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test/verify/yosupo-vertex-add-subtree-sum.test.cpp
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- Last update: 2024-09-07 20:55:28+09:00
- Problem: https://judge.yosupo.jp/problem/vertex_add_subtree_sum
- Link: https://en.wikipedia.org/wiki/Fenwick_tree
Depends on
graph/graph_template.hpp
- Heavy-Light Decomposition(HL分解, HLD)
(graph/tree/heavy_light_decomposition.hpp)
- template/template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_subtree_sum"
#include "template/template.hpp"
#include <vector>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace atcoder
#include "graph/tree/heavy_light_decomposition.hpp"
int main() {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int N, Q; cin >> N >> Q;
vector<int>a(N);
for(int i=0; i<N; i++) cin >> a[i];
HLD hld(N);
for (int i=1; i<N; i++) {
int p; cin >> p;
hld.graph.add_edge(i,p);
hld.graph.add_edge(p,i);
}
hld.build();
atcoder::fenwick_tree<ll> fw(N);
for (int i=0; i<N; i++) {
fw.add(hld.id[i], a[i]);
}
for (int q=0; q<Q; q++) {
int op; cin >> op;
if (op == 0) {
int u, x; cin >> u >> x;
fw.add(hld.id[u], x);
}
else if (op == 1) {
int u; cin >> u;
auto [l,r] = hld.subtree_query(u);
cout << fw.sum(l, r) << endl;;
}
}
return 0;
}#line 1 "test/verify/yosupo-vertex-add-subtree-sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_subtree_sum"
#line 1 "template/template.hpp"
#include <iostream>
#include <cassert>
using namespace std;
using ll = long long;
template<class T> inline bool chmax(T& a, const T& b) {if (a<b) {a=b; return true;} return false;}
template<class T> inline bool chmin(T& a, const T& b) {if (b<a) {a=b; return true;} return false;}
const int INTINF = 1000001000;
const int INTMAX = 2147483647;
const ll LLMAX = 9223372036854775807;
const ll LLINF = 1000000000000000000;
#line 3 "test/verify/yosupo-vertex-add-subtree-sum.test.cpp"
#include <vector>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace atcoder
#line 1 "graph/tree/heavy_light_decomposition.hpp"
#line 5 "graph/tree/heavy_light_decomposition.hpp"
#include <algorithm>
#line 7 "graph/tree/heavy_light_decomposition.hpp"
#include <utility>
#line 1 "graph/graph_template.hpp"
#line 5 "graph/graph_template.hpp"
template <typename T>
struct Edge {
int from; int to;
T cost;
// default constructor
Edge () : from(-1), to(-1), cost(T(0)) {}
Edge(int _from, int _to, T _cost) : from(_from), to(_to), cost(_cost) {}
// unweighted
Edge(int _from, int _to) : from(_from), to(_to), cost(T(1)) {}
bool operator==(const Edge& rhs) const {
return from == rhs.from && to == rhs.to && cost == rhs.cost;
}
bool operator<(const Edge& rhs) const {
return cost < rhs.cost;
}
bool operator>(const Edge& rhs) const {
return cost > rhs.cost;
}
};
template <typename T>
struct Graph : std::vector<std::vector<Edge<T>>> {
using std::vector<std::vector<Edge<T>>>::vector; // inherit constructors
void add_edge(int i, Edge<T> e) {
(*this)[i].push_back(e);
}
void add_edge(Edge<T> e) {
(*this)[e.from].push_back(e);
}
// weighted
void add_edge(int _from, int _to, T _cost) {
(*this)[_from].push_back(Edge(_from, _to, _cost));
}
// unweighted
void add_edge(int _from, int _to) {
(*this)[_from].push_back(Edge(_from, _to, T(1)));
}
};
