Problem p02665 (C++) — buggy submission, verdict: Memory Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
  ll n;
  cin >> n;
  vector<ll> a(n + 1);
  for (int i = 0; i < n + 1; ++i) {
    cin >> a[i];
  }

  ll node = 1;
  bool f = false;
  vector<ll> ans(n + 1);
  for (int i = 0; i <= n; ++i) {
    ans[i] = node;
    if (node - a[i] < 0) {
      f = true;
      break;
    }
    node = node - a[i];
    if (node < (2LL << 60))
      node *= 2LL;
  }
  if (f) {
    cout << -1 << endl;
    return 0;
  }
  ll now = 0;
  for (int i = n; i >= 0; --i) {
    now += a[i];
    if (ans[i] - now > 0) {
      ans[i] = now;
    } else {
      break;
    }
  }

  ll sum = 0;
  for (int i = 0; i <= n; ++i) {
    sum += ans[i];
  }
  cout << sum << endl;
  return 0;
}


Error: MLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

struct bigint {
  using ll = long long;
  using vll = vector<ll>;

  constexpr static ll base = 1000000000;
  constexpr static ll base_digits = 9;

  vll a;
  ll sign;

  bigint() : sign(1) {}

  bigint(ll v) { *this = v; }

  bigint(const string &s) { read(s); }

  static bigint add_identity() { return bigint(0); }
  static bigint mul_identity() { return bigint(1); }

  void operator=(ll v) {
    sign = 1;
    if (v < 0)
      sign = -1, v = -v;
    for (; v > 0; v = v / base)
      a.push_back(v % base);
  }

  bigint operator+(const bigint &v) const {
    if (sign == v.sign) {
      bigint res = v;

      for (ll i = 0, carry = 0; i < (ll)max(a.size(), v.a.size()) || carry;
           ++i) {
        if (i == (ll)res.a.size())
          res.a.push_back(0);
        res.a[i] += carry + (i < (ll)a.size() ? a[i] : 0);
        carry = res.a[i] >= base;
        if (carry)
          res.a[i] -= base;
      }
      return res;
    }
    return *this - (-v);
  }

  bigint operator-(const bigint &v) const {
    if (sign == v.sign) {
      if (abs() >= v.abs()) {
        bigint res = *this;
        for (ll i = 0, carry = 0; i < (ll)v.a.size() || carry; ++i) {
          res.a[i] -= carry + (i < (ll)v.a.size() ? v.a[i] : 0);
          carry = res.a[i] < 0;
          if (carry)
            res.a[i] += base;
        }
        res.trim();
        return res;
      }
      return -(v - *this);
    }
    return *this + (-v);
  }

  void operator*=(ll v) {
    if (v < 0)
      sign = -sign, v = -v;
    for (ll i = 0, carry = 0; i < (ll)a.size() || carry; ++i) {
      if (i == (ll)a.size())
        a.push_back(0);
      ll cur = a[i] * (ll)v + carry;
      carry = (ll)(cur / base);
      a[i] = (ll)(cur % base);
      // asm("divl %%ecx" : "=a"(carry),"=d"(a[i]) : "A"(cur),"c"(base));
    }
    trim();
  }

  bigint operator*(ll v) const {
    bigint res = *this;
    res *= v;
    return res;
  }

  friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
    ll norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    bigint b = b1.abs() * norm;
    bigint q, r;
    q.a.resize(a.a.size());

    for (ll i = a.a.size() - 1; i >= 0; i--) {
      r *= base;
      r += a.a[i];
      ll s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
      ll s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
      ll d = ((ll)base * s1 + s2) / b.a.back();
      r -= b * d;
      while (r < 0)
        r += b, --d;
      q.a[i] = d;
    }

    q.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    q.trim();
    r.trim();
    return make_pair(q, r / norm);
  }

