This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Summer/2450
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
// Do use segment tree
#include <iostream>
#include <algorithm>
#include "src/Graph/Graph.hpp"
#include "src/Graph/HeavyLightDecomposition.hpp"
#include "src/DataStructure/SegmentTree.hpp"
using namespace std;
struct M {
struct T {
long long sum, max, lmax, rmax;
};
using E= long long;
static inline long long INF= 1ll << 60;
static T ti() { return {0, -INF, -INF, -INF}; }
static T op(const T &a, const T &b) {
T ret;
ret.sum= a.sum + b.sum;
ret.max= max({a.max, b.max, a.rmax + b.lmax});
ret.lmax= max(a.lmax, a.sum + b.lmax);
ret.rmax= max(a.rmax + b.sum, b.rmax);
return ret;
}
static void mp(T &v, const E &f, int sz) {
v.sum= f * sz;
v.max= v.lmax= v.rmax= max(v.sum, f);
}
static void cp(E &pre, const E &suf) { pre= suf; }
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
int N, Q;
cin >> N >> Q;
vector<long long> w(N);
for (int u= 0; u < N; ++u) cin >> w[u];
Graph g(N, N - 1);
for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
HeavyLightDecomposition hld(g);
vector<typename M::T> ar(N);
for (int u= N; u--;) ar[hld.to_seq(u)]= {w[u], w[u], w[u], w[u]};
SegmentTree<M> seg1(ar);
reverse(ar.begin(), ar.end());
SegmentTree<M> seg2(ar);
while (Q--) {
long long t, a, b, c;
cin >> t >> a >> b >> c, --a, --b;
if (t == 1) {
for (auto [x, y]: hld.path(a, b))
if (x < y) seg1.apply(x, y + 1, c), seg2.apply(N - y - 1, N - x, c);
else seg1.apply(y, x + 1, c), seg2.apply(N - x - 1, N - y, c);
} else {
typename M::T ans= M::ti();
for (auto [x, y]: hld.path(a, b)) ans= M::op(ans, x < y ? seg1.prod(x, y + 1) : seg2.prod(N - x - 1, N - y));
cout << ans.max << '\n';
}
}
return 0;
}
#line 1 "test/aoj/2450.HLD.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Summer/2450
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
// Do use segment tree
#include <iostream>
#include <algorithm>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
template <class T> struct name { \
using Iterator= typename std::vector<T>::IT; \
Iterator bg, ed; \
Iterator begin() const { return bg; } \
Iterator end() const { return ed; } \
size_t size() const { return std::distance(bg, ed); } \
CT &operator[](int i) const { return bg[i]; } \
}
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
std::vector<T> dat;
std::vector<int> p;
size_t size() const { return p.size() - 1; }
ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
os << '[';
for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
using std::pair<int, int>::pair;
Edge &operator--() { return --first, --second, *this; }
int to(int v) const { return first ^ second ^ v; }
friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
size_t n;
Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
size_t vertex_size() const { return n; }
size_t edge_size() const { return size(); }
size_t add_vertex() { return n++; }
size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
for (auto [u, v]: *this) a; \
for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
for (int i= size(); i--;) { \
auto [u, v]= (*this)[i]; \
b; \
}
#define _ADJ(a, b) \
vector<int> p(n + 1), c(size() << !dir); \
if (!dir) { \
_ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
} else if (dir > 0) { \
_ADJ_FOR(++p[u], c[--p[u]]= a) \
} else { \
_ADJ_FOR(++p[v], c[--p[v]]= b) \
} \
return {c, p}
CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 2 "src/Graph/HeavyLightDecomposition.hpp"
#include <array>
#include <cassert>
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
std::vector<int> P, PP, D, I, L, R;
public:
HeavyLightDecomposition()= default;
HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
const int n= adj.size();
P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
for (P[r]= -1, I[t++]= r; i < t; ++i)
for (int u: adj[v= I[i]])
if (P[v] != u) P[I[t++]= u]= v;
};
f(root);
for (int r= 0; r < n; ++r)
if (P[r] == -2) f(r);
std::vector<int> Z(n, 1), nx(n, -1);
for (int i= n, v; i--;) {
if (P[v= I[i]] == -1) continue;
