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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#754452 | #9631. Median Replacement | Golem__ | TL | 0ms | 3636kb | C++20 | 12.5kb | 2024-11-16 15:04:56 | 2024-11-16 15:04:57 |
Judging History
answer
// [Irelia]
#include<bits/stdc++.h>
namespace Irelia // [Irelia Library] Irelia
{
#define Irelia__ 201307
#define fcc(i, j, k) for(num (i)=(j); (i)<=(k); ++(i))
#define ccf(i, j, k) for(num (i)=(j); (i)>=(k); --(i))
#define I (*this)
#define same_type(T1, T2) (std::is_same<T1, T2>::value)
#define num_type(T) (same_type(T, num) || same_type(T, Num))
#define fra_type(T) (same_type(T, fra) || same_type(T, Fra))
#define num_or_fra_type(T) (num_type(T) || fra_type(T))
using num = int;
using Num = long long;
using unum = unsigned int;
using uNum = unsigned long long;
using fra = double;
using Fra = long double;
using pnum = std::pair<num, num>;
using pNum = std::pair<Num, Num>;
template<typename T>
using heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
const char newl = '\n', *snewl = " \n";
constexpr Num read()
{
Num ret = 0, s = 1, c = getchar();
for(; !isdigit(c); c = getchar()) if(c == '-') s = -1;
for(; isdigit(c); c = getchar()) ret = (ret << 1) + (ret << 3) + (c ^ 48);
return s * ret;
}
constexpr std::string readstr()
{
std::string ret; char c;
for(; (c = getchar()) <= ' ';);
for(; c > ' '; c = getchar()) ret += c;
return ret;
}
template<typename T>
constexpr void min_(T &a, auto &&b) { if(b < a) a = b; }
template<typename T>
constexpr void max_(T &a, auto &&b) { if(a < b) a = b; }
template<typename Tnf> requires num_or_fra_type(Tnf)
constexpr Tnf inf() { return (std::numeric_limits<Tnf>::max() - Irelia__) / 2; }
template<typename Tn> requires num_type(Tn)
constexpr Tn lowbit(Tn i) { return i & -i; }
template<typename T>
class vector : private std::vector<T>
{
public:
using iterator = std::vector<T>::iterator;
iterator begin() { return std::vector<T>::begin(); }
iterator end() { return std::vector<T>::end(); }
vector() { }
vector(num siz) : std::vector<T>(siz) { }
vector(num siz, auto &&t) : std::vector<T>(siz, t) { }
vector(std::initializer_list<T> il) : std::vector<T>(il) { }
vector(T *pb, T *pe) : std::vector<T>(pb, pe) { }
vector(iterator itb, iterator ite) : std::vector<T>(itb, ite) { }
void clear() { std::vector<T>::clear(); }
operator bool () { return !I.empty(); }
num size() { return std::vector<T>::size(); }
vector &set(num siz) { return I.resize(siz), I; }
T &front() { return std::vector<T>::front(); }
T &back() { return std::vector<T>::back(); }
T &operator [] (num i)
{
#ifdef DEBUG__
assert(0 <= i && i < size());
#endif
return std::vector<T>::operator[](i);
}
void push(auto &&...t) { I.emplace_back(t...); }
void insert(num i, auto &&...t) { I.emplace(begin() + i, t...); }
void pop() { I.pop_back(); }
void erase(num i) { std::vector<T>::erase(begin() + i); }
void fill(auto &&t) { std::fill(begin(), end(), t); }