  bigint operator/(const bigint &v) const { return divmod(*this, v).first; }

  bigint operator%(const bigint &v) const { return divmod(*this, v).second; }

  void operator/=(ll v) {
    if (v < 0)
      sign = -sign, v = -v;
    for (ll i = (ll)a.size() - 1, rem = 0; i >= 0; --i) {
      ll cur = a[i] + rem * (ll)base;
      a[i] = (ll)(cur / v);
      rem = (ll)(cur % v);
    }
    trim();
  }

  bigint operator/(ll v) const {
    bigint res = *this;
    res /= v;
    return res;
  }

  ll operator%(ll v) const {
    if (v < 0)
      v = -v;
    ll m = 0;
    for (ll i = a.size() - 1; i >= 0; --i)
      m = (a[i] + m * (ll)base) % v;
    return m * sign;
  }

  void operator+=(const bigint &v) { *this = *this + v; }

  void operator-=(const bigint &v) { *this = *this - v; }

  void operator*=(const bigint &v) { *this = *this * v; }

  void operator/=(const bigint &v) { *this = *this / v; }

  bool operator<(const bigint &v) const {
    if (sign != v.sign)
      return sign < v.sign;
    if (a.size() != v.a.size())
      return a.size() * sign < v.a.size() * v.sign;
    for (ll i = a.size() - 1; i >= 0; i--)
      if (a[i] != v.a[i])
        return a[i] * sign < v.a[i] * sign;
    return false;
  }

  bool operator>(const bigint &v) const { return v < *this; }

  bool operator<=(const bigint &v) const { return !(v < *this); }

  bool operator>=(const bigint &v) const { return !(*this < v); }

  bool operator==(const bigint &v) const {
    return !(*this < v) && !(v < *this);
  }

  bool operator!=(const bigint &v) const { return *this < v || v < *this; }

  void trim() {
    while (!a.empty() && !a.back())
      a.pop_back();
    if (a.empty())
      sign = 1;
  }

  bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); }

  bigint operator-() const {
    bigint res = *this;
    res.sign = -sign;
    return res;
  }

  bigint abs() const {
    bigint res = *this;
    res.sign *= res.sign;
    return res;
  }

  ll longValue() const {
    ll res = 0;
    for (ll i = a.size() - 1; i >= 0; i--)
      res = res * base + a[i];
    return res * sign;
  }

  friend bigint gcd(const bigint &a, const bigint &b) {
    return b.isZero() ? a : gcd(b, a % b);
  }

  friend bigint lcm(const bigint &a, const bigint &b) {
    return a / gcd(a, b) * b;
  }

  void read(const string &s) {
    sign = 1;
    a.clear();
    ll pos = 0;
    while (pos < (ll)s.size() && (s[pos] == '-' || s[pos] == '+')) {
      if (s[pos] == '-')
        sign = -sign;
      ++pos;
    }
    for (ll i = s.size() - 1; i >= pos; i -= base_digits) {
      ll x = 0;
      for (ll j = max(pos, i - base_digits + 1); j <= i; j++)
        x = x * 10 + s[j] - '0';
      a.push_back(x);
    }
    trim();
  }

  friend istream &operator>>(istream &stream, bigint &v) {
    string s;
    stream >> s;
    v.read(s);
    return stream;
  }

  friend ostream &operator<<(ostream &stream, const bigint &v) {
    if (v.sign == -1)
      stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for (ll i = (ll)v.a.size() - 2; i >= 0; --i)
      stream << setw(base_digits) << setfill('0') << v.a[i];
    return stream;
  }

  static vll convert_base(const vll &a, ll old_digits, ll new_digits) {
    vll p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for (ll i = 1; i < (ll)p.size(); i++)
      p[i] = p[i - 1] * 10;
    vll res;
    ll cur = 0;
    ll cur_digits = 0;
    for (ll i = 0; i < (ll)a.size(); i++) {
      cur += a[i] * p[cur_digits];
      cur_digits += old_digits;
      while (cur_digits >= new_digits) {
        res.push_back(signed(cur % p[new_digits]));
        cur /= p[new_digits];
        cur_digits -= new_digits;
      }
    }
    res.push_back((signed)cur);
    while (!res.empty() && !res.back())
      res.pop_back();
    return res;
  }

