Problem p03566 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <stdio.h>
#include <string.h>
#include <string>
#include <utility>
#include <vector>

using namespace std;

static const double EPS = 1e-9;
template <class T> bool INRANGE(T x, T a, T b) { return a <= x && x <= b; }
template <class T> void amin(T &a, T v) {
  if (a > v)
    a = v;
}
template <class T> void amax(T &a, T v) {
  if (a < v)
    a = v;
}
int ROUND(double x) { return (int)(x + 0.5); }
bool ISINT(double x) { return fabs(ROUND(x) - x) <= EPS; }
bool ISEQUAL(double x, double y) {
  return fabs(x - y) <= EPS * max(1.0, max(fabs(x), fabs(y)));
}
double SQSUM(double x, double y) { return x * x + y * y; }
template <class T> vector<T> make_vector(int n, T t) { return vector<T>(n, t); }

template <class... Ts> auto make_vector(int n, Ts... ts) {
  return vector<decltype(make_vector(ts...))>(n, make_vector(ts...));
}

#define PI (acos(-1))
#define ARRAY_NUM(a) (sizeof(a) / sizeof(a[0]))
#define NG (-1)
#define BIG ((int)1e9 + 10)
#define BIGLL ((ll)4e18)
#define SZ(a) ((int)(a).size())
#define SQ(a) ((a) * (a))
#define REP(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define ALL(x) (x).begin(), (x).end()
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE" : "IMPOSSIBLE") << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << endl

#define BitSet(arg, posn) ((arg) |= (1LL << (posn)))
#define BitClr(arg, posn) ((arg) &= ~(1LL << (posn)))
#define BitFlp(arg, posn) ((arg) ^= (1LL << (posn)))
#define IsBit(arg, posn) static_cast<bool>((arg) & (1LL << (posn)))

// #define DEBUG(x) cerr<<#x<<": "<<(x)<<endl
// #define DEBUG_VEC(v) cerr<<#v<<": ";REP(__i,(v).size())cerr<<((v)[__i])<<",
// ";cerr<<endl

typedef unsigned long long ull;
typedef long long ll;

struct in {
  int n;
  in() {}
  in(int n_) : n(n_){};
  template <class T> operator T() {
    T ret;
    cin >> ret;
    return ret;
  }
  template <class T> operator vector<T>() {
    vector<T> ret(n);
    for (int i = 0; i < n; i++)
      cin >> ret[i];
    return ret;
  }
};

// modint: mod 計算を int を扱うように扱える構造体
template <int MOD> struct ModInt {
  long long val;
  constexpr ModInt(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr ModInt operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr ModInt operator+(const ModInt &r) const noexcept {
    return ModInt(*this) += r;
  }
  constexpr ModInt operator-(const ModInt &r) const noexcept {
    return ModInt(*this) -= r;
  }
  constexpr ModInt operator*(const ModInt &r) const noexcept {
    return ModInt(*this) *= r;
  }
  constexpr ModInt operator/(const ModInt &r) const noexcept {
    return ModInt(*this) /= r;
  }
  constexpr ModInt &operator+=(const ModInt &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr ModInt &operator-=(const ModInt &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr ModInt &operator*=(const ModInt &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr ModInt &operator/=(const ModInt &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const ModInt &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const ModInt &r) const noexcept {
    return this->val != r.val;
  }

  friend ostream &operator<<(ostream &os, const ModInt<MOD> &x) noexcept {
    return os << x.val;
  }
  friend istream &operator>>(istream &is, ModInt<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr ModInt<MOD> modpow(const ModInt<MOD> &a,
                                      long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

// 二項係数ライブラリ
template <class T> struct BiCoef {
  constexpr BiCoef() {}
  constexpr BiCoef(int n) noexcept : mFact(n, 1), mInv(n, 1), mFInv(n, 1) {
    Init(n);
  }

  constexpr void Init(int n) noexcept {
    mFact.assign(n, 1), mInv.assign(n, 1), mFInv.assign(n, 1);
    int factMod = mFact[0].getmod();
    for (int i = 2; i < n; i++) {
      mFact[i] = mFact[i - 1] * i;
      mInv[i] = -mInv[factMod % i] * (factMod / i);
      mFInv[i] = mFInv[i - 1] * mInv[i];
    }
  }

  constexpr T Fact(int n) const noexcept {
    if (n < 0)
      return 0;
    return mFact[n];
  }

