cplib-cpp
This documentation is automatically generated by online-judge-tools/verification-helper
tree/test/vertex-add-path-sum.test.cpp
- View this file on GitHub
- Last update: 2025-01-01 21:39:17+09:00
- Problem: https://judge.yosupo.jp/problem/vertex_add_path_sum
Depends on
- segmenttree/point-update-range-get_nonrecursive.hpp
- Heavy-light decomposition （HLD, 木の重軽分解）
(tree/heavy_light_decomposition.hpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include "../../segmenttree/point-update-range-get_nonrecursive.hpp"
#include "../heavy_light_decomposition.hpp"
#include <iostream>
#include <vector>
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, Q, q, u, v;
cin >> N >> Q;
vector<long long> A(N);
for (auto &x : A) cin >> x;
vector<pair<int, int>> edges(N - 1);
for (auto &[u, v] : edges) cin >> u >> v;
heavy_light_decomposition hld(N, edges);
hld.build();
PointUpdateRangeSum<long long> segtree(hld.segtree_rearrange(A), 0LL);
while (Q--) {
cin >> q >> u >> v;
if (q) {
long long ret = 0;
hld.for_each_vertex(u, v, [&](int l, int r) -> void { ret += segtree.get(l, r + 1); });
cout << ret << '\n';
} else {
A[u] += v;
segtree.update(hld.subtree_begin[u], A[u]);
}
}
}#line 1 "tree/test/vertex-add-path-sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#line 2 "segmenttree/point-update-range-get_nonrecursive.hpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <stack>
#include <vector>
// CUT begin
// Nonrecursive Segment Tree (point-update, range-get)
// - Conditions for operations:
// - merge_data: [TDATA, TDATA] -> TDATA, e(x, y) == e(y, x)
// - data2ret: [TDATA, TQUERY] -> TRET
// - merge_ret: [TRET, TRET] -> TRET, g(defaultRET, x) == x, g(x, y) = g(y, x)
// - commutability f(e(x, y), q) == g(f(x, q), f(y, q))
template <typename TDATA, typename TRET, typename TQUERY> struct NonrecursiveSegmentTree {
int N;
TRET defaultRET;
virtual TDATA merge_data(const TDATA &, const TDATA &) = 0;
virtual TRET data2ret(const TDATA &, const TQUERY &) = 0;
virtual TRET merge_ret(const TRET &, const TRET &) = 0;
std::vector<TDATA> data;
inline TDATA &at(int i) { return data[i]; }
inline void _merge(int i) { at(i) = merge_data(at(i << 1), at((i << 1) + 1)); }
void initialize(const std::vector<TDATA> &seq, TRET RET_ZERO) {
N = seq.size();
defaultRET = RET_ZERO;
data = seq;
data.insert(data.end(), seq.begin(), seq.end());
for (int i = N - 1; i; i--) _merge(i);
}
NonrecursiveSegmentTree() = default;
void update(int pos, const TDATA &x) {
assert(pos >= 0 and pos < N);
at(pos + N) = x;
for (int i = pos + N; i > 1;) i >>= 1, _merge(i);
}
// [l, r), 0-indexed
TRET get(int l, int r, TQUERY query = NULL) {
assert(l >= 0 and r <= N);
TRET retl = defaultRET, retr = defaultRET;
l += N, r += N;
while (l < r) {
if (l & 1) retl = merge_ret(retl, data2ret(data[l++], query));
if (r & 1) retr = merge_ret(data2ret(data[--r], query), retr);
l >>= 1, r >>= 1;
}
return merge_ret(retl, retr);
}
// Calculate smallest r that satisfies condition(g(f(x_l, q), ..., f(x_{r - 1}, q)) == true
// Assumption: Monotonicity of g(x_l, ..., x_r) about r (l: fixed)
// Complexity: O(log N)
int binary_search(int l, std::function<bool(TRET)> condition, TQUERY query = NULL) {
std::stack<int> rs;
l += N;
int r = N * 2;
TRET retl = defaultRET;
if (condition(retl)) return l - N;
while (l < r) {
if (l & 1) {
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
l++;
retl = ret_tmp;
}
if (r & 1) rs.push(--r);
l >>= 1, r >>= 1;
}
while (!rs.empty()) {
l = rs.top();
rs.pop();
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
retl = ret_tmp;
}
return N;
}
template <typename T1, typename T2, typename T3>
friend std::ostream &operator<<(std::ostream &os, NonrecursiveSegmentTree<T1, T2, T3> s) {
os << "[SegmentTree (len: " << s.N << ')';
for (int i = 0; i < s.N; i++) os << s.at(i + s.N) << ',';
os << "]";
return os;
}
};
// Range Minimum Query
// - get: return min(x_l, ..., x_{r - 1})
template <typename T> struct RangeMinimumQuery : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return std::min(vl, vr); };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return std::min(vl, vr); };
RangeMinimumQuery(const std::vector<T> &seq, T defaultmin)
: SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, defaultmin);
};
};
template <typename T> struct PointUpdateRangeSum : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return vl + vr; };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return vl + vr; };
PointUpdateRangeSum(const std::vector<T> &seq, T zero) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, zero);
};
};
// Range Counting less than q Query
// - get: return (#{i | l <= i < r, x_i < q}, total sum of them).
