Submission #1251099

#	Time	Username	Problem	Language	Result	Execution time	Memory
1251099		Benq	Triple Peaks (IOI25_triples)	C++20	100 / 100	1358 ms	64840 KiB

triples

#include "triples.h"

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <vector>
using namespace std;

using ll = long long;
using db = long double; // or double, if TL is tight
using str = string;     // yay python!

// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define mp make_pair
#define f first
#define s second

#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;

// vectors
#define sz(x) int(size(x))
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()

#define lb lower_bound
#define ub upper_bound
tcT > int lwb(const V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
tcT > int upb(const V<T> &a, const T &b) { return int(ub(all(a), b) - bg(a)); }

// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define rep(a) F0R(_, a)
#define each(a, x) for (auto &a : x)

const int MOD = 998244353; // 1e9+7;
const int MX = (int)2e5 + 5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!!
mt19937 rng(0);
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;

// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(
    int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
  return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }

ll cdiv(ll a, ll b) {
  return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
  return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down

tcT > bool ckmin(T &a, const T &b) {
  return b < a ? a = b, 1 : 0;
} // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
} // set a = max(a,b)

tcTU > T fstTrue(T lo, T hi, U f) {
  ++hi;
  assert(lo <= hi); // assuming f is increasing
  while (lo < hi) { // find first index such that f is true
    T mid = lo + (hi - lo) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
  --lo;
  assert(lo <= hi); // assuming f is decreasing
  while (lo < hi) { // find first index such that f is true
    T mid = lo + (hi - lo + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
  sort(all(v));
  v.erase(unique(all(v)), end(v));
}
tcTU > void safeErase(T &t, const U &u) {
  auto it = t.find(u);
  assert(it != end(t));
  t.erase(it);
}

inline namespace IO {
#define SFINAE(x, ...)                                                         \
  template <class, class = void> struct x : std::false_type {};                \
  template <class T> struct x<T, std::void_t<__VA_ARGS__>> : std::true_type {}

SFINAE(DefaultI, decltype(std::cin >> std::declval<T &>()));
SFINAE(DefaultO, decltype(std::cout << std::declval<T &>()));
SFINAE(IsTuple, typename std::tuple_size<T>::type);
SFINAE(Iterable, decltype(std::begin(std::declval<T>())));

template <auto &is> struct Reader {
  template <class T> void Impl(T &t) {
    if constexpr (DefaultI<T>::value)
      is >> t;
    else if constexpr (Iterable<T>::value) {
      for (auto &x : t)
        Impl(x);
    } else if constexpr (IsTuple<T>::value) {
      std::apply([this](auto &...args) { (Impl(args), ...); }, t);
    } else
      static_assert(IsTuple<T>::value, "No matching type for read");
  }
  template <class... Ts> void read(Ts &...ts) { ((Impl(ts)), ...); }
};

template <class... Ts> void re(Ts &...ts) { Reader<cin>{}.read(ts...); }
#define def(t, args...)                                                        \
  t args;                                                                      \
  re(args);

template <auto &os, bool debug, bool print_nd> struct Writer {
  string comma() const { return debug ? "," : ""; }
  template <class T> constexpr char Space(const T &) const {
    return print_nd && (Iterable<T>::value or IsTuple<T>::value) ? '\n' : ' ';
  }
  template <class T> void Impl(T const &t) const {
    if constexpr (DefaultO<T>::value)
      os << t;
    else if constexpr (Iterable<T>::value) {
      if (debug)
        os << '{';
      int i = 0;
      for (auto &&x : t)
        ((i++) ? (os << comma() << Space(x), Impl(x)) : Impl(x));
      if (debug)
        os << '}';
    } else if constexpr (IsTuple<T>::value) {
      if (debug)
        os << '(';
      std::apply(
          [this](auto const &...args) {
            int i = 0;
            (((i++) ? (os << comma() << " ", Impl(args)) : Impl(args)), ...);
          },
          t);
      if (debug)
        os << ')';
    } else
      static_assert(IsTuple<T>::value, "No matching type for print");
  }
  template <class T> void ImplWrapper(T const &t) const {
    if (debug)
      os << "\033[0;31m";
    Impl(t);
    if (debug)
      os << "\033[0m";
  }
  template <class... Ts> void print(Ts const &...ts) const {
    ((Impl(ts)), ...);
  }
  template <class F, class... Ts>
  void print_with_sep(const std::string &sep, F const &f,
                      Ts const &...ts) const {
    ImplWrapper(f), ((os << sep, ImplWrapper(ts)), ...), os << '\n';
  }
  void print_with_sep(const std::string &) const { os << '\n'; }
};