void reverse() { std::reverse(begin(), end()); }
template<typename Tcom = std::less<T>>
void sort() { std::sort(begin(), end(), Tcom()); }
template<typename Tcom = std::less<T>>
num lower(auto &&t) { return std::lower_bound(begin(), end(), t, Tcom()) - begin(); }
template<typename Tcom = std::less<T>>
num upper(auto &&t) { return std::upper_bound(begin(), end(), t, Tcom()) - begin(); }
template<typename Tcom = std::less<T>>
void discretize()
{
sort<Tcom>(), set(std::unique(begin(), end(),
[&](T &a, T &b) { return !Tcom()(a, b) && !Tcom()(b, a); }) - begin());
}
};
#define every(e, G, o) for(num (e)=(G).las[(o)]; (e); (e)=(G).pre[(e)])
template<typename Tn> requires num_type(Tn)
class graph
{
public:
num V, E; vector<num> las, pre, to, fro; vector<Tn> wei, cap;
graph(num V = 0) : V(V), E(0), las(V + 1), pre(2), to(2), fro(2), wei(2), cap(2) { }
void add(num u, num v, Tn w = 0, Tn c = 0)
{ pre.push(las[u]), las[u] = ++E + 1, to.push(v), fro.push(u), wei.push(w), cap.push(c); }
void addb(num u, num v, Tn w = 0, Tn c = 0) { add(u, v, w, c), add(v, u, w, c); }
};
}
namespace Irelia // [Irelia Library] modulus
{
template<num mod>
class modnum
{
private:
num i;
public:
modnum(num i = 0) : i(i) { }
num operator () () { return i; }
modnum &operator ++ () { if(++i == mod) i = 0; return I; }
modnum operator ++ (num) { modnum ret = I; return ++I, ret; }
modnum operator + (modnum m) { num ret = i + m.i; if(ret >= mod) ret -= mod; return ret; }
modnum &operator += (modnum m) { if((i += m.i) >= mod) i -= mod; return I; }
modnum &operator -- () { if(!i--) i = mod - 1; return I; }
modnum operator -- (num) { modnum ret = I; return --I, ret; }
modnum operator - () { num ret = i ? mod - i : 0; return ret; }
modnum operator - (modnum m) { num ret = i - m.i; if(ret < 0) ret += mod; return ret; }
modnum &operator -= (modnum m) { if((i -= m.i) < 0) i += mod; return I; }
modnum operator * (modnum m) { return 1ULL * i * m.i % mod; }
modnum &operator *= (modnum m) { return i = 1ULL * i * m.i % mod, I; }
modnum operator / (modnum m) { return I * m.inv(); }
modnum &operator /= (modnum m) { return I *= m.inv(); }
modnum power(num e)
{ modnum ret = 1, d = I; for(; e; e >>= 1, d *= d) if(e & 1) ret *= d; return ret; }
modnum inv() { return power(mod - 2); }
friend std::ostream &operator << (std::ostream &os, modnum m) { return std::cout << m.i; }
};
}
namespace Irelia // [Irelia Library] poly
{
template<num mod, num pr>
class poly : public vector<modnum<mod>>
{
static poly ur;
public:
using iterator = vector<modnum<mod>>::iterator;
poly() { }
poly(num len) : vector<modnum<mod>>(len) { }
poly(std::initializer_list<modnum<mod>> il) : vector<modnum<mod>>(il) { }
poly(modnum<mod> *pb, modnum<mod> *pe) : vector<modnum<mod>>(pb, pe) { }
poly(iterator itb, iterator ite) : vector<modnum<mod>>(itb, ite) { }
poly &set(num len) { return vector<modnum<mod>>::set(len), I; }
static void set_ur(num len)
{
if(ur.size() < len)
