Problem p02716 (C++) — buggy submission, verdict: Time Limit Exceeded

// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <locale>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

// typedef
//------------------------------------------
typedef long long LL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<LL> VLL;
typedef vector<VI> VVI;
typedef vector<VB> VVB;
typedef vector<VS> VVS;
typedef vector<VLL> VVLL;
typedef vector<VVI> VVVI;
typedef vector<VVLL> VVVLL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<int, string> PIS;
typedef pair<string, int> PSI;
typedef pair<string, string> PSS;
typedef vector<PII> VPII;
typedef vector<PLL> VPLL;
typedef vector<VPII> VVPII;
typedef vector<VPLL> VVPLL;
typedef vector<VS> VVS;
typedef map<int, int> MII;
typedef map<LL, LL> MLL;
typedef map<string, int> MSI;
typedef map<int, string> MIS;

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#define EACH(i, arr)                                                           \\
  for (typeof((arr).begin()) i = (arr).begin(); i != (arr).end(); ++i)
#define EXIST(str, e) ((str).find(e) != (str).end())
#define COUNT(arr, v) count((arr).begin(), (arr).end(), v)
#define SEARCH(v, w) search((v).begin(), (v).end(), (w).begin(), (w).end())
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define ROTATE_LEFT(arr, c)                                                    \\
  rotate((arr).begin(), (arr).begin() + (c), (arr).end())
#define ROTATE_RIGHT(arr, c)                                                   \\
  rotate((arr).rbegin(), (arr).rbegin() + (c), (arr).rend())
#define SUMI(arr) accumulate((arr).begin(), (arr).end(), 0)
#define SUMD(arr) accumulate((arr).begin(), (arr).end(), 0.)
#define SUMLL(arr) accumulate((arr).begin(), (arr).end(), 0LL)
#define MULD(arr)                                                              \\
  accumulate((arr).begin(), (arr).end(), 1., multiplies<double>())
#define UB(arr, n) upper_bound((arr).begin(), (arr).end(), n)
#define LB(arr, n) lower_bound((arr).begin(), (arr).end(), n)
#define PB push_back
#define MP make_pair
#define ft first
#define sd second

// input output
//------------------------------------------
#define GL(s) getline(cin, (s))
#define INIT()                                                                 \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0)
#define OUT(d) std::cout << (d)
#define OUT_L(d) std::cout << (d) << endl
#define FOUT(n, data) std::cout << std::fixed << std::setprecision(n) << (data)
#define FOUT_L(n, data)                                                        \\
  std::cout << std::fixed << std::setprecision(n) << (data) << "\\n"
#define EL() printf("\\n")
#define SHOW_VECTOR(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOW_MAP(v)                                                            \\
  {                                                                            \\
    std::cerr << #v << endl;                                                   \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx.first << " " << xxx.second << "\\n";                     \\
    }                                                                          \\
  }
#define Yes() printf("Yes\\n")
#define No() printf("No\\n")
#define YES() printf("YES\\n")
#define NO() printf("NO\\n")
#define Yay() printf("Yay!\\n")
#define Nnn() printf(":(\\n")
#define CE(x, y) ((x + y - 1) / (y))

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

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

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
  out << "[" << p.first << ", " << p.second << "]"
      << "\\n";
  return out;
}

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

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

// repetition
//------------------------------------------
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) for (int i = n - 1; i >= 0; i--)
#define FORLL(i, a, b) for (LL i = LL(a); i < LL(b); ++i)
#define RFORLL(i, a, b) for (LL i = LL(b) - 1; i >= LL(a); --i)
#define REPLL(i, n) for (LL i = 0; i < LL(n); ++i)
#define RREPLL(i, n) for (LL i = LL(n) - 1; i >= 0; --i)
#define FOREACH(x, arr) for (auto &(x) : (arr))

