QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#667689 | #9492. 树上简单求和 | hos_lyric# | 5 | 1916ms | 24152kb | C++14 | 14.6kb | 2024-10-23 02:38:32 | 2024-10-23 02:38:32 |
Judging History
answer
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
// T: monoid representing information of an interval.
// T() should return the identity.
// T(S s) should represent a single element of the array.
// T::push(T &l, T &r) should push the lazy update.
// T::pull(const T &l, const T &r) should pull two intervals.
template <class T> struct SegmentTreeRange {
int logN, n;
vector<T> ts;
SegmentTreeRange() : logN(0), n(0) {}
explicit SegmentTreeRange(int n_) {
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
}
template <class S> explicit SegmentTreeRange(const vector<S> &ss) {
const int n_ = ss.size();
for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
ts.resize(n << 1);
for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
build();
}
T &at(int i) {
return ts[n + i];
}
void build() {
for (int u = n; --u; ) pull(u);
}
inline void push(int u) {
ts[u].push(ts[u << 1], ts[u << 1 | 1]);
}
inline void pull(int u) {
ts[u].pull(ts[u << 1], ts[u << 1 | 1]);
}
// Applies T::f(args...) to [a, b).
template <class F, class... Args>
void ch(int a, int b, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return;
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) (ts[aa++].*f)(args...);
if (bb & 1) (ts[--bb].*f)(args...);
}
for (int h = 1; h <= logN; ++h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) pull(aa);
} else {
if ((aa << h) != a) pull(aa);
if ((bb << h) != b) pull(bb);
}
}
}
// Calculates the product for [a, b).
T get(int a, int b) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return T();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
T prodL, prodR, t;
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) { t.pull(prodL, ts[aa++]); prodL = t; }
if (bb & 1) { t.pull(ts[--bb], prodR); prodR = t; }
}
t.pull(prodL, prodR);
return t;
}
// Calculates T::f(args...) of a monoid type for [a, b).
// op(-, -) should calculate the product.
// e() should return the identity.
template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
auto
#else
decltype((std::declval<T>().*F())())
#endif
get(int a, int b, Op op, E e, F f, Args &&... args) {
assert(0 <= a); assert(a <= b); assert(b <= n);
if (a == b) return e();
a += n; b += n;
for (int h = logN; h; --h) {
const int aa = a >> h, bb = b >> h;
if (aa == bb) {
if ((aa << h) != a || (bb << h) != b) push(aa);
} else {
if ((aa << h) != a) push(aa);
if ((bb << h) != b) push(bb);
}
}
auto prodL = e(), prodR = e();
for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...));
if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR);
}
return op(prodL, prodR);
}
// Find min b s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from left to right.
// Returns n + 1 if there is no such b.
template <class F, class... Args>
int findRight(int a, F f, Args &&... args) {
assert(0 <= a); assert(a <= n);
if ((T().*f)(args...)) return a;
if (a == n) return n + 1;
a += n;
for (int h = logN; h; --h) push(a >> h);
for (; ; a >>= 1) if (a & 1) {
if ((ts[a].*f)(args...)) {
for (; a < n; ) {
push(a);
if (!(ts[a <<= 1].*f)(args...)) ++a;
}
return a - n + 1;
}
++a;
if (!(a & (a - 1))) return n + 1;
}
}
// Find max a s.t. T::f(args...) returns true,
// when called for the partition of [a, b) from right to left.
// Returns -1 if there is no such a.