template <typename T>
struct CountAndSumLessThan
: public NonrecursiveSegmentTree<std::vector<std::pair<T, T>>, std::pair<int, T>, T> {
using TDATA = std::vector<std::pair<T, T>>;
using TRET = std::pair<int, T>;
using TQUERY = T;
TDATA merge_data(const TDATA &vl, const TDATA &vr) override {
TDATA ret = vl;
ret.insert(ret.end(), vr.begin(), vr.end());
std::sort(ret.begin(), ret.end());
if (ret.size()) {
ret[0].second = ret[0].first;
for (size_t i = 1; i < ret.size(); i++)
ret[i].second = ret[i - 1].second + ret[i].first;
}
return ret;
}
TRET data2ret(const TDATA &vec, const TQUERY &q) override {
int i = std::lower_bound(vec.begin(), vec.end(), std::make_pair(q, q)) - vec.begin();
if (!i)
return std::make_pair(0, 0);
else
return std::make_pair(i, vec[i - 1].second);
}
TRET merge_ret(const TRET &l, const TRET &r) override {
return std::make_pair(l.first + r.first, l.second + r.second);
}
using SegTree = NonrecursiveSegmentTree<TDATA, TRET, TQUERY>;
CountAndSumLessThan(const std::vector<T> &seq) : SegTree::NonrecursiveSegmentTree() {
std::vector<TDATA> init;
for (auto x : seq) init.emplace_back(TDATA{std::pair<T, T>(x, x)});
SegTree::initialize(init, TRET(0, 0));
}
};
#line 5 "tree/heavy_light_decomposition.hpp"
#include <queue>
#line 7 "tree/heavy_light_decomposition.hpp"
#include <utility>
#line 9 "tree/heavy_light_decomposition.hpp"
// Heavy-light decomposition of trees (forest)
// Based on http://beet-aizu.hatenablog.com/entry/2017/12/12/235950
struct heavy_light_decomposition {
int V;
int k;
std::vector<std::vector<int>> e;
std::vector<int> par; // par[i] = parent of vertex i (Default: -1)
std::vector<int> depth; // depth[i] = distance between root and vertex i
std::vector<int> subtree_sz; // subtree_sz[i] = size of subtree whose root is i
std::vector<int> heavy_child; // heavy_child[i] = child of vertex i on heavy path (Default: -1)
std::vector<int> tree_id; // tree_id[i] = id of tree vertex i belongs to
// subtree_begin[i] = aligned id for vertex i (consecutive on heavy edges)
std::vector<int> subtree_begin, subtree_end;
std::vector<int> vis_order; // vis_order[subtree_begin[i]] = i
std::vector<int> head; // head[i] = id of vertex on heavy path of vertex i, nearest to root
heavy_light_decomposition(int n, const std::vector<std::pair<int, int>> &edges)
: V(n), k(0), e(n), par(n), depth(n), subtree_sz(n), heavy_child(n), tree_id(n, -1),
subtree_begin(n), subtree_end(n), vis_order(0), head(n) {
for (auto [u, v] : edges) {
assert(u != v);
e.at(u).emplace_back(v);
e.at(v).emplace_back(u);
}
}
void _build_dfs_1(int root) {
std::vector<std::pair<int, int>> st;
par[root] = -1;
depth[root] = 0;
st.emplace_back(root, 0);
while (!st.empty()) {
int now = st.back().first;
int &i = st.back().second;
if (i < (int)e[now].size()) {
int nxt = e[now][i++];
if (nxt == par[now]) continue;
par[nxt] = now;
depth[nxt] = depth[now] + 1;
st.emplace_back(nxt, 0);
} else {
st.pop_back();
int max_sub_sz = 0;
subtree_sz[now] = 1;
heavy_child[now] = -1;
for (auto nxt : e[now]) {
if (nxt == par[now]) continue;
subtree_sz[now] += subtree_sz[nxt];
if (max_sub_sz < subtree_sz[nxt]) {
max_sub_sz = subtree_sz[nxt], heavy_child[now] = nxt;
}
}
}
}
}
void _build_dfs_2(int now, int tree_id_now) {
std::vector<std::pair<int, bool>> st;
st.emplace_back(now, true);
head[now] = now;
while (!st.empty()) {
auto [now, mode] = st.back();
st.pop_back();
if (mode) {
tree_id[now] = tree_id_now;
subtree_begin[now] = k++;
vis_order.push_back(now);
st.emplace_back(now, false);
for (int nxt : e[now]) {
if (nxt == par[now] or nxt == heavy_child[now]) continue;
head[nxt] = nxt;
st.emplace_back(nxt, true);
}
if (heavy_child[now] != -1) {
head[heavy_child[now]] = head[now];
