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#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#include "include/mtl/segment_tree.hpp"
#include "include/mtl/modular.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll MOD = 998244353;
using mint = Modular<MOD>;
struct M {
mint a=1, b=0;
M operator*(M r) const {
return {a*r.a, b*r.a+r.b};
}
M& operator*=(M r) {return *this = *this * r;}
};
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
int N,Q; cin>>N>>Q;
vector<M> F(N); for (auto& f : F) cin>>f.a>>f.b;
SegmentTree<M> st(F.begin(), F.end());
for (int q = 0; q < Q; q++) {
int t; cin>>t;
if (t == 0) {
int p,c,d; cin>>p>>c>>d;
st.set(p, {c,d});
} else if (t == 1) {
int l,r,x; cin>>l>>r>>x;
auto comp = st.query(l,r);
auto ans = comp.a*x + comp.b;
cout << ans << endl;
}
}
return 0;
}
#line 1 "test/yosupo/point_set_range_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#line 2 "include/mtl/bit_manip.hpp"
#include <cstdint>
#include <cassert>
#if __cplusplus >= 202002L
#ifndef MTL_CPP20
#define MTL_CPP20
#endif
#include <bit>
#endif
namespace bm {
/// Count 1s for each 8 bits
inline constexpr uint64_t popcnt_e8(uint64_t x) {
x = (x & 0x5555555555555555) + ((x>>1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x>>2) & 0x3333333333333333);
x = (x & 0x0F0F0F0F0F0F0F0F) + ((x>>4) & 0x0F0F0F0F0F0F0F0F);
return x;
}
/// Count 1s
inline constexpr unsigned popcnt(uint64_t x) {
#ifdef MTL_CPP20
return std::popcount(x);
#else
return (popcnt_e8(x) * 0x0101010101010101) >> 56;
#endif
}
/// Alias to mtl::popcnt(x)
constexpr unsigned popcount(uint64_t x) {
return popcnt(x);
}
/// Count trailing 0s. s.t. *11011000 -> 3
inline constexpr unsigned ctz(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_zero(x);
#else
return popcnt((x & (-x)) - 1);
#endif
}
/// Alias to mtl::ctz(x)
constexpr unsigned countr_zero(uint64_t x) {
return ctz(x);
}
/// Count trailing 1s. s.t. *11011011 -> 2
inline constexpr unsigned cto(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_one(x);
#else
return ctz(~x);
#endif
}
/// Alias to mtl::cto(x)
constexpr unsigned countr_one(uint64_t x) {
return cto(x);
}
inline constexpr unsigned ctz8(uint8_t x) {
return x == 0 ? 8 : popcnt_e8((x & (-x)) - 1);
}
/// [00..0](8bit) -> 0, [**..*](not only 0) -> 1
inline constexpr uint8_t summary(uint64_t x) {
constexpr uint64_t hmask = 0x8080808080808080ull;
constexpr uint64_t lmask = 0x7F7F7F7F7F7F7F7Full;
auto a = x & hmask;
auto b = x & lmask;
b = hmask - b;
b = ~b;
auto c = (a | b) & hmask;
c *= 0x0002040810204081ull;
return uint8_t(c >> 56);
}
/// Extract target area of bits
inline constexpr uint64_t bextr(uint64_t x, unsigned start, unsigned len) {
uint64_t mask = len < 64 ? (1ull<<len)-1 : 0xFFFFFFFFFFFFFFFFull;
return (x >> start) & mask;
}
/// 00101101 -> 00111111 -count_1s-> 6
inline constexpr unsigned log2p1(uint8_t x) {
if (x & 0x80)
return 8;
uint64_t p = uint64_t(x) * 0x0101010101010101ull;
p -= 0x8040201008040201ull;
p = ~p & 0x8080808080808080ull;
p = (p >> 7) * 0x0101010101010101ull;
p >>= 56;
return p;
}
/// 00101100 -mask_mssb-> 00100000 -to_index-> 5
inline constexpr unsigned mssb8(uint8_t x) {
assert(x != 0);
return log2p1(x) - 1;
}
/// 00101100 -mask_lssb-> 00000100 -to_index-> 2
inline constexpr unsigned lssb8(uint8_t x) {
assert(x != 0);
return popcnt_e8((x & -x) - 1);
}
/// Count leading 0s. 00001011... -> 4
inline constexpr unsigned clz(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_zero(x);
#else
if (x == 0)
return 64;
auto i = mssb8(summary(x));
auto j = mssb8(bextr(x, 8 * i, 8));
return 63 - (8 * i + j);
#endif
}
/// Alias to mtl::clz(x)
constexpr unsigned countl_zero(uint64_t x) {
return clz(x);
}
/// Count leading 1s. 11110100... -> 4
inline constexpr unsigned clo(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_one(x);
#else
return clz(~x);
#endif
}
/// Alias to mtl::clo(x)
constexpr unsigned countl_one(uint64_t x) {
return clo(x);
}