template <class F, class... Args>
int findLeft(int b, F f, Args &&... args) {
assert(0 <= b); assert(b <= n);
if ((T().*f)(args...)) return b;
if (b == 0) return -1;
b += n;
for (int h = logN; h; --h) push((b - 1) >> h);
for (; ; b >>= 1) if ((b & 1) || b == 2) {
if ((ts[b - 1].*f)(args...)) {
for (; b <= n; ) {
push(b - 1);
if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
}
return b - n - 1;
}
--b;
if (!(b & (b - 1))) return -1;
}
}
};
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
// update range a[i] <- a[i] + b
// get sum a[l, r)
template <class T> struct NodeSum {
int sz;
T sum;
T lz;
NodeSum() : sz(0), sum(0), lz(0) {}
NodeSum(const T &val) : sz(1), sum(val), lz(0) {}
void push(NodeSum &l, NodeSum &r) {
l.add(lz);
r.add(lz);
lz = 0;
}
void pull(const NodeSum &l, const NodeSum &r) {
sz = l.sz + r.sz;
sum = l.sum + r.sum;
}
void add(const T &val) {
sum += val * sz;
lz += val;
}
T getSum() const {
return sum;
}
bool accSum(T &acc, const T &tar) const {
if (acc + sum >= tar) return true;
acc += sum;
return false;
}
};
template <class T> T getSum(SegmentTreeRange<NodeSum<T>> &seg, int a, int b) {
return seg.get(a, b,
[&](const T &l, const T &r) -> T { return l + r; },
[&]() -> T { return 0; },
&NodeSum<T>::getSum);
}
// (sum of [a, b]) >= target
template <class T> int findRight(SegmentTreeRange<NodeSum<T>> &seg, int a, const T &tar) {
T acc = 0;
return seg.findRight(a, &NodeSum<T>::accSum, acc, tar);
}
template <class T> int findLeft(SegmentTreeRange<NodeSum<T>> &seg, int b, const T &tar) {
T acc = 0;
return seg.findLeft(b, &NodeSum<T>::accSum, acc, tar);
}
////////////////////////////////////////////////////////////////////////////////
struct Hld {
int n, rt;
// needs to be tree
// vertex lists
// modified in build(rt) (parent removed, heavy child first)
vector<vector<int>> graph;
vector<int> sz, par, dep;
int zeit;
vector<int> dis, fin, sid;
// head vertex (minimum depth) in heavy path
vector<int> head;
Hld() : n(0), rt(-1), zeit(0) {}
explicit Hld(int n_) : n(n_), rt(-1), graph(n), zeit(0) {}
void ae(int u, int v) {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
graph[u].push_back(v);
graph[v].push_back(u);
}
void dfsSz(int u) {
sz[u] = 1;
for (const int v : graph[u]) {
auto it = std::find(graph[v].begin(), graph[v].end(), u);
if (it != graph[v].end()) graph[v].erase(it);
par[v] = u;
dep[v] = dep[u] + 1;
dfsSz(v);
sz[u] += sz[v];
}
}
void dfsHld(int u) {
dis[u] = zeit++;
const int deg = graph[u].size();
if (deg > 0) {
int vm = graph[u][0];
int jm = 0;
for (int j = 1; j < deg; ++j) {
const int v = graph[u][j];
if (sz[vm] < sz[v]) {
vm = v;
jm = j;
}
}
swap(graph[u][0], graph[u][jm]);
head[vm] = head[u];
dfsHld(vm);
for (int j = 1; j < deg; ++j) {
const int v = graph[u][j];
head[v] = v;
dfsHld(v);
}
}
fin[u] = zeit;
}
void build(int rt_) {
assert(0 <= rt_); assert(rt_ < n);
rt = rt_;
sz.assign(n, 0);
par.assign(n, -1);
dep.assign(n, -1);
dep[rt] = 0;
dfsSz(rt);
zeit = 0;
dis.assign(n, -1);
fin.assign(n, -1);
head.assign(n, -1);
head[rt] = rt;
dfsHld(rt);
assert(zeit == n);
sid.assign(n, -1);
for (int u = 0; u < n; ++u) sid[dis[u]] = u;
}
friend ostream &operator<<(ostream &os, const Hld &hld) {
const int maxDep = *max_element(hld.dep.begin(), hld.dep.end());
vector<string> ss(2 * maxDep + 1);
int pos = 0, maxPos = 0;
for (int j = 0; j < hld.n; ++j) {
