test/verify/yukicoder-465.test.cpp

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• Last update: 2026-08-10 15:44:16+00:00
• Problem: https://yukicoder.me/problems/no/465

Depends on

• Palindromic Tree (回文木) (string/palindromic-tree.hpp)

Code

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

#include <cstdint>
#include <iostream>
#include <string>
#include <vector>

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

using namespace std;

int main() {
  string S;
  cin >> S;
  int N = (int)S.size();
  vector<int64_t> dp1(N + 1), dp2(N + 1);
  vector<int64_t> 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_t 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

#include <cstdint>
#include <iostream>
#include <string>
#include <vector>

#line 2 "string/palindromic-tree.hpp"

#include <map>
#line 6 "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 {
    std::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
    std::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) {}
  };

  std::vector<Node> ns;
  int ptr;
  std::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, std::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 std::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(std::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>
  std::vector<int> update_dp(const I& init, const U& apply) {
    int i = (int)vs.size() - 1;
    int id = ptr;
    std::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 std::string& s) {
    for (auto& x : s) add(x);
  }

  std::vector<int> build_frequency() const {
    std::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;
  }

  std::vector<T> output(int idx) const {
    if (idx == 0) return {-1};
    if (idx == 1) return {0};
    std::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 9 "test/verify/yukicoder-465.test.cpp"

using namespace std;

int main() {
  string S;
  cin >> S;
  int N = (int)S.size();
  vector<int64_t> dp1(N + 1), dp2(N + 1);
  vector<int64_t> 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_t 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	AC	2 ms	4 MB
g++	00_sample_2	AC	2 ms	4 MB
g++	00_sample_3	AC	2 ms	4 MB
g++	10_alomomola	AC	2 ms	4 MB
g++	10_iwi	AC	2 ms	4 MB
g++	20_amararama	AC	13 ms	7 MB
g++	20_evitative	AC	60 ms	23 MB
g++	21_girafarig	AC	12 ms	8 MB
g++	21_nisioisin	AC	49 ms	22 MB
g++	22_redivider	AC	99 ms	103 MB
g++	22_rotavator	AC	110 ms	132 MB
g++	30_aibohphobia	AC	185 ms	185 MB
g++	30_ifihadahifi	AC	145 ms	147 MB
g++	30_kinnikinnik	AC	107 ms	122 MB
g++	30_seveneves	AC	123 ms	99 MB
g++	31_neveroddoreven	AC	150 ms	179 MB
g++	31_onlineenilno	AC	134 ms	173 MB
g++	31_wassamassaw	AC	138 ms	175 MB
g++	32_dorkrockcorkrod	AC	153 ms	188 MB
g++	32_ratsliveonnoevilstar	AC	149 ms	188 MB
g++	32_satanoscillatemymetallicsonatas	AC	134 ms	188 MB
g++	33_atoyotaracefastsafecaratoyota	AC	240 ms	23 MB
g++	33_godsawiwasdog	AC	157 ms	188 MB
clang++	00_sample_1	AC	2 ms	4 MB
clang++	00_sample_2	AC	2 ms	4 MB
clang++	00_sample_3	AC	2 ms	4 MB
clang++	10_alomomola	AC	2 ms	4 MB
clang++	10_iwi	AC	2 ms	4 MB
clang++	20_amararama	AC	12 ms	7 MB
clang++	20_evitative	AC	51 ms	23 MB
clang++	21_girafarig	AC	11 ms	8 MB
clang++	21_nisioisin	AC	44 ms	22 MB
clang++	22_redivider	AC	94 ms	101 MB
clang++	22_rotavator	AC	107 ms	133 MB
clang++	30_aibohphobia	AC	177 ms	182 MB
clang++	30_ifihadahifi	AC	146 ms	148 MB
clang++	30_kinnikinnik	AC	104 ms	124 MB
clang++	30_seveneves	AC	112 ms	101 MB
clang++	31_neveroddoreven	AC	137 ms	181 MB
clang++	31_onlineenilno	AC	125 ms	173 MB
clang++	31_wassamassaw	AC	124 ms	174 MB
clang++	32_dorkrockcorkrod	AC	145 ms	188 MB
clang++	32_ratsliveonnoevilstar	AC	139 ms	187 MB
clang++	32_satanoscillatemymetallicsonatas	AC	130 ms	188 MB
clang++	33_atoyotaracefastsafecaratoyota	AC	47 ms	23 MB
clang++	33_godsawiwasdog	AC	166 ms	188 MB

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