if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
}
for (int v= n; v--;) PP[v]= v;
for (int v: I)
if (nx[v] != -1) PP[nx[v]]= v;
for (int v: I)
if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
for (int i= n; i--;) L[I[i]]= i;
for (int v: I) {
int ir= R[v]= L[v] + Z[v];
for (int u: adj[v])
if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
if (nx[v] != -1) L[nx[v]]= L[v] + 1;
}
for (int i= n; i--;) I[L[i]]= i;
}
int to_seq(int v) const { return L[v]; }
int to_vertex(int i) const { return I[i]; }
size_t size() const { return P.size(); }
int parent(int v) const { return P[v]; }
int head(int v) const { return PP[v]; }
int root(int v) const {
for (v= PP[v];; v= PP[P[v]])
if (P[v] == -1) return v;
}
bool connected(int u, int v) const { return root(u) == root(v); }
// u is in v
bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
int subtree_size(int v) const { return R[v] - L[v]; }
int lca(int u, int v) const {
for (;; v= P[PP[v]]) {
if (L[u] > L[v]) std::swap(u, v);
if (PP[u] == PP[v]) return u;
}
}
int la(int v, int k) const {
assert(k <= D[v]);
for (int u;; k-= L[v] - L[u] + 1, v= P[u])
if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
}
int jump(int u, int v, int k) const {
if (!k) return u;
if (u == v) return -1;
if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
}
int depth(int v) const { return D[v]; }
int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
// half-open interval [l,r)
std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
// sequence of closed intervals [l,r]
std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
std::vector<std::pair<int, int>> up, down;
while (PP[u] != PP[v]) {
if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
}
if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
return up.insert(up.end(), down.rbegin(), down.rend()), up;
}
};
#line 2 "src/DataStructure/SegmentTree.hpp"
#include <memory>
#line 3 "src/Internal/detection_idiom.hpp"
#define _DETECT_BOOL(name, ...) \
template <class, class= void> struct name: std::false_type {}; \
template <class T> struct name<T, std::void_t<__VA_ARGS__>>: std::true_type {}; \
template <class T> static constexpr bool name##_v= name<T>::value
#define _DETECT_TYPE(name, type1, type2, ...) \
template <class T, class= void> struct name { \
using type= type2; \
}; \
template <class T> struct name<T, std::void_t<__VA_ARGS__>> { \
using type= type1; \
}
#line 7 "src/DataStructure/SegmentTree.hpp"
template <class M> class SegmentTree {
_DETECT_BOOL(monoid, typename T::T, decltype(&T::op), decltype(&T::ti));
_DETECT_BOOL(dual, typename T::T, typename T::E, decltype(&T::mp), decltype(&T::cp));
_DETECT_TYPE(nullptr_or_E, typename T::E, std::nullptr_t, typename T::E);
using T= typename M::T;
using E= typename nullptr_or_E<M>::type;
int n;
std::unique_ptr<T[]> dat;
std::unique_ptr<E[]> laz;
std::unique_ptr<bool[]> flg;
inline void update(int k) { dat[k]= M::op(dat[k << 1], dat[k << 1 | 1]); }
inline bool map(int k, E x, int sz) {
if constexpr (std::is_invocable_r_v<bool, decltype(M::mp), T &, E, int>) return M::mp(dat[k], x, sz);
else if constexpr (std::is_invocable_r_v<bool, decltype(M::mp), T &, E>) return M::mp(dat[k], x);
else if constexpr (std::is_invocable_r_v<void, decltype(M::mp), T &, E, int>) return M::mp(dat[k], x, sz), true;
else return M::mp(dat[k], x), true;
}
inline void prop(int k, E x, int sz) {
if (k < n) {
if (flg[k]) M::cp(laz[k], x);
else laz[k]= x;
flg[k]= true;
if constexpr (monoid_v<M>)
if (!map(k, x, sz)) push(k, sz), update(k);
} else {
if constexpr (monoid_v<M>) map(k, x, 1);
else map(k - n, x, 1);
}
}
inline void push(int k, int sz) {
if (flg[k]) prop(k << 1, laz[k], sz >> 1), prop(k << 1 | 1, laz[k], sz >> 1), flg[k]= false;
}
inline bool valid(int k) const {
int d= __builtin_clz(k) - __builtin_clz(n);
return (n >> d) != k || ((n >> d) << d) == n;
}
public:
SegmentTree() {}
SegmentTree(int n): n(n), dat(std::make_unique<T[]>(n << monoid_v<M>)) {
if constexpr (monoid_v<M>) std::fill_n(dat.get(), n << 1, M::ti());
if constexpr (dual_v<M>) laz= std::make_unique<E[]>(n), flg= std::make_unique<bool[]>(n), std::fill_n(flg.get(), n, false);