{
num las = ur.size(); ur.set(len);
for(num d = las; d < len; d <<= 1)
ur[d] = modnum<mod>(pr).power((mod - 1 >> 2) / d);
fcc(i, las, len - 1) ur[i] = ur[i ^ lowbit(i)] * ur[lowbit(i)];
}
}
void NTT(num len)
{
modnum<mod> t; set_ur(len >> 1);
if(I.size() < len) set(len);
for(num d = len >> 1; d; d >>= 1)
for(num i = 0, u = 0; i < len; i += d << 1, ++u)
for(num j = i, k = i + d; j < i + d; ++j, ++k)
t = I[k] * ur[u], I[k] = I[j] - t, I[j] += t;
}
void INTT(num len)
{
modnum<mod> t; set_ur(len >> 1);
if(I.size() < len) set(len);
for(num d = 1; d < len; d <<= 1)
for(num i = 0, u = 0; i < len; i += d << 1, ++u)
for(num j = i, k = i + d; j < i + d; ++j, ++k)
t = I[k], I[k] = (I[j] - I[k]) * ur[u], I[j] += t;
std::reverse(I.begin() + 1, I.end()), t = modnum<mod>(len).inv();
fcc(i, 0, len - 1) I[i] *= t;
}
poly operator + (auto &&P) { return poly(I) += P; }
poly &operator += (auto &&P)
{ if(I.size() < P.size()) set(P.size()); fcc(i, 0, P.size() - 1) I[i] += P[i]; return I; }
poly operator - (auto &&P) { return poly(I) -= P; }
poly &operator -= (auto &&P)
{ if(I.size() < P.size()) set(P.size()); fcc(i, 0, P.size() - 1) I[i] -= P[i]; return I; }
poly operator * (auto &&P) { return poly(I) *= P; }
poly &operator *= (auto &&P)
{
num len = I.size() + P.size() - 1, bc = std::bit_ceil<unum>(len);
if(len < 100)
{
poly R(len);
fcc(i, 0, I.size() - 1) fcc(j, 0, P.size() - 1) R[i + j] += I[i] * P[j];
return I = R;
}
NTT(bc), P.NTT(bc);
fcc(i, 0, bc - 1) I[i] *= P[i];
return INTT(bc), set(len);
}
poly inv()
{
num bc = std::bit_ceil<unum>(I.size()); poly P, Q, R({ I[0].inv() });
for(num d = 2; d <= bc; d <<= 1)
{
P = poly(I.begin(), I.begin() + std::min(I.size(), d)), Q = R;
P.NTT(d << 1), Q.NTT(d << 1);
fcc(i, 0, (d << 1) - 1) P[i] *= Q[i] * Q[i];
P.INTT(d << 1), R = R + R - P.set(d);
}
return R.set(I.size());
}
poly operator / (auto &&P) { return poly(I) /= P; }
poly &operator /= (auto &&P) { return I *= P.inv(); }
poly deriv() { poly R(I.size()); fcc(i, 1, I.size() - 1) R[i - 1] = I[i] * i; return R; }
poly integ() { poly R(I.size()); fcc(i, 1, I.size() - 1) R[i] = I[i - 1] / i; return R; }
poly ln() { return (deriv() * inv()).integ(); }
poly exp()
{
poly P = deriv(), Q, R(I.size());
std::function<void(num, num)> DAC = [&](num l, num r)
{
if(l == r) return l ? (R[l] /= l) : (R[l] = 1), void();
num m = l + r >> 1; DAC(l, m);
Q = poly(R.begin() + l, R.begin() + m + 1) * poly(P.begin(), P.begin() + r - l);
fcc(i, m + 1, r) R[i] += Q[i - l - 1];
DAC(m + 1, r);
};
return DAC(0, I.size() - 1), R;
}
modnum<mod> operator () (modnum<mod> x)
{ modnum<mod> y = 0; ccf(i, I.size() - 1, 0) y = y * x + I[i]; return y; }
static poly Lagrange(vector<modnum<mod>> X, vector<modnum<mod>> Y)
{
#ifdef DEBUG__
assert(X.size() == Y.size());
#endif
num len = X.size(); poly P(len + 1), Q, R(len); P[0] = 1;
fcc(i, 0, len - 1) ccf(j, i, 0) P[j + 1] += P[j], P[j] *= -X[i];
fcc(i, 0, len - 1)
{
modnum<mod> mul = 1;