inline constexpr unsigned clz8(uint8_t x) {
return x == 0 ? 8 : 7 - mssb8(x);
}
inline constexpr uint64_t bit_reverse(uint64_t x) {
x = ((x & 0x00000000FFFFFFFF) << 32) | ((x & 0xFFFFFFFF00000000) >> 32);
x = ((x & 0x0000FFFF0000FFFF) << 16) | ((x & 0xFFFF0000FFFF0000) >> 16);
x = ((x & 0x00FF00FF00FF00FF) << 8) | ((x & 0xFF00FF00FF00FF00) >> 8);
x = ((x & 0x0F0F0F0F0F0F0F0F) << 4) | ((x & 0xF0F0F0F0F0F0F0F0) >> 4);
x = ((x & 0x3333333333333333) << 2) | ((x & 0xCCCCCCCCCCCCCCCC) >> 2);
x = ((x & 0x5555555555555555) << 1) | ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
return x;
}
/// Check if x is power of 2. 00100000 -> true, 00100001 -> false
constexpr bool has_single_bit(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::has_single_bit(x);
#else
return x != 0 && (x & (x - 1)) == 0;
#endif
}
/// Bit width needs to represent x. 00110110 -> 6
constexpr int bit_width(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::bit_width(x);
#else
return 64 - clz(x);
#endif
}
/// Ceil power of 2. 00110110 -> 01000000
constexpr uint64_t bit_ceil(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_ceil(x);
#else
if (x == 0) return 1;
return 1ull << bit_width(x - 1);
#endif
}
/// Floor power of 2. 00110110 -> 00100000
constexpr uint64_t bit_floor(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_floor(x);
#else
if (x == 0) return 0;
return 1ull << (bit_width(x) - 1);
#endif
}
} // namespace bm
#line 3 "include/mtl/segment_tree.hpp"
#include <cstddef>
#include <vector>
#include <stack>
#if __cplusplus >= 202002L
#include <concepts>
template<class M>
concept SegmentTreeMonoid = requires (M m) {
{m * m} -> std::same_as<M>;
};
#endif
template <class M>
class SegmentTree {
#if __cplusplus >= 202002L
static_assert(SegmentTreeMonoid<M>);
#endif
public:
using monoid_type = M;
using value_type = monoid_type;
private:
size_t size_;
std::vector<value_type> tree_;
public:
explicit SegmentTree(size_t size) : size_(size), tree_(size*2) {}
template <class Iter>
explicit SegmentTree(Iter begin, Iter end) : SegmentTree(std::distance(begin, end)) {
if (size_==0) return;
std::copy(begin, end, tree_.begin() + size_);
for (size_t i = size_-1; i > 0; i--)
tree_[i] = tree_[i<<1] * tree_[(i<<1)+1];
}
value_type get(size_t index) const {
return tree_[size_ + index];
}
value_type operator[](size_t index) const {
return get(index);
}
private:
template<class T>
void _set(size_t index, T&& val) {
auto i = size_ + index;
tree_[i] = std::forward<T>(val);
i >>= 1;
while (i > 0) {
tree_[i] = tree_[i<<1] * tree_[(i<<1)+1];
i >>= 1;
}
}
public:
template<class T>
void set(size_t index, T&& val) {
return _set(index, std::forward<T>(val));
}
void set(size_t index, const value_type& val) {
_set(index, val);
}
void set(size_t index, value_type&& val) {
_set(index, std::move(val));
}
value_type query(size_t l, size_t r) const {
value_type lhs,rhs;
for (auto _l = l+size_, _r = r+size_; _l < _r; _l>>=1, _r>>=1) {
if (_l&1) lhs = lhs * tree_[_l++];
if (_r&1) rhs = tree_[--_r] * rhs;
}
return lhs * rhs;
}
template<class F>
size_t max_right(size_t begin, size_t end, F f) const {
if (begin == end) return end;
monoid_type p;
std::stack<std::pair<size_t, monoid_type>> rps;
auto l = size_ + begin;
auto r = size_ + end;
while (l < r and f(p * tree_[l])) {
if (l&1) p = p * tree_[l++];
if (r&1) {
rps.emplace(r, tree_[r-1]);
r--;
}
l>>=1; r>>=1;
}
if (l >= r) {
while (rps.size()) {
auto& [r, rp] = rps.top();
if (!f(p * rp)) {
l = r-1;
break;
}
p = p * rp;
rps.pop();
}
if (rps.empty()) return end;
}
while (l < size_) {
assert(!f(p * tree_[l]));
l <<= 1;
if (f(p * tree_[l]))
p = p * tree_[l++];
}
return l - size_;
}
template<class F>
size_t min_left(size_t begin, size_t end, F f) const {
if (end == begin) return begin;
monoid_type p;
std::stack<std::pair<size_t, monoid_type>> lps;
auto l = size_ + begin;
auto r = size_ + end;
while (l < r and f(tree_[r-1] * p)) {
if (l&1) {
lps.emplace(l, tree_[l]);
l++;
}