}
template <class F> SegmentTree(int n, const F &init): n(n), dat(std::make_unique<T[]>(n << monoid_v<M>)) {
auto a= dat.get() + (n & -monoid_v<M>);
for (int i= 0; i < n; ++i) a[i]= init(i);
if constexpr (monoid_v<M>) build();
if constexpr (dual_v<M>) laz= std::make_unique<E[]>(n), flg= std::make_unique<bool[]>(n), std::fill_n(flg.get(), n, false);
}
SegmentTree(int n, T x): SegmentTree(n, [x](int) { return x; }) {}
SegmentTree(const std::vector<T> &v): SegmentTree(v.size(), [&v](int i) { return v[i]; }) {}
SegmentTree(const T *bg, const T *ed): SegmentTree(ed - bg, [bg](int i) { return bg[i]; }) {}
void build() {
static_assert(monoid_v<M>, "\"build\" is not available\n");
for (int i= n; --i;) update(i);
}
inline void unsafe_set(int i, T x) {
static_assert(monoid_v<M>, "\"unsafe_set\" is not available\n");
dat[i + n]= x;
}
inline void set(int i, T x) {
get(i);
if constexpr (monoid_v<M>)
for (dat[i+= n]= x; i>>= 1;) update(i);
else dat[i]= x;
}
inline void mul(int i, T x) {
static_assert(monoid_v<M>, "\"mul\" is not available\n");
set(i, M::op(get(i), x));
}
inline T get(int i) {
i+= n;
if constexpr (dual_v<M>)
for (int j= 31 - __builtin_clz(i); j; --j) push(i >> j, 1 << j);
if constexpr (monoid_v<M>) return dat[i];
else return dat[i - n];
}
inline T operator[](int i) { return get(i); }
inline T prod(int l, int r) {
static_assert(monoid_v<M>, "\"prod\" is not available\n");
l+= n, r+= n;
if constexpr (dual_v<M>) {
for (int j= 31 - __builtin_clz(l); ((l >> j) << j) != l; --j) push(l >> j, 1 << j);
for (int j= 31 - __builtin_clz(r); ((r >> j) << j) != r; --j) push(r >> j, 1 << j);
}
T s1= M::ti(), s2= M::ti();
for (; l < r; l>>= 1, r>>= 1) {
if (l & 1) s1= M::op(s1, dat[l++]);
if (r & 1) s2= M::op(dat[--r], s2);
}
return M::op(s1, s2);
}
inline void apply(int l, int r, E x) {
static_assert(dual_v<M>, "\"apply\" is not available\n");
l+= n, r+= n;
for (int j= 31 - __builtin_clz(l); ((l >> j) << j) != l; j--) push(l >> j, 1 << j);
for (int j= 31 - __builtin_clz(r); ((r >> j) << j) != r; j--) push(r >> j, 1 << j);
for (int a= l, b= r, sz= 1; a < b; a>>= 1, b>>= 1, sz<<= 1) {
if (a & 1) prop(a++, x, sz);
if (b & 1) prop(--b, x, sz);
}
if constexpr (monoid_v<M>) {
for (int j= __builtin_ctz(l) + 1; l >> j; ++j) update(l >> j);
for (int j= __builtin_ctz(r) + 1; r >> j; ++j) update(r >> j);
}
}
template <class C> int max_right(int l, const C &check) {
static_assert(monoid_v<M>, "\"max_right\" is not available\n");
assert(check(M::ti()));
if (check(prod(l, n))) return n;
T s= M::ti(), t;
int sz= 1;
for (get(l), l+= n;; s= t, ++l) {
while (!(l & 1) && valid(l >> 1)) l>>= 1, sz<<= 1;
if (!check(t= M::op(s, dat[l]))) {
while (l < n) {
if constexpr (dual_v<M>) push(l, sz);
l<<= 1, sz>>= 1;
if (check(t= M::op(s, dat[l]))) s= t, ++l;
}
return l - n;
}
}
}
template <class C> int min_left(int r, const C &check) {
static_assert(monoid_v<M>, "\"min_left\" is not available\n");
assert(check(M::ti()));
if (check(prod(0, r))) return 0;
T s= M::ti(), t;
int sz= 1;
for (get(--r), r+= n;; s= t, --r) {
while (!valid(r)) r= r << 1 | 1, sz>>= 1;
while ((r & 1) && valid(r >> 1)) r>>= 1, sz<<= 1;
if (!check(t= M::op(dat[r], s))) {
while (r < n) {
if constexpr (dual_v<M>) push(r, sz);
r= r << 1 | 1, sz>>= 1;
if (check(t= M::op(dat[r], s))) s= t, --r;
}
return r + 1 - n;
}
}
}
};
#line 10 "test/aoj/2450.HLD.test.cpp"
using namespace std;
struct M {
struct T {
long long sum, max, lmax, rmax;
};
using E= long long;
static inline long long INF= 1ll << 60;
static T ti() { return {0, -INF, -INF, -INF}; }
static T op(const T &a, const T &b) {
T ret;
ret.sum= a.sum + b.sum;
ret.max= max({a.max, b.max, a.rmax + b.lmax});
ret.lmax= max(a.lmax, a.sum + b.lmax);
ret.rmax= max(a.rmax + b.sum, b.rmax);
return ret;
}
static void mp(T &v, const E &f, int sz) {
v.sum= f * sz;
v.max= v.lmax= v.rmax= max(v.sum, f);
}
static void cp(E &pre, const E &suf) { pre= suf; }
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
int N, Q;
cin >> N >> Q;
vector<long long> w(N);
