ns[t].suffix_link].len;
  }

  int add(const T &x) {
    int idx = (int) vs.size();
    vs.emplace_back(x);
    int cur = find_prev_palindrome(ptr);
    auto res = ns[cur].link.insert(make_pair(x, (int) ns.size()));
    ptr = res.first->second;
    if(res.second) {
      ns.emplace_back(-1, ns[cur].len + 2);
      if(ns.back().len == 1) {
        ns.back().suffix_link = 1;
      } else {
        ns.back().suffix_link = ns[find_prev_palindrome(ns[cur].suffix_link)].link[x];
      }
      if(diff(ptr) == diff(ns.back().suffix_link)) {
        ns.back().delta_link = ns[ns.back().suffix_link].delta_link;
      } else {
        ns.back().delta_link = ns.back().suffix_link;
      }
    }
    ns[ptr].idx.emplace_back(idx);
    return ptr;
  }

  // add(x) のあとに呼び出す
  // * init(node_idx, pos):   頂点 node_idx を S[pos,i] が回文のときの初期値にする
  // * apply(node_idx, pre_idx): 頂点 node_idx に 頂点 pre_idx の結果を加える
  // * update: S[i]を末尾とする回文の頂点番号の集合
  template< typename I, typename U >
  vector< int > update_dp(const I &init, const U &apply) {
    int i = (int) vs.size() - 1;
    int id = ptr;
    vector< int > update;
    while(ns[id].len > 0) {
      init(id, i + 1 - ns[ns[id].delta_link].len - diff(id));
      if(ns[id].suffix_link != ns[id].delta_link) {
        apply(id, ns[id].suffix_link);
      }
      update.emplace_back(id);
      id = ns[id].delta_link;
    }
    return update;
  }

  void add(const string &s) {
    for(auto &x: s) add(x);
  }

  vector< int > build_frequency() const {
    vector< int > ret(ns.size());
    for(int i = (int) ns.size() - 1; i > 0; i--) {
      ret[i] += (int) ns[i].idx.size();
      ret[ns[i].suffix_link] += ret[i];
    }
    return ret;
  }

  vector< T > output(int idx) const {
    if(idx == 0) return {-1};
    if(idx == 1) return {0};
    vector< T > ret;
    output_dfs(0, idx, ret);
    output_dfs(1, idx, ret);
    int start = (int) ret.size() - 1;
    if(ns[idx].len & 1) --start;
    for(int i = start; i >= 0; i--) {
      ret.emplace_back(ret[i]);
    }
    return ret;
  }

  int size() const {
    return (int) ns.size();
  }

  Node &operator[](int idx) {
    return ns[idx];
  }
};
#line 6 "test/verify/yukicoder-465.test.cpp"

int main() {
  string S;
  cin >> S;
  int N = (int) S.size();
  vector< int64 > dp1(N + 1), dp2(N + 1);
  vector< int64 > buf(N + 3);
  PalindromicTree t;
  for(int i = 0; i < N; i++) {
    int id = t.add(S[i]);
    if(t[id].len == i + 1) dp1[i + 1] = 1;
    auto ret = t.update_dp([&](int id, int pos) {
                             buf[id] = dp1[pos];
                           },
                           [&](int id, int par) {
                             buf[id] += buf[par];
                           });
    for(auto &p: ret) dp2[i + 1] += buf[p];
  }
  PalindromicTree ts;
  int64 ret = 0, sum = 0;
  for(int i = N - 1; i >= 0; i--) {
    ret += 1LL * dp2[i] * sum;
    int id = ts.add(S[i]);
    if(ts[id].len == N - i) {
      sum++;
    }
  }
  cout << ret << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_1.txt	AC	6 ms	4 MB
g++	00_sample_2.txt	AC	6 ms	4 MB
g++	00_sample_3.txt	AC	6 ms	4 MB
g++	10_alomomola.txt	AC	6 ms	4 MB
g++	10_iwi.txt	AC	6 ms	4 MB
g++	20_amararama.txt	AC	21 ms	7 MB
g++	20_evitative.txt	AC	76 ms	23 MB
g++	21_girafarig.txt	AC	22 ms	8 MB
g++	21_nisioisin.txt	AC	70 ms	21 MB
g++	22_redivider.txt	AC	126 ms	103 MB
g++	22_rotavator.txt	AC	129 ms	133 MB
g++	30_aibohphobia.txt	AC	231 ms	184 MB
g++	30_ifihadahifi.txt	AC	173 ms	145 MB
g++	30_kinnikinnik.txt	AC	130 ms	122 MB
g++	30_seveneves.txt	AC	151 ms	99 MB
g++	31_neveroddoreven.txt	AC	160 ms	177 MB
g++	31_onlineenilno.txt	AC	145 ms	173 MB
g++	31_wassamassaw.txt	AC	143 ms	174 MB
g++	32_dorkrockcorkrod.txt	AC	170 ms	186 MB
g++	32_ratsliveonnoevilstar.txt	AC	162 ms	186 MB
g++	32_satanoscillatemymetallicsonatas.txt	AC	150 ms	188 MB
g++	33_atoyotaracefastsafecaratoyota.txt	AC	60 ms	23 MB
g++	33_godsawiwasdog.txt	AC	174 ms	189 MB
clang++	00_sample_1.txt	AC	6 ms	4 MB
clang++	00_sample_2.txt	AC	6 ms	4 MB
clang++	00_sample_3.txt	AC	6 ms	4 MB
clang++	10_alomomola.txt	AC	6 ms	4 MB
clang++	10_iwi.txt	AC	6 ms	4 MB
clang++	20_amararama.txt	AC	17 ms	7 MB
clang++	20_evitative.txt	AC	59 ms	23 MB
clang++	21_girafarig.txt	AC	17 ms	8 MB
clang++	21_nisioisin.txt	AC	54 ms	22 MB
clang++	22_redivider.txt	AC	108 ms	103 MB
clang++	22_rotavator.txt	AC	124 ms	133 MB
clang++	30_aibohphobia.txt	AC	215 ms	182 MB
clang++	30_ifihadahifi.txt	AC	165 ms	147 MB
clang++	30_kinnikinnik.txt	AC	124 ms	122 MB
clang++	30_seveneves.txt	AC	137 ms	100 MB
clang++	31_neveroddoreven.txt	AC	155 ms	181 MB
clang++	31_onlineenilno.txt	AC	140 ms	174 MB
clang++	31_wassamassaw.txt	AC	143 ms	173 MB
clang++	32_dorkrockcorkrod.txt	AC	162 ms	186 MB
clang++	32_ratsliveonnoevilstar.txt	AC	159 ms	188 MB
clang++	32_satanoscillatemymetallicsonatas.txt	AC	145 ms	186 MB
clang++	33_atoyotaracefastsafecaratoyota.txt	AC	49 ms	23 MB
clang++	33_godsawiwasdog.txt	AC	170 ms	187 MB