//------------------------------------------
//------------------------------------------

template <int_fast64_t Modulas = 1000000007ul> class ModInt {
  using u64 = int_fast64_t;

public:
  u64 x;

  constexpr ModInt() : x(0) {}
  constexpr ModInt(int_fast64_t v) : x((v % Modulas + Modulas) % Modulas) {}
  constexpr ModInt operator+(const ModInt rhs) const noexcept {
    return ModInt(*this) += rhs;
  }
  constexpr ModInt operator-(const ModInt rhs) const noexcept {
    return ModInt(*this) -= rhs;
  }
  constexpr ModInt operator*(const ModInt rhs) const noexcept {
    return ModInt(*this) *= rhs;
  }
  constexpr ModInt operator/(const ModInt rhs) const noexcept {
    return ModInt(*this) /= rhs;
  }
  constexpr ModInt operator/(const long long rhs) const noexcept {
    return ModInt(*this) /= rhs;
  }
  constexpr ModInt operator+=(const ModInt rhs) noexcept {
    x += rhs.x;
    if (x >= Modulas)
      x -= Modulas;
    return *this;
  }
  constexpr ModInt operator+=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) += hs;
    return *this;
  }
  constexpr ModInt operator-=(const ModInt rhs) noexcept {
    if (x < rhs.x)
      x += Modulas;
    x -= rhs.x;
    return *this;
  }
  constexpr ModInt operator-=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) -= hs;
    return *this;
  }
  constexpr ModInt operator*=(const ModInt rhs) noexcept {
    x = x * rhs.x % Modulas;
    return *this;
  }
  constexpr ModInt operator*=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) *= hs;
    return *this;
  }
  constexpr ModInt &operator/=(ModInt rhs) noexcept {
    u64 exp = Modulas - 2;
    while (exp > 0) {
      if (exp & 1ul)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1ul;
    }
    return *this;
  }
  constexpr ModInt &operator/=(long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) /= hs;
    return *this;
  }

  constexpr ModInt &operator++() noexcept {
    x++;
    if (x >= Modulas)
      x -= Modulas;
    return *this;
  }
  constexpr ModInt &operator--() noexcept {
    if (x == 0)
      x += Modulas;
    x--;
    return *this;
  }
  constexpr bool operator<(const ModInt rhs) const noexcept {
    return x < rhs.x;
  }
  constexpr bool operator==(const ModInt rhs) const noexcept {
    return this->x == rhs.x;
  }
  constexpr bool operator!=(const ModInt rhs) const noexcept {
    return !(*this == rhs);
  }
  friend istream &operator>>(istream &in, ModInt &m) {
    in >> m.x;
    if (m.x < 0)
      m.x += Modulas;
    m.x %= Modulas;
    return in;
  }
  friend ostream &operator<<(ostream &out, const ModInt &p) {
    out << p.x;
    return out;
  }
  constexpr ModInt pow(u64 p) const {
    ModInt ret(1);
    ModInt mul(x);
    while (p > 0) {
      if (p & 1ul)
        ret *= mul;
      mul *= mul;
      p >>= 1ul;
    }
    return ret;
  }
  constexpr ModInt operator~() const noexcept {
    u64 exp = Modulas - 2;
    return pow(exp);
  }

  constexpr static ModInt arith_sum(ModInt<Modulas> a, ModInt<Modulas> d,
                                    ModInt<Modulas> n) noexcept {
    return (a * ModInt<Modulas>(2) + (n - 1) * d) * n / ModInt<Modulas>(2);
  }
};

constexpr LL INF = 1e16;

LL dfs(int v, int r, VLL &A, vector<map<LL, LL>> &dp, LL N, int done = 0) {
  if (done >= 4)
    return -INF;
  if (dp[v].count(r))
    return dp[v][r];
  if (r == 0)
    return 0;
  if (v >= N) {
    if (r == 0)
      return 0;
    else
      return -INF;
  }
  LL ret = -INF;
  for (int i = 0; i < 3; i++) {
    if (v + i < N and i + done <= 3) {
      ret = max(ret, A[v + i] + dfs(v + i + 2, r - 1, A, dp, N, done + i));
    }
  }
  dp[v][r] = ret;
  //    return dp[v][r] = ret;
  return ret;
}

int main() {

  LL N;
  cin >> N;

  VLL A(N);
  cin >> A;

  vector<map<LL, LL>> dp(700000);

  LL ans = dfs(0, N / 2, A, dp, N);
  cout << ans << endl;
}


Error: TLE

Fixed submission:

// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <locale>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

// typedef
//------------------------------------------
typedef long long LL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<LL> VLL;
typedef vector<VI> VVI;
typedef vector<VB> VVB;
typedef vector<VS> VVS;
typedef vector<VLL> VVLL;
typedef vector<VVI> VVVI;
typedef vector<VVLL> VVVLL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<int, string> PIS;
typedef pair<string, int> PSI;
typedef pair<string, string> PSS;
typedef vector<PII> VPII;
typedef vector<PLL> VPLL;
typedef vector<VPII> VVPII;
typedef vector<VPLL> VVPLL;
typedef vector<VS> VVS;
typedef map<int, int> MII;
typedef map<LL, LL> MLL;
typedef map<string, int> MSI;
typedef map<int, string> MIS;

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#define EACH(i, arr)                                                           \\
  for (typeof((arr).begin()) i = (arr).begin(); i != (arr).end(); ++i)
#define EXIST(str, e) ((str).find(e) != (str).end())
#define COUNT(arr, v) count((arr).begin(), (arr).end(), v)
#define SEARCH(v, w) search((v).begin(), (v).end(), (w).begin(), (w).end())
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define ROTATE_LEFT(arr, c)                                                    \\
  rotate((arr).begin(), (arr).begin() + (c), (arr).end())
#define ROTATE_RIGHT(arr, c)                                                   \\
  rotate((arr).rbegin(), (arr).rbegin() + (c), (arr).rend())
#define SUMI(arr) accumulate((arr).begin(), (arr).end(), 0)
#define SUMD(arr) accumulate((arr).begin(), (arr).end(), 0.)
#define SUMLL(arr) accumulate((arr).begin(), (arr).end(), 0LL)
#define MULD(arr)                                                              \\
  accumulate((arr).begin(), (arr).end(), 1., multiplies<double>())
#define UB(arr, n) upper_bound((arr).begin(), (arr).end(), n)
#define LB(arr, n) lower_bound((arr).begin(), (arr).end(), n)
#define PB push_back
#define MP make_pair
#define ft first
#define sd second

// input output
//------------------------------------------
#define GL(s) getline(cin, (s))
#define INIT()                                                                 \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0)
#define OUT(d) std::cout << (d)
#define OUT_L(d) std::cout << (d) << endl
#define FOUT(n, data) std::cout << std::fixed << std::setprecision(n) << (data)
#define FOUT_L(n, data)                                                        \\
  std::cout << std::fixed << std::setprecision(n) << (data) << "\\n"
#define EL() printf("\\n")
#define SHOW_VECTOR(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOW_MAP(v)                                                            \\
  {                                                                            \\
    std::cerr << #v << endl;                                                   \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx.first << " " << xxx.second << "\\n";                     \\
    }                                                                          \\
  }
#define Yes() printf("Yes\\n")
#define No() printf("No\\n")
#define YES() printf("YES\\n")
#define NO() printf("NO\\n")
#define Yay() printf("Yay!\\n")
#define Nnn() printf(":(\\n")
#define CE(x, y) ((x + y - 1) / (y))

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

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

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
  out << "[" << p.first << ", " << p.second << "]"
      << "\\n";
  return out;
}

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

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

// repetition
//------------------------------------------
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) for (int i = n - 1; i >= 0; i--)
#define FORLL(i, a, b) for (LL i = LL(a); i < LL(b); ++i)
#define RFORLL(i, a, b) for (LL i = LL(b) - 1; i >= LL(a); --i)
#define REPLL(i, n) for (LL i = 0; i < LL(n); ++i)
#define RREPLL(i, n) for (LL i = LL(n) - 1; i >= 0; --i)
#define FOREACH(x, arr) for (auto &(x) : (arr))