const int u = hld.sid[j];
const int d = hld.dep[u];
if (hld.head[u] == u) {
if (j != 0) {
pos = maxPos + 1;
ss[2 * d - 1].resize(pos, '-');
ss[2 * d - 1] += '+';
}
} else {
ss[2 * d - 1].resize(pos, ' ');
ss[2 * d - 1] += '|';
}
ss[2 * d].resize(pos, ' ');
ss[2 * d] += std::to_string(u);
if (maxPos < static_cast<int>(ss[2 * d].size())) {
maxPos = ss[2 * d].size();
}
}
for (int d = 0; d <= 2 * maxDep; ++d) os << ss[d] << '\n';
return os;
}
bool contains(int u, int v) const {
return (dis[u] <= dis[v] && dis[v] < fin[u]);
}
int lca(int u, int v) const {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
for (; head[u] != head[v]; ) (dis[u] > dis[v]) ? (u = par[head[u]]) : (v = par[head[v]]);
return (dis[u] > dis[v]) ? v : u;
}
int jumpUp(int u, int d) const {
assert(0 <= u); assert(u < n);
assert(d >= 0);
if (dep[u] < d) return -1;
const int tar = dep[u] - d;
for (u = head[u]; ; u = head[par[u]]) {
if (dep[u] <= tar) return sid[dis[u] + (tar - dep[u])];
}
}
int jump(int u, int v, int d) const {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
assert(d >= 0);
const int l = lca(u, v);
const int du = dep[u] - dep[l], dv = dep[v] - dep[l];
if (d <= du) {
return jumpUp(u, d);
} else if (d <= du + dv) {
return jumpUp(v, du + dv - d);
} else {
return -1;
}
}
// [u, v) or [u, v]
template <class F> void doPathUp(int u, int v, bool inclusive, F f) const {
assert(contains(v, u));
for (; head[u] != head[v]; u = par[head[u]]) f(dis[head[u]], dis[u] + 1);
if (inclusive) {
f(dis[v], dis[u] + 1);
} else {
if (v != u) f(dis[v] + 1, dis[u] + 1);
}
}
// not path order, include lca(u, v) or not
template <class F> void doPath(int u, int v, bool inclusive, F f) const {
const int l = lca(u, v);
doPathUp(u, l, false, f);
doPathUp(v, l, inclusive, f);
}
// (vs, ps): compressed tree
// vs: DFS order (sorted by dis)
// vs[ps[x]]: the parent of vs[x]
// ids[vs[x]] = x, not set for non-tree vertex
vector<int> ids;
pair<vector<int>, vector<int>> compress(vector<int> us) {
// O(n) first time
ids.resize(n, -1);
std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
return (dis[u] < dis[v]);
});
us.erase(std::unique(us.begin(), us.end()), us.end());
int usLen = us.size();
assert(usLen >= 1);
for (int x = 1; x < usLen; ++x) us.push_back(lca(us[x - 1], us[x]));
std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
return (dis[u] < dis[v]);
});
us.erase(std::unique(us.begin(), us.end()), us.end());
usLen = us.size();
for (int x = 0; x < usLen; ++x) ids[us[x]] = x;
vector<int> ps(usLen, -1);
for (int x = 1; x < usLen; ++x) ps[x] = ids[lca(us[x - 1], us[x])];
return make_pair(us, ps);
}
};
////////////////////////////////////////////////////////////////////////////////
using Mint = unsigned long long;
int N, Q;
vector<Mint> C;
vector<int> A[2], B[2];
vector<int> X, Y;
vector<Mint> K;
Hld hld[2];
namespace subA {
vector<Mint> run() {
SegmentTreeRange<NodeSum<Mint>> seg(N);
for (int u = 0; u < N; ++u) seg.at(hld[0].dis[u]) = C[u];
seg.build();
auto get = [&](int u) -> Mint {
return getSum(seg, hld[0].dis[u], hld[0].dis[u] + 1);
};
vector<Mint> ans(Q, 0);
for (int q = 0; q < Q; ++q) {
hld[0].doPath(X[q], Y[q], true, [&](int l, int r) -> void {
seg.ch(l, r, &NodeSum<Mint>::add, K[q]);
});
{
int x = X[q], y = Y[q];
for (; hld[1].dep[x] > hld[1].dep[y]; x = hld[1].par[x]) ans[q] += get(x);