for (int u= 0; u < N; ++u) cin >> w[u];
Graph g(N, N - 1);
for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
HeavyLightDecomposition hld(g);
vector<typename M::T> ar(N);
for (int u= N; u--;) ar[hld.to_seq(u)]= {w[u], w[u], w[u], w[u]};
SegmentTree<M> seg1(ar);
reverse(ar.begin(), ar.end());
SegmentTree<M> seg2(ar);
while (Q--) {
long long t, a, b, c;
cin >> t >> a >> b >> c, --a, --b;
if (t == 1) {
for (auto [x, y]: hld.path(a, b))
if (x < y) seg1.apply(x, y + 1, c), seg2.apply(N - y - 1, N - x, c);
else seg1.apply(y, x + 1, c), seg2.apply(N - x - 1, N - y, c);
} else {
typename M::T ans= M::ti();
for (auto [x, y]: hld.path(a, b)) ans= M::op(ans, x < y ? seg1.prod(x, y + 1) : seg2.prod(N - x - 1, N - y));
cout << ans.max << '\n';
}
}
return 0;
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++-13 | testcase_00 |
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6 ms | 4 MB |
g++-13 | testcase_01 |
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5 ms | 4 MB |
g++-13 | testcase_02 |
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5 ms | 3 MB |
g++-13 | testcase_03 |
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5 ms | 4 MB |
g++-13 | testcase_04 |
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5 ms | 4 MB |
g++-13 | testcase_05 |
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98 ms | 8 MB |
g++-13 | testcase_06 |
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139 ms | 25 MB |
g++-13 | testcase_07 |
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170 ms | 46 MB |
g++-13 | testcase_08 |
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6 ms | 4 MB |
g++-13 | testcase_09 |
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25 ms | 4 MB |
g++-13 | testcase_10 |
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187 ms | 46 MB |
g++-13 | testcase_11 |
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6 ms | 4 MB |
g++-13 | testcase_12 |
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5 ms | 4 MB |
g++-13 | testcase_13 |
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5 ms | 4 MB |
g++-13 | testcase_14 |
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7 ms | 4 MB |
g++-13 | testcase_15 |
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24 ms | 4 MB |
g++-13 | testcase_16 |
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147 ms | 6 MB |
g++-13 | testcase_17 |
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262 ms | 14 MB |
g++-13 | testcase_18 |
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312 ms | 25 MB |
g++-13 | testcase_19 |
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398 ms | 46 MB |
g++-13 | testcase_20 |
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6 ms | 4 MB |
g++-13 | testcase_21 |
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5 ms | 4 MB |
g++-13 | testcase_22 |
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10 ms | 4 MB |
g++-13 | testcase_23 |
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112 ms | 5 MB |
g++-13 | testcase_24 |
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260 ms | 20 MB |
g++-13 | testcase_25 |
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394 ms | 46 MB |
g++-13 | testcase_26 |
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6 ms | 4 MB |
g++-13 | testcase_27 |
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210 ms | 8 MB |
g++-13 | testcase_28 |
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315 ms | 25 MB |
g++-13 | testcase_29 |
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394 ms | 46 MB |
g++-13 | testcase_30 |
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6 ms | 3 MB |
g++-13 | testcase_31 |
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7 ms | 4 MB |
g++-13 | testcase_32 |
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29 ms | 4 MB |
g++-13 | testcase_33 |
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138 ms | 10 MB |
g++-13 | testcase_34 |
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175 ms | 25 MB |
g++-13 | testcase_35 |