  static vll karatsubaMultiply(const vll &a, const vll &b) {
    ll n = a.size();
    vll res(n + n);
    if (n <= 32) {
      for (ll i = 0; i < n; i++)
        for (ll j = 0; j < n; j++)
          res[i + j] += a[i] * b[j];
      return res;
    }

    ll k = n >> 1;
    vll a1(a.begin(), a.begin() + k);
    vll a2(a.begin() + k, a.end());
    vll b1(b.begin(), b.begin() + k);
    vll b2(b.begin() + k, b.end());

    vll a1b1 = karatsubaMultiply(a1, b1);
    vll a2b2 = karatsubaMultiply(a2, b2);

    for (ll i = 0; i < k; i++)
      a2[i] += a1[i];
    for (ll i = 0; i < k; i++)
      b2[i] += b1[i];

    vll r = karatsubaMultiply(a2, b2);
    for (ll i = 0; i < (ll)a1b1.size(); i++)
      r[i] -= a1b1[i];
    for (ll i = 0; i < (ll)a2b2.size(); i++)
      r[i] -= a2b2[i];

    for (ll i = 0; i < (ll)r.size(); i++)
      res[i + k] += r[i];
    for (ll i = 0; i < (ll)a1b1.size(); i++)
      res[i] += a1b1[i];
    for (ll i = 0; i < (ll)a2b2.size(); i++)
      res[i + n] += a2b2[i];
    return res;
  }

  bigint operator*(const bigint &v) const {
    constexpr static ll nbase = 10000;
    constexpr static ll nbase_digits = 4;

    vll a = convert_base(this->a, base_digits, nbase_digits);
    vll b = convert_base(v.a, base_digits, nbase_digits);

    //*/
    while (a.size() < b.size())
      a.push_back(0);
    while (b.size() < a.size())
      b.push_back(0);
    while (a.size() & (a.size() - 1))
      a.push_back(0), b.push_back(0);
    vll c = karatsubaMultiply(a, b);
    /*/
    if(a.empty()) a.push_back(0);
    if(b.empty()) b.push_back(0);
    vll c=FFT::multiply(a,b);
    //*/

    bigint res;
    res.sign = sign * v.sign;
    for (ll i = 0, carry = 0; i < (ll)c.size(); i++) {
      ll cur = c[i] + carry;
      res.a.push_back((ll)(cur % nbase));
      carry = (ll)(cur / nbase);
      if (i + 1 == (int)c.size() && carry > 0)
        c.push_back(0);
    }

    res.a = convert_base(res.a, nbase_digits, base_digits);
    res.trim();
    return res;
  }
};

int main() {
  ll n;
  cin >> n;
  vector<ll> a(n + 1);
  for (int i = 0; i < n + 1; ++i) {
    cin >> a[i];
  }

  bigint now = 1;
  bool f = false;
  vector<bigint> ans(n + 1);
  for (int i = 0; i <= n; ++i) {
    ans[i] = now;
    now = now - a[i];
    if (now < 0) {
      f = true;
      break;
    }
    now *= 2;
  }
  if (f) {
    cout << -1 << endl;
    return 0;
  }

  bigint now2 = 0;
  for (int i = n; i >= 0; --i) {
    now2 = now2 + a[i];
    if (ans[i] >= now2) {
      ans[i] = now2;
    } else {
      break;
    }
  }

  if (ans[0] != 1) {
    cout << -1 << endl;
    return 0;
  }
  bigint sum = 0;
  for (int i = 0; i <= n; ++i) {
    sum += ans[i];
  }
  cout << sum << endl;
  return 0;
}