for (; hld[1].dep[x] < hld[1].dep[y]; y = hld[1].par[y]) ans[q] += get(y);
for (; x != y; x = hld[1].par[x], y = hld[1].par[y]) ans[q] += get(x) + get(y);
ans[q] += get(x);
}
}
return ans;
}
} // subA
int main() {
for (; ~scanf("%d%d", &N, &Q); ) {
C.resize(N);
for (int u = 0; u < N; ++u) {
scanf("%llu", &C[u]);
}
for (int h = 0; h < 2; ++h) {
A[h].resize(N - 1);
B[h].resize(N - 1);
for (int i = 0; i < N - 1; ++i) {
scanf("%d%d", &A[h][i], &B[h][i]);
--A[h][i];
--B[h][i];
}
}
X.resize(Q);
Y.resize(Q);
K.resize(Q);
for (int q = 0; q < Q; ++q) {
scanf("%d%d%llu", &X[q], &Y[q], &K[q]);
--X[q];
--Y[q];
}
for (int h = 0; h < 2; ++h) {
hld[h] = Hld(N);
for (int i = 0; i < N - 1; ++i) {
hld[h].ae(A[h][i], B[h][i]);
}
hld[h].build(0);
}
const auto ans = subA::run();
for (int q = 0; q < Q; ++q) {
printf("%llu\n", ans[q]);
}
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 5
Accepted
Test #1:
score: 5
Accepted
time: 16ms
memory: 4432kb
input:
3000 3000 7236742292501328495 17973811477309806363 16075782662531676171 17971236571771878676 11392080645527132110 3685563455925680459 9773593720088356683 8313828403245053795 7736401634567449043 1634817828009987181 6951124933529719486 12775126714635387213 15460977209223753216 397573676785925632 31372...
output:
12105153858659381124 18367442707572066757 11668241962484097878 11288238120352358472 1742468310074622166 9942835997686093671 3305677510569607477 17741602000425004088 14984128302052618266 1075081718074605786 6509217537832509095 16750513627843273113 8569443169249732820 14475184194298579044 156111071108...
result:
ok 3000 lines
Test #2:
score: 5
Accepted
time: 23ms
memory: 4452kb
input:
3000 3000 1612333876155866602 8538417838700679227 6080765231437578796 17905224638340228394 12270907925903144224 17944105326358594564 17302041033966840611 1006351124625222126 496336153231744288 9393087977687876980 9553975238547373621 9361882717200384390 15051881329169144319 9757999873162420435 882725...
output:
11133131376095771981 7909873024850695144 16250639243139481926 14562550655578101207 8274205996508264973 178549413271904466 2368406276743327913 7464009386554813982 9439464815411774627 1471756740732097060 15201641099137019227 6774030298556871576 18156105511913219667 1553508745644446823 4225137078364117...
result:
ok 3000 lines
Test #3:
score: 5
Accepted
time: 103ms
memory: 4648kb
input:
3000 3000 9709246061666095435 1861649101703072889 10620139893353930613 17635186539135419482 710209455559527146 6075101384669982511 1120305006358459674 9703156967435388252 1397046737759839382 5259056712870179169 8253156305433022999 710199693203327302 15130650033641744675 10720111924616886955 15543351...
output:
7834604406305153073 5037061270969117785 16481572776620825702 15177894197606565804 3120320619896892806 18008650876379132344 7417108723176816402 13515164814425439399 3299769942258542105 15897528270699011770 11642805469843844638 16764682282380318054 4824039114054405772 4859834102876213962 1234210473247...
result:
ok 3000 lines
Test #4:
score: 5
Accepted
time: 6ms
memory: 4952kb
input:
3000 3000 16538965545220923528 18062192327708400751 10422465150728338588 3471522151129113073 1236650672072793692 1942240200040301168 13090729759591037952 15335798523677372669 9912100622761466753 11177948788405690381 3710859061697501523 4984944638666762977 17278589713462878008 6371292801024547050 868...