  constexpr T Comb(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return mFact[n] * mFInv[k] * mFInv[n - k];
  }

  constexpr T Perm(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return mFact[n] * mFInv[k] * mFInv[n - k];
  }

  constexpr T Homo(int n, int r) const {
    if (n < 0 || r < 0)
      return 0;
    return r == 0 ? 1 : Comb(n + r - 1, r);
  }

  constexpr T inv(int n) const noexcept {
    if (n < 0)
      return 0;
    return mInv[n];
  }

  constexpr T finv(int n) const noexcept {
    if (n < 0)
      return 0;
    return mFInv[n];
  }

  vector<T> mFact;
  vector<T> mInv;
  vector<T> mFInv;
};

const int MOD = 1000000007;
using mint = ModInt<MOD>;
// BiCoef<mint> bc(1234567); // 1M * 3 * 8B(ll) = 24MB

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  ll N;
  cin >> N;
  vector<ll> t = in(N);
  vector<ll> v = in(N);

  vector<ll> maxv(30000, BIGLL);

  maxv[0] = 0;
  ll nowt = 0;
  for (int i = 0; i < N; ++i) {
    for (int dt = 0; dt <= 2 * t[i]; ++dt) {
      amin(maxv[nowt + dt], 2 * v[i]);
    }

    nowt += 2 * t[i];
  }

  maxv[nowt] = 0;

  ll lastT = nowt;

  for (ll tt = lastT; tt >= 1; tt--) {
    amin(maxv[tt - 1], maxv[tt] + 1);
  }

  ll nowv = 0;
  ll ans = 0;
  for (int tt = 0; tt < lastT; tt++) {
    if (nowv + 1 <= maxv[tt]) {
      ans += (2 * nowv + 1);
      nowv++;
    } else if (nowv <= maxv[tt]) {
      ans += (2 * nowv);
      nowv;
    } else if (nowv - 1 <= maxv[tt]) {
      ans += (2 * nowv - 1);
      nowv--;
    } else {
      assert(0);
    }

    assert(nowv >= 0);
  }

  printf("%.20f\n", (ans + 1) / 8.0);

  return 0;
}


Fixed submission:
#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <stdio.h>
#include <string.h>
#include <string>
#include <utility>
#include <vector>

using namespace std;

static const double EPS = 1e-9;
template <class T> bool INRANGE(T x, T a, T b) { return a <= x && x <= b; }
template <class T> void amin(T &a, T v) {
  if (a > v)
    a = v;
}
template <class T> void amax(T &a, T v) {
  if (a < v)
    a = v;
}
int ROUND(double x) { return (int)(x + 0.5); }
bool ISINT(double x) { return fabs(ROUND(x) - x) <= EPS; }
bool ISEQUAL(double x, double y) {
  return fabs(x - y) <= EPS * max(1.0, max(fabs(x), fabs(y)));
}
double SQSUM(double x, double y) { return x * x + y * y; }
template <class T> vector<T> make_vector(int n, T t) { return vector<T>(n, t); }

template <class... Ts> auto make_vector(int n, Ts... ts) {
  return vector<decltype(make_vector(ts...))>(n, make_vector(ts...));
}

#define PI (acos(-1))
#define ARRAY_NUM(a) (sizeof(a) / sizeof(a[0]))
#define NG (-1)
#define BIG ((int)1e9 + 10)
#define BIGLL ((ll)4e18)
#define SZ(a) ((int)(a).size())
#define SQ(a) ((a) * (a))
#define REP(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define ALL(x) (x).begin(), (x).end()
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE" : "IMPOSSIBLE") << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << endl

#define BitSet(arg, posn) ((arg) |= (1LL << (posn)))
#define BitClr(arg, posn) ((arg) &= ~(1LL << (posn)))
#define BitFlp(arg, posn) ((arg) ^= (1LL << (posn)))
#define IsBit(arg, posn) static_cast<bool>((arg) & (1LL << (posn)))

// #define DEBUG(x) cerr<<#x<<": "<<(x)<<endl
// #define DEBUG_VEC(v) cerr<<#v<<": ";REP(__i,(v).size())cerr<<((v)[__i])<<",
// ";cerr<<endl

typedef unsigned long long ull;
typedef long long ll;

struct in {
  int n;
  in() {}
  in(int n_) : n(n_){};
  template <class T> operator T() {
    T ret;
    cin >> ret;
    return ret;
  }
  template <class T> operator vector<T>() {
    vector<T> ret(n);
    for (int i = 0; i < n; i++)
      cin >> ret[i];
    return ret;
  }
};