if (r&1) p = tree_[r-1] * p;
l>>=1; r>>=1;
}
if (l >= r) {
while (lps.size()) {
auto& [l, lp] = lps.top();
if (!f(lp * p)) {
r = l+1;
break;
}
p = lp * p;
lps.pop();
}
if (lps.empty()) return begin;
}
while (r <= size_) {
assert(!f(tree_[r-1] * p));
r <<= 1;
if (f(tree_[r-1] * p))
p = tree_[--r] * p;
}
return r - size_;
}
template<bool (*F)(value_type)>
size_t min_left(size_t begin, size_t end) const {
return min_left(begin, [](value_type x) { return F(x); });
}
};
#line 3 "include/mtl/modular.hpp"
#include <iostream>
#line 5 "include/mtl/modular.hpp"
template <int MOD>
class Modular {
private:
unsigned int val_;
public:
static constexpr unsigned int mod() { return MOD; }
template<class T>
static constexpr unsigned int safe_mod(T v) {
auto x = (long long)(v%(long long)mod());
if (x < 0) x += mod();
return (unsigned int) x;
}
constexpr Modular() : val_(0) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && std::is_unsigned<T>::value
> * = nullptr>
constexpr Modular(T v) : val_(v%mod()) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && !std::is_unsigned<T>::value
> * = nullptr>
constexpr Modular(T v) : val_(safe_mod(v)) {}
constexpr unsigned int val() const { return val_; }
constexpr Modular& operator+=(Modular x) {
val_ += x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr Modular operator-() const { return {mod() - val_}; }
constexpr Modular& operator-=(Modular x) {
val_ += mod() - x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr Modular& operator*=(Modular x) {
auto v = (long long) val_ * x.val();
if (v >= mod()) v %= mod();
val_ = v;
return *this;
}
constexpr Modular pow(long long p) const {
assert(p >= 0);
Modular t = 1;
Modular u = *this;
while (p) {
if (p & 1)
t *= u;
u *= u;
p >>= 1;
}
return t;
}
friend constexpr Modular pow(Modular x, long long p) {
return x.pow(p);
}
constexpr Modular inv() const { return pow(mod()-2); }
constexpr Modular& operator/=(Modular x) { return *this *= x.inv(); }
constexpr Modular operator+(Modular x) const { return Modular(*this) += x; }
constexpr Modular operator-(Modular x) const { return Modular(*this) -= x; }
constexpr Modular operator*(Modular x) const { return Modular(*this) *= x; }
constexpr Modular operator/(Modular x) const { return Modular(*this) /= x; }
constexpr Modular& operator++() { return *this += 1; }
constexpr Modular operator++(int) { Modular c = *this; ++(*this); return c; }
constexpr Modular& operator--() { return *this -= 1; }
constexpr Modular operator--(int) { Modular c = *this; --(*this); return c; }
constexpr bool operator==(Modular x) const { return val() == x.val(); }
constexpr bool operator!=(Modular x) const { return val() != x.val(); }
constexpr bool is_square() const {
return pow((mod()-1)/2) == 1;
}
/**
* Return x s.t. x * x = a mod p
* reference: https://zenn.dev/peria/articles/c6afc72b6b003c
*/
constexpr Modular sqrt() const {
if (!is_square())
throw std::runtime_error("not square");
auto mod_eight = mod() % 8;
if (mod_eight == 3 || mod_eight == 7) {
return pow((mod()+1)/4);
} else if (mod_eight == 5) {
auto x = pow((mod()+3)/8);
if (x * x != *this)
x *= Modular(2).pow((mod()-1)/4);
return x;
} else {
Modular d = 2;
while (d.is_square())
d += 1;
auto t = mod()-1;
int s = bm::ctz(t);
t >>= s;
auto a = pow(t);
auto D = d.pow(t);
int m = 0;
Modular dt = 1;
Modular du = D;
for (int i = 0; i < s; i++) {
if ((a*dt).pow(1u<<(s-1-i)) == -1) {
m |= 1u << i;
dt *= du;
}
du *= du;
}
return pow((t+1)/2) * D.pow(m/2);
}
}
friend std::ostream& operator<<(std::ostream& os, const Modular& x) {
return os << x.val();
}
friend std::istream& operator>>(std::istream& is, Modular& x) {
return is >> x.val_;
}
};
using Modular998244353 = Modular<998244353>;
using Modular1000000007 = Modular<(int)1e9+7>;
template<int Id=0>
class DynamicModular {
private:
static unsigned int mod_;
unsigned int val_;
public:
static unsigned int mod() { return mod_; }
static void set_mod(unsigned int m) { mod_ = m; }
