Problem p02670 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <bitset>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <unordered_set>
#include <vector>

using namespace std;
using ll = long long;
using ull = unsigned long long;
// const ll mod =  998244353 ;
const ll mod = 1000000007;
const ll inf = 1e18;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};

#define REP(i, n) for (ll i = 0; i < (n); ++i)
#define REP_FROM(i, j, n) for (ll i = (j); i < (n); ++i)
#define REP_REV(i, n) for (ll i = n - 1; i >= 0; --i)
#define REP_FROM_REV(i, j, n) for (ll i = n - 1; i >= j; --i)
#define all(x) (x).begin(), (x).end()
#define sz(x) ll(x.size())

template <typename T> inline T chmax(T &a, const T b) {
  return a = (a < b) ? b : a;
}

template <typename T> inline T chmin(T &a, const T b) {
  return a = (a > b) ? b : a;
}

ll power(ll base, ll exponent) {
  if (exponent % 2) {
    return power(base, exponent - 1) * base % mod;
  } else if (exponent) {
    ll root_ans = power(base, exponent / 2);
    return root_ans * root_ans % mod;
  } else {
    return 1;
  }
}

ll inverse(ll x) { return power(x, mod - 2); }

ll gcd(ll a, ll b) {
  if (a < b)
    gcd(b, a);
  ll r;
  while (r = a % b) {
    a = b;
    b = r;
  }
  return b;
}

template <typename T> ll sum(T begin, T end) {
  return accumulate(begin, end, 0ll);
}

struct combination {
  vector<ll> fact, inv;

  combination(int sz) : fact(sz + 1), inv(sz + 1) {
    fact[0] = 1;
    for (int i = 1; i <= sz; i++) {
      fact[i] = fact[i - 1] * i % mod;
    }
    inv[sz] = power(fact[sz], mod - 2);
    for (int i = sz - 1; i >= 0; i--) {
      inv[i] = inv[i + 1] * (i + 1) % mod;
    }
  }

  ll C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return (fact[p] * inv[q] % mod * inv[p - q] % mod);
  }
};

using Pair = pair<ll, ll>;

template <ll Modulus> struct ModInt {
  ll a;

  constexpr ModInt(const ll x = 0) noexcept : a((x % mod + mod) % mod) {}

  constexpr ll &value() noexcept { return a; }

  constexpr const ll &value() const noexcept { return a; }

  constexpr ModInt operator+(const ModInt x) const noexcept {
    return ModInt(*this) += x;
  }

  constexpr ModInt operator-(const ModInt x) const noexcept {
    return ModInt(*this) -= x;
  }

  constexpr ModInt operator*(const ModInt x) const noexcept {
    return ModInt(*this) *= x;
  }

  constexpr ModInt operator/(const ModInt x) const noexcept {
    return ModInt(*this) /= x;
  }

  constexpr ModInt &operator+=(const ModInt x) noexcept {
    a += x.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }

  constexpr ModInt &operator-=(const ModInt x) noexcept {
    if (a < x.a) {
      a += Modulus;
    }
    a -= x.a;
    return *this;
  }

  constexpr ModInt &operator*=(const ModInt x) noexcept {
    a = a * x.a % Modulus;
    return *this;
  }

  constexpr ModInt &operator/=(ModInt x) noexcept {
    ll exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= x;
      }
      x *= x;
      exp /= 2;
    }
    return *this;
  }

  constexpr ModInt operator-() noexcept { return ModInt(-a); }

  friend ostream &operator<<(ostream &os, const ModInt &m) {
    os << m.a;
    return os;
  }
};

using mint = ModInt<mod>;

signed main() {
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  int n;
  cin >> n;
  vector<vector<ll>> dp(n + 2, vector<ll>(n + 2));
  vector<int> a(n * n);
  vector<vector<ll>> s(n + 2, vector<ll>(n + 2, 1));

  REP(i, n * n) cin >> a[i];
  REP(i, n) {
    REP(j, n) { dp[i + 1][j + 1] = min({i + 1, j + 1, n - i, n - j}) - 1; }
  }
  auto toPoint = [&](int id) -> Pair {
    id--;
    return {id % n + 1, id / n + 1};
  };
  ll ans = 0;
  REP(t, n * n) {
    auto p = toPoint(a[t]);
    int y = p.first;
    int x = p.second;
    s[y][x] = 0;
    queue<Pair> q;
    ans += max(dp[y][x], 0ll);
    ll tmp = inf;
    REP(i, 4) { tmp = min(tmp, dp[y + dy[i]][x + dx[i]]); }
    REP(i, 4) {
      if (dp[y + dy[i]][x + dx[i]] > dp[y][x]) {
        dp[y + dy[i]][x + dx[i]]--;
        q.emplace(y + dy[i], x + dx[i]);
      }
    }
    while (q.size()) {
      auto c = q.front();
      q.pop();
      int y = c.first;
      int x = c.second;
      REP(i, 4) {
        if (dp[y + dy[i]][x + dx[i]] > dp[y][x] + s[y][x]) {
          dp[y + dy[i]][x + dx[i]]--;
          q.emplace(y + dy[i], x + dx[i]);
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <unordered_set>
#include <vector>

using namespace std;
using ll = long long;
using ull = unsigned long long;
// const ll mod =  998244353 ;
const ll mod = 1000000007;
const ll inf = 1e18;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};