template <class... Ts> void pr(Ts const &...ts) {
  Writer<cout, false, true>{}.print(ts...);
}
template <class... Ts> void ps(Ts const &...ts) {
  Writer<cout, false, true>{}.print_with_sep(" ", ts...);
}
} // namespace IO

inline namespace Debug {
template <typename... Args> void err(Args... args) {
  Writer<cerr, true, false>{}.print_with_sep(" | ", args...);
}
template <typename... Args> void errn(Args... args) {
  Writer<cerr, true, true>{}.print_with_sep(" | ", args...);
}

void err_prefix(str func, int line, string args) {
  cerr << "\033[0;31m\u001b[1mDEBUG\033[0m"
       << " | "
       << "\u001b[34m" << func << "\033[0m"
       << ":"
       << "\u001b[34m" << line << "\033[0m"
       << " - "
       << "[" << args << "] = ";
}

#ifdef LOCAL
#define dbg(args...) err_prefix(__FUNCTION__, __LINE__, #args), err(args)
#define dbgn(args...) err_prefix(__FUNCTION__, __LINE__, #args), errn(args)
#else
#define dbg(...)
#define dbgn(args...)
#endif

const auto beg_time = std::chrono::high_resolution_clock::now();
// https://stackoverflow.com/questions/47980498/accurate-c-c-clock-on-a-multi-core-processor-with-auto-overclock?noredirect=1&lq=1
double time_elapsed() {
  return chrono::duration<double>(std::chrono::high_resolution_clock::now() -
                                  beg_time)
      .count();
}
} // namespace Debug

inline namespace FileIO {
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
  cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
  cout << fixed << setprecision(12);
  // cin.exceptions(cin.failbit);
  // throws exception when do smth illegal
  // ex. try to read letter into int
  if (sz(s))
    setIn(s + ".in"), setOut(s + ".out"); // for old USACO
}
} // namespace FileIO

long long count_triples(std::vector<int> H) {
  // a, b
  // a, b, a + b
  // a, a + b, b
  // b, a + b, a (special)
  // b, a, a + b
  // a + b, a, b
  // a + b, b, a

  int N = sz(H);
  set<AR<int, 3>> cands;

  auto try_triple = [&](int x, int y, int z) {
    if (!(x < y && y < z))
      return;
    if (!(0 <= x && z < N))
      return;
    vi difs{y - x, z - y, z - x};
    vi expected{H.at(x), H.at(y), H.at(z)};
    sor(difs);
    sor(expected);
    if (difs != expected)
      return;
    if (H.at(x) == z - y && H.at(z) == y - x)
      return;
    cands.ins({x, y, z});
  };

  F0R(i, N) {
    {
      int j = i + H.at(i);
      if (0 <= j && j < N) {
        try_triple(i, j, j + H.at(j));
        try_triple(i, j, i + H.at(j));
        try_triple(i, j - H.at(j), j);
        try_triple(i, i + H.at(j), j);
      }
    }
    {
      int j = i - H.at(i);
      if (0 <= j && j < N) {
        try_triple(j, i - H.at(j), i);
      }
    }
  }
  V<vi> with_sum(2 * N), with_diff(2 * N);
  auto get_diff = [&](int i) { return i - H.at(i) + N; };
  auto get_sum = [&](int i) { return i + H.at(i); };
  // {x, H[x]} {y, H[y]}, {z, H[z]}
  // H[x] + H[z] == z - x

  for (int i = 0; i < N; ++i) {
    with_diff.at(get_diff(i)).pb(get_sum(i));
    with_sum.at(get_sum(i)).pb(get_diff(i));
  }
  V<vi> edge_sum(2 * N), edge_diff(2 * N);
  for (int i = 0; i < N; ++i) {
    // dbg("sum", get_sum(i), "diff", get_diff(i));
    if (sz(with_diff.at(get_diff(i))) < sz(with_sum.at(get_sum(i)))) {
      edge_sum.at(get_sum(i)).pb(get_diff(i));
    } else {
      edge_diff.at(get_diff(i)).pb(get_sum(i));
    }
  }

  vi ctr(2 * N);
  int ans = 0;
  F0R(s, 2 * N) {
    for (int d : with_sum.at(s))
      ++ctr.at(d); // i - H[i] + N along the diag-down line
    // dbg(s, with_sum.at(s));
    for (int d : edge_sum.at(s)) {
      // dbg("??", s, d, with_sum.at(s), with_diff.at(d));
      for (int s2 : with_diff.at(d))
        if (s2 < N) {
          // dbg("CHECKING", s, d - N, s2);
          ans += ctr.at(s2 + N);
        }
    }
    for (int d : with_sum.at(s))
      --ctr.at(d);
  }
  F0R(d, 2 * N) {
    for (int s : with_diff.at(d))
      ++ctr.at(s);
    for (int s : edge_diff.at(d)) {
      // dbg("??2", s, d, with_sum.at(s), with_diff.at(d));
      for (int d2 : with_sum.at(s))
        if (d2 >= N) {
          ans += ctr.at(d2 - N);
        }
    }
    for (int s : with_diff.at(d))
      --ctr.at(s);
  }