template<class T>
static constexpr unsigned int safe_mod(T v) {
auto x = (long long)(v%(long long)mod());
if (x < 0) x += mod();
return (unsigned int) x;
}
constexpr DynamicModular() : val_(0) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && std::is_unsigned<T>::value
> * = nullptr>
constexpr DynamicModular(T v) : val_(v%mod()) {}
template<class T,
std::enable_if_t<
std::is_integral<T>::value && !std::is_unsigned<T>::value
> * = nullptr>
constexpr DynamicModular(T v) : val_(safe_mod(v)) {}
constexpr unsigned int val() const { return val_; }
constexpr DynamicModular& operator+=(DynamicModular x) {
val_ += x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr DynamicModular operator-() const { return {mod() - val_}; }
constexpr DynamicModular& operator-=(DynamicModular x) {
val_ += mod() - x.val();
if (val_ >= mod()) val_ -= mod();
return *this;
}
constexpr DynamicModular& operator*=(DynamicModular x) {
auto v = (long long) val_ * x.val();
if (v >= mod()) v %= mod();
val_ = v;
return *this;
}
constexpr DynamicModular pow(long long p) const {
assert(p >= 0);
DynamicModular t = 1;
DynamicModular u = *this;
while (p) {
if (p & 1)
t *= u;
u *= u;
p >>= 1;
}
return t;
}
friend constexpr DynamicModular pow(DynamicModular x, long long p) {
return x.pow(p);
}
// TODO: implement when mod is not prime
constexpr DynamicModular inv() const { return pow(mod()-2); }
constexpr DynamicModular& operator/=(DynamicModular x) { return *this *= x.inv(); }
constexpr DynamicModular operator+(DynamicModular x) const { return DynamicModular(*this) += x; }
constexpr DynamicModular operator-(DynamicModular x) const { return DynamicModular(*this) -= x; }
constexpr DynamicModular operator*(DynamicModular x) const { return DynamicModular(*this) *= x; }
constexpr DynamicModular operator/(DynamicModular x) const { return DynamicModular(*this) /= x; }
constexpr DynamicModular& operator++() { return *this += 1; }
constexpr DynamicModular operator++(int) { DynamicModular c = *this; ++(*this); return c; }
constexpr DynamicModular& operator--() { return *this -= 1; }
constexpr DynamicModular operator--(int) { DynamicModular c = *this; --(*this); return c; }
constexpr bool operator==(DynamicModular x) const { return val() == x.val(); }
constexpr bool operator!=(DynamicModular x) const { return val() != x.val(); }
constexpr bool is_square() const {
return val() == 0 or pow((mod()-1)/2) == 1;
}
/**
* Return x s.t. x * x = a mod p
* reference: https://zenn.dev/peria/articles/c6afc72b6b003c
*/
constexpr DynamicModular sqrt() const {
// assert mod is prime
if (!is_square())
throw std::runtime_error("not square");
if (val() < 2)
return val();
auto mod_eight = mod() % 8;
if (mod_eight == 3 || mod_eight == 7) {
return pow((mod()+1)/4);
} else if (mod_eight == 5) {
auto x = pow((mod()+3)/8);
if (x * x != *this)
x *= DynamicModular(2).pow((mod()-1)/4);
return x;
} else {
DynamicModular d = 2;
while (d.is_square())
++d;
auto t = mod()-1;
int s = bm::ctz(t);
t >>= s;
auto a = pow(t);
auto D = d.pow(t);
int m = 0;
DynamicModular dt = 1;
DynamicModular du = D;
for (int i = 0; i < s; i++) {
if ((a*dt).pow(1u<<(s-1-i)) == -1) {
m |= 1u << i;
dt *= du;
}
du *= du;
}
return pow((t+1)/2) * D.pow(m/2);
}
}
friend std::ostream& operator<<(std::ostream& os, const DynamicModular& x) {
return os << x.val();
}
friend std::istream& operator>>(std::istream& is, DynamicModular& x) {
return is >> x.val_;
}
};
template<int Id>
unsigned int DynamicModular<Id>::mod_;
#line 264 "include/mtl/modular.hpp"
template<class ModInt>
struct ModularUtil {
static constexpr int mod = ModInt::mod();
static struct inv_table {
std::vector<ModInt> tb{0,1};
inv_table() : tb({0,1}) {}
} inv_;
void set_inv(int n) {
int m = inv_.tb.size();
if (m > n) return;
inv_.tb.resize(n+1);
for (int i = m; i < n+1; i++)
inv_.tb[i] = -inv_.tb[mod % i] * (mod / i);
}
ModInt& inv(int i) {
set_inv(i);
return inv_.tb[i];
}
};
template<class ModInt>