fcc(j, 0, len - 1) if(i != j) mul *= X[i] - X[j];
mul = Y[i] / mul, Q = P;
ccf(j, len - 1, 0) R[j] += Q[j + 1] * mul, Q[j] += Q[j + 1] * X[i];
}
return R;
}
};
template<num mod, num pr>
poly<mod, pr> poly<mod, pr>::ur({ modnum<mod>(1) });
}
using namespace Irelia;
const num mod = 1E9 + 7;
using Mod = modnum<mod>;
using Poly = poly<mod, 3>;
void solve()
{
num N = read(), D;
vector<num> L(N + 1), R(N + 1), dis({ 0, 1 });
fcc(i, 1, N) L[i] = read(), dis.push(L[i]);
fcc(i, 1, N) R[i] = read(), dis.push(R[i] + 1);
dis.discretize(), D = dis.size() - 1;
Mod ans = 0, mul = 1;
fcc(i, 1, N) mul *= R[i] - L[i] + 1;
auto work = [&](num x)
{
vector<std::array<Mod, 3>> dp(N + 1);
fcc(j, 0, 2) dp[0][j] = 1;
fcc(i, 1, N) fcc(j, 0, 2)
{
if(L[i] < x) dp[i][j] = dp[i - 1][std::max(0, j - 1)] * (std::min(R[i] + 1, x) - L[i]);
if(!j && R[i] >= x) dp[i][j] += dp[i - 1][2] * (R[i] - std::max(L[i], x) + 1);
}
return mul - dp[N][0];
};
fcc(d, 1, D - 1)
{
num l = dis[d], r = dis[d + 1] - 1;
fcc(x, l, r) ans += work(x);
// if(r - l + 1 <= N + 1) fcc(x, l, r) ans -= work(x);
// else
// {
// Poly X(N + 1), Y(N + 1);
// fcc(i, 0, N) X[i] = i + l, Y[i] = work(i + l);
// Poly P = Poly::Lagrange(X, Y);
// fcc(i, l, r) assert(P(i)() == work(i)());
// P.push(0), P = P.integ(), ans -= P(r) - P(l - 1);
// }
}
std::cout << ans << newl;
}
num main()
{
#ifndef ONLINE_JUDGE
freopen(".in", "r", stdin);
freopen(".out", "w", stdout);
#endif
std::ios::sync_with_stdio(0), std::cin.tie(0);
for(num T = read(); T --> 0;) solve();
return 0 ^ 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3636kb
input:
10 5 5 1 4 3 2 14 2 5 3 2 5 4 5 1 2 3 13 7 1 2 3 5 5 2 5 3 1 10 2 12 3 2 5 5 5 3 1 5 57 5 3 1 5 5 2 2 3 3 5 4 5 4 4 5 5 4 5 3 5 3 13 7 3 5 3 5 5 1 4 2 3 14 3 4 2 3 5 1 2 5 4 5 2 8 5 7 5 5 1 1 3 5 1 8 2 3 8 1 5 4 4 4 2 3 5 10 5 2 3
output:
180 170 650 265 182 173 120 296 192 131
result:
ok 10 lines
Test #2:
score: 0
Accepted
time: 0ms
memory: 3620kb
input:
10 5 1 2 2 5 3 6 4 2 6 3 5 4 4 1 4 3 6 7 2 5 3 5 5 3 4 2 4 5 7 5 2 6 5 1 5 3 5 2 7 7 3 5 2 5 1 3 3 2 2 10 5 3 2 2 5 4 4 4 5 3 4 11 9 5 3 5 5 3 2 1 3 13 5 2 1 5 5 5 4 1 2 5 10 6 1 2 5 5 3 5 3 4 2 5 9 3 5 2 5 1 1 3 2 1 7 3 3 3 1
output:
120 230 144 110 110 289 324 89 140 122
result:
ok 10 lines
Test #3:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
10 5 3 1 3 4 4 9 1 3 10 4 5 1 1 3 1 1 9 1 3 3 1 5 5 1 2 3 1 74 1 2 3 1 5 2 5 5 3 4 5 6 8 3 4 5 2 1 3 4 5 2 4 6 4 5 5 2 4 2 1 3 2 11 3 2 3 5 1 5 4 4 2 1 14 6 6 2 5 4 1 3 5 1 9 2 4 5 1 5 4 1 2 4 4 6 1 6 4 4 5 3 2 5 3 5 8 8 5 3 5
output:
196 76 140 172 72 80 486 84 65 224
result:
ok 10 lines
Test #4:
score: -100
Time Limit Exceeded
input:
10 5 676437428 903889545 700650370 965758082 146716866 676437431 903889567 700650370 965758082 146716866 5 517457740 64600397 388618400 783268973 388618400 517457797 64600397 388618400 783268973 388618400 5 971452763 106948541 259878781 537741075 9504353 971452780 106948544 259878781 537741075 95043...