  // F0R(a, N) FOR(b, a + 1, N) FOR(c, b + 1, N) {
  //   if (H[a] + H[c] == H[b] && H[a] == c - b && H[c] == b - a)
  //     ++ans;
  // }

  // (1, 1), (3, 3), (4, 2)
  // each(c, cands) dbg(c);
  // dbg(ans, sz(cands));
  // dbg(ans, sz(cands));
  return ans + sz(cands);
}

std::vector<int> construct_range(int M, int K) {
  // x = i - H[i]
  // y = i + H[i]
  // x < y
  // x + y achieves even numbers in range 0 ... 2 * N - 2
  // want to minimize distinct {x, y}'s

  int N = M;

  vb seen(2 * N);
  vi contrib(N + 2);
  vb in_S(N + 2);
  vi S;
  auto valid_sum = [&](int s) { return s % 2 == 0 && s >= 0 && s < 2 * N; };
  auto add_contrib = [&](int num, int inc) {
    if (0 <= num && num < sz(contrib))
      contrib.at(num) += inc;
  };
  auto add_sum = [&](int s) {
    assert(valid_sum(s));
    assert(!seen.at(s));
    seen.at(s) = true;
    for (int y : S) {
      int x = s - y;
      add_contrib(x, -1);
    }
  };
  vpi pairs;
  auto add_S = [&](int x, int expected) {
    if (x >= 0)
      assert(!in_S.at(x));
    vi sums_to_add;
    for (int y : S) {
      int s = x + y;
      if (valid_sum(s) && !seen.at(s)) {
        pairs.pb({min(x, y), max(x, y)});
        sums_to_add.push_back(s);
      }
    }
    assert(sz(sums_to_add) == expected);
    for (int s = 0; s < 2 * N; s += 2)
      if (!seen.at(s)) {
        add_contrib(s - x, 1);
      }
    if (x >= 0)
      in_S.at(x) = true;
    S.pb(x);
    for (int s : sums_to_add)
      add_sum(s);
  };
  add_S(-1, 0);
  for (int x : {1, 3, N + 1, N - 3}) {
    add_S(x, contrib.at(x));
  }
  // -1 to N + 1
  while (true) {
    // dbg("CHECKING", S);
    pi best{0, 1};
    F0R(i, N + 2) if (!in_S.at(i)) ckmax(best, mp(contrib.at(i), -i));
    if (best.f == 0)
      break;
    best.s *= -1;
    add_S(best.s, contrib.at(best.s));
  }
  // dbg(pairs);

  vi H(N);
  assert(sz(pairs) == N);
  for (auto [x, y] : pairs) {
    assert(x < y);
    // dbg("HI", x, y);
    assert((x + y) % 2 == 0);
    H.at((y + x) / 2) = (y - x) / 2;
  }
  each(t, H) assert(1 <= t && t < N);
  // dbg(count_triples(H));
  if (N == 20) {
    F0R(it, 10000) {
      // dbg(it, count_triples(H));
      int i = rng() % N;
      pair<int, vi> best{0, {}};
      vi cands;
      FOR(v, 1, N) cands.pb(v);
      shuffle(all(cands), rng);
      for (int v : cands) {
        H.at(i) = v;
        int x = count_triples(H);
        if (x > best.f)
          best = {x, H};
      }
      H = best.s;
    }
  }
  return H;
}

// given S
// y not in S
// {[x in S] + y} < 2N
// [[x in S] + y] not in S

Compilation message (stderr)

triples.cpp: In function 'void FileIO::setIn(str)':
triples.cpp:257:28: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  257 | void setIn(str s) { freopen(s.c_str(), "r", stdin); }
      |                     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
triples.cpp: In function 'void FileIO::setOut(str)':
triples.cpp:258:29: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  258 | void setOut(str s) { freopen(s.c_str(), "w", stdout); }
      |                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 0: 0 / 0
• Subtask 1: 8 / 8
• Subtask 2: 6 / 6
• Subtask 3: 10 / 10
• Subtask 4: 11 / 11
• Subtask 5: 16 / 16
• Subtask 6: 19 / 19
• Subtask 7: 5 / 5
• Subtask 8: 5 / 5
• Subtask 9: 5 / 5
• Subtask 10: 5 / 5
• Subtask 11: 5 / 5
• Subtask 12: 5 / 5