st.emplace_back(heavy_child[now], true);
}
} else {
subtree_end[now] = k;
}
}
}
void build(std::vector<int> roots = {0}) {
int tree_id_now = 0;
for (int r : roots) {
_build_dfs_1(r);
_build_dfs_2(r, tree_id_now++);
}
}
template <class T> std::vector<T> segtree_rearrange(const std::vector<T> &data) const {
assert(int(data.size()) == V);
std::vector<T> ret;
ret.reserve(vis_order.size());
for (int v : vis_order) ret.emplace_back(data[v]);
return ret;
}
void for_vertex(int u, const std::function<void(int)> &f) const { f(subtree_begin[u]); }
// query for vertices on path [u, v] (INCLUSIVE)
void
for_each_vertex(int u, int v, const std::function<void(int ancestor, int descendant)> &f) const {
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
f(std::max(subtree_begin[head[v]], subtree_begin[u]), subtree_begin[v]);
if (head[u] == head[v]) break;
v = par[head[v]];
}
}
void for_each_vertex_noncommutative(
int from, int to, const std::function<void(int ancestor, int descendant)> &fup,
const std::function<void(int ancestor, int descendant)> &fdown) const {
int u = from, v = to;
const int lca = lowest_common_ancestor(u, v), dlca = depth[lca];
while (u >= 0 and depth[u] > dlca) {
const int p = (depth[head[u]] > dlca ? head[u] : lca);
fup(subtree_begin[p] + (p == lca), subtree_begin[u]), u = par[p];
}
static std::vector<std::pair<int, int>> lrs;
int sz = 0;
while (v >= 0 and depth[v] >= dlca) {
const int p = (depth[head[v]] >= dlca ? head[v] : lca);
if (int(lrs.size()) == sz) lrs.emplace_back(0, 0);
lrs.at(sz++) = {p, v}, v = par.at(p);
}
while (sz--) fdown(subtree_begin[lrs.at(sz).first], subtree_begin[lrs.at(sz).second]);
}
// query for edges on path [u, v]
void for_each_edge(int u, int v, const std::function<void(int, int)> &f) const {
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
if (head[u] != head[v]) {
f(subtree_begin[head[v]], subtree_begin[v]);
v = par[head[v]];
} else {
if (u != v) f(subtree_begin[u] + 1, subtree_begin[v]);
break;
}
}
}
// query for vertices in subtree rooted at u
void for_subtree(int u, const std::function<void(int, int)> &f) const {
f(subtree_begin[u], subtree_end[u] - 1);
}
// lowest_common_ancestor: O(log V)
int lowest_common_ancestor(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
if (head[u] == head[v]) return u;
v = par[head[v]];
}
}
int distance(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
return depth[u] + depth[v] - 2 * depth[lowest_common_ancestor(u, v)];
}
// Level ancestor, O(log V)
// if k-th parent is out of range, return -1
int kth_parent(int v, int k) const {
if (k < 0) return -1;
while (v >= 0) {
int h = head.at(v), len = depth.at(v) - depth.at(h);
if (k <= len) return vis_order.at(subtree_begin.at(v) - k);
k -= len + 1, v = par.at(h);
}
return -1;
}
// Jump on tree, O(log V)
int s_to_t_by_k_steps(int s, int t, int k) const {
if (k < 0) return -1;
if (k == 0) return s;
int lca = lowest_common_ancestor(s, t);
if (k <= depth.at(s) - depth.at(lca)) return kth_parent(s, k);
return kth_parent(t, depth.at(s) + depth.at(t) - depth.at(lca) * 2 - k);
}
};
#line 6 "tree/test/vertex-add-path-sum.test.cpp"
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, Q, q, u, v;
cin >> N >> Q;
vector<long long> A(N);
for (auto &x : A) cin >> x;
vector<pair<int, int>> edges(N - 1);
for (auto &[u, v] : edges) cin >> u >> v;
heavy_light_decomposition hld(N, edges);
hld.build();
PointUpdateRangeSum<long long> segtree(hld.segtree_rearrange(A), 0LL);
while (Q--) {
cin >> q >> u >> v;
if (q) {
long long ret = 0;
hld.for_each_vertex(u, v, [&](int l, int r) -> void { ret += segtree.get(l, r + 1); });
cout << ret << '\n';
} else {
A[u] += v;
segtree.update(hld.subtree_begin[u], A[u]);
}
}
}