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216 ms | 44 MB |
g++-13 | testcase_36 |
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221 ms | 45 MB |
g++-13 | testcase_37 |
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220 ms | 46 MB |
g++-13 | testcase_38 |
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219 ms | 46 MB |
clang++-18 | testcase_00 |
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5 ms | 4 MB |
clang++-18 | testcase_01 |
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5 ms | 4 MB |
clang++-18 | testcase_02 |
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5 ms | 4 MB |
clang++-18 | testcase_03 |
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5 ms | 4 MB |
clang++-18 | testcase_04 |
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5 ms | 4 MB |
clang++-18 | testcase_05 |
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91 ms | 8 MB |
clang++-18 | testcase_06 |
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132 ms | 25 MB |
clang++-18 | testcase_07 |
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164 ms | 46 MB |
clang++-18 | testcase_08 |
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6 ms | 4 MB |
clang++-18 | testcase_09 |
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22 ms | 4 MB |
clang++-18 | testcase_10 |
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174 ms | 46 MB |
clang++-18 | testcase_11 |
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6 ms | 4 MB |
clang++-18 | testcase_12 |
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5 ms | 4 MB |
clang++-18 | testcase_13 |
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5 ms | 4 MB |
clang++-18 | testcase_14 |
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7 ms | 4 MB |
clang++-18 | testcase_15 |
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22 ms | 4 MB |
clang++-18 | testcase_16 |
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127 ms | 6 MB |
clang++-18 | testcase_17 |
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225 ms | 14 MB |
clang++-18 | testcase_18 |
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273 ms | 25 MB |
clang++-18 | testcase_19 |
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360 ms | 46 MB |
clang++-18 | testcase_20 |
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6 ms | 4 MB |
clang++-18 | testcase_21 |
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5 ms | 4 MB |
clang++-18 | testcase_22 |
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10 ms | 4 MB |
clang++-18 | testcase_23 |
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95 ms | 5 MB |
clang++-18 | testcase_24 |
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231 ms | 20 MB |
clang++-18 | testcase_25 |
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354 ms | 46 MB |
clang++-18 | testcase_26 |
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6 ms | 4 MB |
clang++-18 | testcase_27 |
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181 ms | 8 MB |
clang++-18 | testcase_28 |
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274 ms | 25 MB |
clang++-18 | testcase_29 |
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362 ms | 46 MB |
clang++-18 | testcase_30 |
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6 ms | 4 MB |
clang++-18 | testcase_31 |
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7 ms | 4 MB |
clang++-18 | testcase_32 |
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26 ms | 4 MB |
clang++-18 | testcase_33 |
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125 ms | 11 MB |
clang++-18 | testcase_34 |
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160 ms | 25 MB |
clang++-18 | testcase_35 |
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196 ms | 44 MB |
clang++-18 | testcase_36 |
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208 ms | 45 MB |
clang++-18 | testcase_37 |
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200 ms | 46 MB |
clang++-18 | testcase_38 |
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200 ms | 46 MB |