output:
8182453933067329108 13535217473847106938 17067385337010269798 3806121648880466130 11322569288575153037 11079197311131660121 9670138330007803226 6554062218199796758 965954569567598779 18055887214749050688 6142620503089407421 8690117812667761187 9547139298346295115 8890987597519353054 1755036654049586...
result:
ok 3000 lines
Test #5:
score: 5
Accepted
time: 101ms
memory: 4664kb
input:
3000 3000 17759588706587888497 10550000524636484378 11601004513528075994 7150322911283804521 4459707248078569712 10692395730842402625 8940418793863522991 12967068928670540447 9954278250450015940 13702413838608801301 10598390500439869870 15110245227553613794 490862872212325709 15164980555660957366 94...
output:
9743736929788175512 16812303667256960040 14694223512340829897 550204232580650311 1175342872438242313 17622261358285047637 7413682703975031220 12643066512274062227 1868985217436232595 5471830334855681322 8070132260376389587 3970361922096052085 218281824643752746 991917103472727104 2960248244218479023...
result:
ok 3000 lines
Subtask #2:
score: 0
Time Limit Exceeded
Dependency #1:
100%
Accepted
Test #6:
score: 12
Accepted
time: 0ms
memory: 3788kb
input:
5 7 0 3 2 6 4 1 2 2 4 1 5 5 3 3 4 4 2 2 5 5 1 5 3 0 3 2 5 4 4 4 4 4 3 5 2 0 3 4 3 5 5 6
output:
15 21 10 13 17 26 18
result:
ok 7 lines
Test #7:
score: 12
Accepted
time: 1916ms
memory: 24152kb
input:
70000 70000 3805295436278888199 9842309351516174725 1566744796319231180 2206519284152256579 2715928675931950447 6346821976624501261 16020972671480798719 14702021753902144915 17127828773798978442 15779168055669690475 4964561323934614661 9395102787554964450 6377076753365184543 15167378195767668817 288...
output:
5971729064136092190 6457394048987305727 13604212649915736394 8639973959364892219 437861319070967556 16133076880026962355 5384937395694479961 4591478439775690843 16071919565966962790 15485626634068969082 10235993901046758372 3449528613427081475 8064280362779764074 12784984512326434905 424951714880051...
result:
ok 70000 lines
Test #8:
score: 0
Time Limit Exceeded
input:
70000 70000 17769190865915081913 3772925482507158804 10559962993069063712 16307277356502651642 12014171661057147061 1923543107882042577 13408785599350410314 17786178374951015816 2038922879833426794 2540043772647346461 15419977514837351390 5175974305273838292 16815288359165841441 6295059675346852046 ...
output:
result:
Subtask #3:
score: 0
Skipped
Dependency #2:
0%
Subtask #4:
score: 0
Time Limit Exceeded
Test #21:
score: 0
Time Limit Exceeded
input:
200000 200000 622783158027686223 2242697872372232537 8481648430436878777 10092474834140799044 15403999682625301609 12614289513474949582 9180944589267018841 7823784919308285798 8257785171198951273 5134508521895120821 8041682272181381093 3835432206618893170 2653803171409877650 5589823419153460372 1007...
output:
result:
Subtask #5:
score: 0
Time Limit Exceeded
Test #27:
score: 0
Time Limit Exceeded
input:
200000 200000 1958469220619413759 14991498002015735322 6054491201406941902 18206143187746582567 15082377615826460430 2936248617457291604 10073577150351675920 16534472678586906457 2207599132486246393 10301540360769075442 1492580560381080472 551692353431379140 13238280352539145808 8462626987240986565 ...
output:
result:
Subtask #6:
score: 0
Time Limit Exceeded
Test #34:
score: 0
Time Limit Exceeded
input:
200000 200000 6794776813641982926 1561596256197101737 10910039723053043515 7892247858295192798 12233819960547881004 17695389034783066733 9173201689566865598 17626618141377486739 7358781671024283919 6787559733384974662 3884392438269280436 14872846228351316833 9037842441501571648 14299818404271084016 ...
output:
result:
Subtask #7:
score: 0
Skipped
Dependency #1:
100%
Accepted
Dependency #2:
0%