#define REP(i, n) for (ll i = 0; i < (n); ++i)
#define REP_FROM(i, j, n) for (ll i = (j); i < (n); ++i)
#define REP_REV(i, n) for (ll i = n - 1; i >= 0; --i)
#define REP_FROM_REV(i, j, n) for (ll i = n - 1; i >= j; --i)
#define all(x) (x).begin(), (x).end()
#define sz(x) ll(x.size())

template <typename T> inline T chmax(T &a, const T b) {
  return a = (a < b) ? b : a;
}

template <typename T> inline T chmin(T &a, const T b) {
  return a = (a > b) ? b : a;
}

ll power(ll base, ll exponent) {
  if (exponent % 2) {
    return power(base, exponent - 1) * base % mod;
  } else if (exponent) {
    ll root_ans = power(base, exponent / 2);
    return root_ans * root_ans % mod;
  } else {
    return 1;
  }
}

ll inverse(ll x) { return power(x, mod - 2); }

ll gcd(ll a, ll b) {
  if (a < b)
    gcd(b, a);
  ll r;
  while (r = a % b) {
    a = b;
    b = r;
  }
  return b;
}

template <typename T> ll sum(T begin, T end) {
  return accumulate(begin, end, 0ll);
}

struct combination {
  vector<ll> fact, inv;

  combination(int sz) : fact(sz + 1), inv(sz + 1) {
    fact[0] = 1;
    for (int i = 1; i <= sz; i++) {
      fact[i] = fact[i - 1] * i % mod;
    }
    inv[sz] = power(fact[sz], mod - 2);
    for (int i = sz - 1; i >= 0; i--) {
      inv[i] = inv[i + 1] * (i + 1) % mod;
    }
  }

  ll C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return (fact[p] * inv[q] % mod * inv[p - q] % mod);
  }
};

using Pair = pair<ll, ll>;

template <ll Modulus> struct ModInt {
  ll a;

  constexpr ModInt(const ll x = 0) noexcept : a((x % mod + mod) % mod) {}

  constexpr ll &value() noexcept { return a; }

  constexpr const ll &value() const noexcept { return a; }

  constexpr ModInt operator+(const ModInt x) const noexcept {
    return ModInt(*this) += x;
  }

  constexpr ModInt operator-(const ModInt x) const noexcept {
    return ModInt(*this) -= x;
  }

  constexpr ModInt operator*(const ModInt x) const noexcept {
    return ModInt(*this) *= x;
  }

  constexpr ModInt operator/(const ModInt x) const noexcept {
    return ModInt(*this) /= x;
  }

  constexpr ModInt &operator+=(const ModInt x) noexcept {
    a += x.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }

  constexpr ModInt &operator-=(const ModInt x) noexcept {
    if (a < x.a) {
      a += Modulus;
    }
    a -= x.a;
    return *this;
  }

  constexpr ModInt &operator*=(const ModInt x) noexcept {
    a = a * x.a % Modulus;
    return *this;
  }

  constexpr ModInt &operator/=(ModInt x) noexcept {
    ll exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= x;
      }
      x *= x;
      exp /= 2;
    }
    return *this;
  }

  constexpr ModInt operator-() noexcept { return ModInt(-a); }

  friend ostream &operator<<(ostream &os, const ModInt &m) {
    os << m.a;
    return os;
  }
};

using mint = ModInt<mod>;

signed main() {
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  int n;
  cin >> n;
  vector<vector<ll>> dp(n + 2, vector<ll>(n + 2));
  vector<int> a(n * n);
  set<Pair> s;
  REP(i, n * n) cin >> a[i];
  REP(i, n) {
    REP(j, n) { dp[i + 1][j + 1] = min({i + 1, j + 1, n - i, n - j}) - 1; }
  }
  auto toPoint = [&](int id) -> Pair {
    id--;
    return {id % n + 1, id / n + 1};
  };
  ll ans = 0;
  REP(t, n * n) {
    auto p = toPoint(a[t]);
    int y = p.first;
    int x = p.second;
    s.emplace(y, x);
    queue<Pair> q;
    ans += max(dp[y][x], 0ll);
    ll tmp = inf;
    REP(i, 4) { tmp = min(tmp, dp[y + dy[i]][x + dx[i]]); }
    REP(i, 4) {
      if (dp[y + dy[i]][x + dx[i]] > dp[y][x]) {
        dp[y + dy[i]][x + dx[i]]--;
        q.emplace(y + dy[i], x + dx[i]);
      }
    }
    while (q.size()) {
      auto c = q.front();
      q.pop();
      int y = c.first;
      int x = c.second;
      REP(i, 4) {
        if (dp[y + dy[i]][x + dx[i]] > dp[y][x] + 1 - s.count(c)) {
          dp[y + dy[i]][x + dx[i]]--;
          q.emplace(y + dy[i], x + dx[i]);
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}