typename ModularUtil<ModInt>::inv_table ModularUtil<ModInt>::inv_;
#include <array>
namespace math {
constexpr int mod_pow_constexpr(int x, int p, int m) {
long long t = 1;
long long u = x;
while (p) {
if (p & 1) {
t *= u;
t %= m;
}
u *= u;
u %= m;
p >>= 1;
}
return (int) t;
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 880803841) return 26;
if (m == 998244353) return 3;
std::array<int, 20> divs{};
int cnt = 0;
int x = m-1;
if (x % 2 == 0) {
divs[cnt++] = 2;
x >>= bm::ctz(x);
}
for (int d = 3; d*d <= x; d += 2) {
if (x % d == 0) {
divs[cnt++] = d;
while (x % d == 0)
x /= d;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2; g < m; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (mod_pow_constexpr(g, (m-1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
return -1;
}
template<int m>
constexpr int primitive_root = primitive_root_constexpr(m);
}
#line 4 "test/yosupo/point_set_range_composite.test.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll MOD = 998244353;
using mint = Modular<MOD>;
struct M {
mint a=1, b=0;
M operator*(M r) const {
return {a*r.a, b*r.a+r.b};
}
M& operator*=(M r) {return *this = *this * r;}
};
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
int N,Q; cin>>N>>Q;
vector<M> F(N); for (auto& f : F) cin>>f.a>>f.b;
SegmentTree<M> st(F.begin(), F.end());
for (int q = 0; q < Q; q++) {
int t; cin>>t;
if (t == 0) {
int p,c,d; cin>>p>>c>>d;
st.set(p, {c,d});
} else if (t == 1) {
int l,r,x; cin>>l>>r>>x;
auto comp = st.query(l,r);
auto ans = comp.a*x + comp.b;
cout << ans << endl;
}
}
return 0;
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 |
![]() |
5 ms | 3 MB |
g++ | max_random_00 |
![]() |
467 ms | 15 MB |
g++ | max_random_01 |
![]() |
465 ms | 15 MB |
g++ | max_random_02 |
![]() |
467 ms | 15 MB |
g++ | max_random_03 |
![]() |
482 ms | 15 MB |
g++ | max_random_04 |
![]() |
470 ms | 15 MB |
g++ | random_00 |
![]() |
386 ms | 12 MB |
g++ | random_01 |
![]() |
417 ms | 14 MB |
g++ | random_02 |
![]() |
360 ms | 4 MB |
g++ | random_03 |
![]() |
73 ms | 13 MB |
g++ | random_04 |
![]() |
116 ms | 10 MB |
g++ | small_00 |
![]() |
6 ms | 3 MB |
g++ | small_01 |
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6 ms | 3 MB |
g++ | small_02 |
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6 ms | 3 MB |
g++ | small_03 |
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6 ms | 3 MB |
g++ | small_04 |
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6 ms | 3 MB |
clang++ | example_00 |
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6 ms | 3 MB |
clang++ | max_random_00 |
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481 ms | 15 MB |
clang++ | max_random_01 |
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531 ms | 15 MB |
clang++ | max_random_02 |
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586 ms | 15 MB |
clang++ | max_random_03 |
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490 ms | 15 MB |
clang++ | max_random_04 |
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658 ms | 15 MB |
clang++ | random_00 |
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392 ms | 12 MB |
clang++ | random_01 |
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405 ms | 14 MB |
clang++ | random_02 |
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390 ms | 4 MB |
clang++ | random_03 |
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89 ms | 13 MB |
clang++ | random_04 |
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153 ms | 10 MB |
clang++ | small_00 |
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7 ms | 3 MB |
clang++ | small_01 |
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6 ms | 3 MB |
clang++ | small_02 |
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6 ms | 3 MB |
clang++ | small_03 |
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6 ms | 3 MB |
clang++ | small_04 |
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7 ms | 3 MB |