//------------------------------------------
//------------------------------------------

template <int_fast64_t Modulas = 1000000007ul> class ModInt {
  using u64 = int_fast64_t;

public:
  u64 x;

  constexpr ModInt() : x(0) {}
  constexpr ModInt(int_fast64_t v) : x((v % Modulas + Modulas) % Modulas) {}
  constexpr ModInt operator+(const ModInt rhs) const noexcept {
    return ModInt(*this) += rhs;
  }
  constexpr ModInt operator-(const ModInt rhs) const noexcept {
    return ModInt(*this) -= rhs;
  }
  constexpr ModInt operator*(const ModInt rhs) const noexcept {
    return ModInt(*this) *= rhs;
  }
  constexpr ModInt operator/(const ModInt rhs) const noexcept {
    return ModInt(*this) /= rhs;
  }
  constexpr ModInt operator/(const long long rhs) const noexcept {
    return ModInt(*this) /= rhs;
  }
  constexpr ModInt operator+=(const ModInt rhs) noexcept {
    x += rhs.x;
    if (x >= Modulas)
      x -= Modulas;
    return *this;
  }
  constexpr ModInt operator+=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) += hs;
    return *this;
  }
  constexpr ModInt operator-=(const ModInt rhs) noexcept {
    if (x < rhs.x)
      x += Modulas;
    x -= rhs.x;
    return *this;
  }
  constexpr ModInt operator-=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) -= hs;
    return *this;
  }
  constexpr ModInt operator*=(const ModInt rhs) noexcept {
    x = x * rhs.x % Modulas;
    return *this;
  }
  constexpr ModInt operator*=(const long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) *= hs;
    return *this;
  }
  constexpr ModInt &operator/=(ModInt rhs) noexcept {
    u64 exp = Modulas - 2;
    while (exp > 0) {
      if (exp & 1ul)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1ul;
    }
    return *this;
  }
  constexpr ModInt &operator/=(long long rhs) noexcept {
    auto hs = ModInt<Modulas>(rhs);
    (*this) /= hs;
    return *this;
  }

  constexpr ModInt &operator++() noexcept {
    x++;
    if (x >= Modulas)
      x -= Modulas;
    return *this;
  }
  constexpr ModInt &operator--() noexcept {
    if (x == 0)
      x += Modulas;
    x--;
    return *this;
  }
  constexpr bool operator<(const ModInt rhs) const noexcept {
    return x < rhs.x;
  }
  constexpr bool operator==(const ModInt rhs) const noexcept {
    return this->x == rhs.x;
  }
  constexpr bool operator!=(const ModInt rhs) const noexcept {
    return !(*this == rhs);
  }
  friend istream &operator>>(istream &in, ModInt &m) {
    in >> m.x;
    if (m.x < 0)
      m.x += Modulas;
    m.x %= Modulas;
    return in;
  }
  friend ostream &operator<<(ostream &out, const ModInt &p) {
    out << p.x;
    return out;
  }
  constexpr ModInt pow(u64 p) const {
    ModInt ret(1);
    ModInt mul(x);
    while (p > 0) {
      if (p & 1ul)
        ret *= mul;
      mul *= mul;
      p >>= 1ul;
    }
    return ret;
  }
  constexpr ModInt operator~() const noexcept {
    u64 exp = Modulas - 2;
    return pow(exp);
  }

  constexpr static ModInt arith_sum(ModInt<Modulas> a, ModInt<Modulas> d,
                                    ModInt<Modulas> n) noexcept {
    return (a * ModInt<Modulas>(2) + (n - 1) * d) * n / ModInt<Modulas>(2);
  }
};

constexpr LL INF = 1e16;

LL dfs(int v, int r, VLL &A, vector<map<LL, LL>> &dp, LL N) {
  if (dp[v].count(r))
    return dp[v][r];
  if (r == 0)
    return 0;
  if (v >= N) {
    if (r == 0)
      return 0;
    else
      return -INF;
  }
  LL ret = -INF;
  for (int i = 0; i < 3; i++) {
    if (v + i < N) {
      ret = max(ret, A[v + i] + dfs(v + i + 2, r - 1, A, dp, N));
    }
  }
  dp[v][r] = ret;
  //    return dp[v][r] = ret;
  return ret;
}

int main() {

  LL N;
  cin >> N;

  VLL A(N);
  cin >> A;

  vector<map<LL, LL>> dp(700000);

  LL ans = dfs(0, N / 2, A, dp, N);
  cout << ans << endl;
}