#line 10 "graph/tree/heavy_light_decomposition.hpp"
// cf : https://ngtkana.hatenablog.com/entry/2024/06/24/200138
struct Interval {
// top_id : interval のもっとも根に近い頂点のid
// bottom_id : interval のもっとも葉に近い頂点のid
// last : LCAを含む interval であるかどうか
// reverse : from → to と top → bottomが逆向きかどうか
int top_id, bottom_id;
bool last;
bool reverse;
Interval(int _top_id, int _bottom_id, bool _last, bool _reverse) : top_id(_top_id), bottom_id(_bottom_id), last(_last), reverse(_reverse) {
}
};
using Path = std::vector<Interval>;
struct HLD {
//vector<vector<int>>children;
std::vector<int>parent;
std::vector<int> id;
std::vector<int> id2;
std::vector<int> head;
std::vector<int>depth;
Graph<int>graph;
HLD (int N) : parent(std::vector<int>(N, -1)), id(std::vector<int>(N)), id2(std::vector<int>(N)), head(std::vector<int>(N)), depth(std::vector<int>(N)), graph(N) {}
void build(int root=0) {
dfs_sz(root);
int k = 0; dfs_hld(root, k);
}
int dfs_sz(int v) {
int ret = 1, mx_sz = 0;
for (Edge<int>& nxt : graph[v]) {
if (nxt.to == parent[v]) continue;
parent[nxt.to] = v;
depth[nxt.to] = depth[v] + 1;
int sz = dfs_sz(nxt.to);
ret += sz;
if (mx_sz < sz) {
mx_sz = sz;
std::swap(graph[v][0], nxt);
}
}
return ret;
}
void dfs_hld(int v, int& k) {
id[v] = k; k++;
for (Edge e : graph[v]) {
if (e.to == parent[v]) continue;
head[e.to] = (e == graph[v][0] ? head[v] : e.to);
dfs_hld(e.to, k);
}
id2[v] = k;
}
int lca(int u, int v) {
while (true) {
if (id[u] > id[v]) std::swap(u, v);
if (head[u] == head[v]) return u;
v = parent[head[v]];
}
}
Path get_path(int u, int v) {
Path upath, vpath;
while (head[u] != head[v]) {
// ちなみにu,vのdepthの大小関係は変わり続けることもある。
// 10 → 12など。
// v's head is deeper
if (depth[head[v]] >= depth[head[u]]) {
assert(depth[head[v]] >= depth[head[u]]);
/*
/ : heavy edge
.... : light edge
head[u]
/
/...
u ...
/ head[v]
/ \
/ \
/ v
*/
// u→v なのでreverse=false
vpath.emplace_back(id[head[v]], id[v], false, false);
v = parent[head[v]];
}
// u's head is deeper
else if (depth[head[v]] < depth[head[u]]) {
/*
/ : heavy edge
.... : light edge
head[v]
/
/...
v ...
/ head[u]
/ \
/ \
/ u
*/
//
upath.emplace_back(id[head[u]], id[u], false, true);
u = parent[head[u]];
}
}
// v is deeper
/*
u
/
/ ←↓
/
v
*/
if (depth[v] > depth[u]) {
upath.emplace_back(id[u], id[v], true, false);
}
// u is deeper
/*
v
/
/ →↑
/
u
*/
else {
upath.emplace_back(id[v], id[u], true, true);
}
Path retpath = upath;
std::reverse(vpath.begin(), vpath.end());
for (Interval path : vpath) retpath.push_back(path);
return retpath;
}
std::pair<int,int> subtree_query(int r) {
assert(r < int(id.size()));
return std::make_pair(id[r], id2[r]);
}
};
#line 139 "test/verify/yosupo-vertex-add-subtree-sum.test.cpp"
int main() {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int N, Q; cin >> N >> Q;
vector<int>a(N);
for(int i=0; i<N; i++) cin >> a[i];
HLD hld(N);
for (int i=1; i<N; i++) {
int p; cin >> p;
hld.graph.add_edge(i,p);
hld.graph.add_edge(p,i);
}
hld.build();
atcoder::fenwick_tree<ll> fw(N);
for (int i=0; i<N; i++) {
fw.add(hld.id[i], a[i]);
}
for (int q=0; q<Q; q++) {
int op; cin >> op;
if (op == 0) {
int u, x; cin >> u >> x;
fw.add(hld.id[u], x);
}
else if (op == 1) {
int u; cin >> u;
auto [l,r] = hld.subtree_query(u);
cout << fw.sum(l, r) << endl;;
}
}
return 0;
}