// modint: mod 計算を int を扱うように扱える構造体
template <int MOD> struct ModInt {
  long long val;
  constexpr ModInt(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr ModInt operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr ModInt operator+(const ModInt &r) const noexcept {
    return ModInt(*this) += r;
  }
  constexpr ModInt operator-(const ModInt &r) const noexcept {
    return ModInt(*this) -= r;
  }
  constexpr ModInt operator*(const ModInt &r) const noexcept {
    return ModInt(*this) *= r;
  }
  constexpr ModInt operator/(const ModInt &r) const noexcept {
    return ModInt(*this) /= r;
  }
  constexpr ModInt &operator+=(const ModInt &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr ModInt &operator-=(const ModInt &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr ModInt &operator*=(const ModInt &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr ModInt &operator/=(const ModInt &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const ModInt &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const ModInt &r) const noexcept {
    return this->val != r.val;
  }

  friend ostream &operator<<(ostream &os, const ModInt<MOD> &x) noexcept {
    return os << x.val;
  }
  friend istream &operator>>(istream &is, ModInt<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr ModInt<MOD> modpow(const ModInt<MOD> &a,
                                      long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

// 二項係数ライブラリ
template <class T> struct BiCoef {
  constexpr BiCoef() {}
  constexpr BiCoef(int n) noexcept : mFact(n, 1), mInv(n, 1), mFInv(n, 1) {
    Init(n);
  }

  constexpr void Init(int n) noexcept {
    mFact.assign(n, 1), mInv.assign(n, 1), mFInv.assign(n, 1);
    int factMod = mFact[0].getmod();
    for (int i = 2; i < n; i++) {
      mFact[i] = mFact[i - 1] * i;
      mInv[i] = -mInv[factMod % i] * (factMod / i);
      mFInv[i] = mFInv[i - 1] * mInv[i];
    }
  }

  constexpr T Fact(int n) const noexcept {
    if (n < 0)
      return 0;
    return mFact[n];
  }

  constexpr T Comb(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return mFact[n] * mFInv[k] * mFInv[n - k];
  }

  constexpr T Perm(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return mFact[n] * mFInv[k] * mFInv[n - k];
  }

  constexpr T Homo(int n, int r) const {
    if (n < 0 || r < 0)
      return 0;
    return r == 0 ? 1 : Comb(n + r - 1, r);
  }

  constexpr T inv(int n) const noexcept {
    if (n < 0)
      return 0;
    return mInv[n];
  }

  constexpr T finv(int n) const noexcept {
    if (n < 0)
      return 0;
    return mFInv[n];
  }

  vector<T> mFact;
  vector<T> mInv;
  vector<T> mFInv;
};

const int MOD = 1000000007;
using mint = ModInt<MOD>;
// BiCoef<mint> bc(1234567); // 1M * 3 * 8B(ll) = 24MB

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  ll N;
  cin >> N;
  vector<ll> t = in(N);
  vector<ll> v = in(N);

  vector<ll> maxv(50000, BIGLL);

  maxv[0] = 0;
  ll nowt = 0;
  for (int i = 0; i < N; ++i) {
    for (int dt = 0; dt <= 2 * t[i]; ++dt) {
      amin(maxv[nowt + dt], 2 * v[i]);
    }

    nowt += 2 * t[i];
  }

  maxv[nowt] = 0;

  ll lastT = nowt;

  for (ll tt = lastT; tt >= 1; tt--) {
    amin(maxv[tt - 1], maxv[tt] + 1);
  }

  ll nowv = 0;
  ll ans = 0;
  for (int tt = 0; tt < lastT; tt++) {
    if (nowv + 1 <= maxv[tt]) {
      ans += (2 * nowv + 1);
      nowv++;
    } else if (nowv <= maxv[tt]) {
      ans += (2 * nowv);
      nowv;
    } else if (nowv - 1 <= maxv[tt]) {
      ans += (2 * nowv - 1);
      nowv--;
    } else {
      assert(0);
    }

    assert(nowv >= 0);
  }

  printf("%.20f\n", (ans + 1) / 8.0);

  return 0;
}