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#define PROBLEM \ "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree" #include "Template/template.hpp" #include "Utility/fastio.hpp" #include "Graph/contour.hpp" #include "DataStructure/bit.hpp" int main() { int n, q; read(n, q); vector<ll> a(n); read(a); ContourQuery buf(n); rep(_, 0, n - 1) { int u, v; read(u, v); buf.add_edge(u, v); } auto len = buf.run(); vector<BIT<ll>> seg(len.size()); rep(i, 0, len.size()) seg[i] = BIT<ll>(len[i]); rep(v, 0, n) { for (auto &[i, p] : buf.point(v)) seg[i].add(p, a[v]); } while (q--) { int t; read(t); if (t == 0) { int v, x; read(v, x); for (auto &[i, p] : buf.point(v)) seg[i].add(p, x); } else { int v, L, R; read(v, L, R); ll ret = 0; for (auto &[i, LR] : buf.range(v, L, R)) { auto [lb, rb] = LR; ret += seg[i].sum(lb, rb); } print(ret); } } return 0; }
#line 1 "Verify/LC_vertex_add_range_contour_sum_on_tree.test.cpp" #define PROBLEM \ "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree" #line 1 "Template/template.hpp" #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template <typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template <typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template <typename T, typename U> T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T> int popcnt(T x) { return __builtin_popcountll(x); } template <typename T> int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template <typename T> int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template <typename T> void _show(int i, T name) { cerr << '\n'; } template <typename T1, typename T2, typename... T3> void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template <typename T, template <class> class C> ostream &operator<<(ostream &os, const C<T> &v) { os << "["; for (auto d : v) os << d << ", "; os << "]"; return os; } #line 2 "Utility/fastio.hpp" #include <unistd.h> namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template <typename T> void rd_real(T &x) { string s; rd(s); x = stod(s); } template <typename T> void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(uint &x) { rd_integer(x); } void rd(ull &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } template <class T, class U> void rd(pair<T, U> &p) { return rd(p.first), rd(p.second); } template <size_t N = 0, typename T> void rd_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); rd(x); rd_tuple<N + 1>(t); } } template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); } template <size_t N = 0, typename T> void rd(array<T, N> &x) { for (auto &d : x) rd(d); } template <class T> void rd(vector<T> &x) { for (auto &d : x) rd(d); } void read() {} template <class H, class... T> void read(H &h, T &...t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c : s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template <typename T> void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template <typename T> void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(uint x) { wt_integer(x); } void wt(ull x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } template <class T, class U> void wt(const pair<T, U> val) { wt(val.first); wt(' '); wt(val.second); } template <size_t N = 0, typename T> void wt_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get<N>(t); wt(x); wt_tuple<N + 1>(t); } } template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); } template <class T, size_t S> void wt(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template <class T> void wt(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward<Tail>(tail)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 6 "Verify/LC_vertex_add_range_contour_sum_on_tree.test.cpp" #line 2 "Graph/centroid.hpp" class CentroidDecomposition{ void get(int v,int p){ sz[v]=1; for(auto& to:g[v])if(to!=p and !used[to]){ get(to,v); sz[v]+=sz[to]; } } int dfs(int v,int p,int rt){ for(auto& to:g[v])if(to!=p and !used[to]){ if(sz[to]>(sz[rt]>>1))return dfs(to,v,rt); } return v; } public: int n; vector<vector<int>> g; vector<int> sz,used; CentroidDecomposition(int n_):n(n_),g(n),sz(n),used(n){} void add_edge(int u,int v){ g[u].push_back(v); g[v].push_back(u); } int find(int rt){ get(rt,-1); int res=dfs(rt,-1,rt); used[res]=1; return res; } }; /** * @brief Centroid Decomposition */ #line 2 "Graph/hld.hpp" struct HLD{ using P=pair<int,int>; vector<vector<int>> g; vector<int> sz,in,out,rev,hs,par,dist; void dfs(int v,int p){ par[v]=p; sz[v]=1; if(p!=-1)dist[v]=dist[p]+1; if(!g[v].empty() and g[v][0]==p)swap(g[v][0],g[v].back()); for(auto& to:g[v])if(to!=p){ dfs(to,v); sz[v]+=sz[to]; if(sz[g[v][0]]<sz[to])swap(g[v][0],to); } } void dfs2(int v,int p,int& k){ in[v]=k++; rev[in[v]]=v; for(auto& to:g[v])if(to!=p){ hs[to]=(g[v][0]==to?hs[v]:to); dfs2(to,v,k); } out[v]=k; } HLD(int _n):g(_n),sz(_n),in(_n),out(_n),rev(_n),hs(_n),par(_n),dist(_n){} void add_edge(int u,int v){ g[u].emplace_back(v); g[v].emplace_back(u); } void run(int rt=0){dfs(rt,-1); hs[rt]=rt; int k=0; dfs2(rt,-1,k);} int lca(int u,int v){ for(;;v=par[hs[v]]){ if(in[u]>in[v])swap(u,v); if(hs[u]==hs[v])return u; } } vector<P> get(int u,int p,bool es=0){ assert(in[p]<=in[u] and out[u]<=out[p]); vector<P> res; while(hs[u]!=hs[p]){ res.push_back({in[hs[u]],in[u]+1}); u=par[hs[u]]; } res.push_back({in[p]+es,in[u]+1}); return res; } int jump(int u,int v,int k){ if(k<0)return -1; int g=lca(u,v); int d0=dist[u]+dist[v]-dist[g]*2; if(d0<k)return -1; int st=u; if(dist[u]-dist[g]<k)st=v,k=d0-k; for(;;){ int to=hs[st]; if(in[st]-k>=in[to])return rev[in[st]-k]; k-=in[st]-in[to]+1; st=par[to]; } } }; /** * @brief Heavy Light Decomposition */ #line 4 "Graph/contour.hpp" struct ContourQuery { using P = pair<int, int>; using T = pair<int, P>; ContourQuery(int _n = 0) : n(_n), m(_n), cd(_n), hld(_n), tree(_n * 3), depth(_n * 3), base(_n * 3), parent(_n * 3, -1), buf(_n * 3), width(_n * 3, 1), seg(_n * 3) {} void add_edge(int u, int v) { cd.add_edge(u, v); hld.add_edge(u, v); } vector<int> run() { hld.run(); root = rec(0); depth[0] = 0; dfs(0, -1); rep(v, 0, m) if (v != root) { seg[v] = width[v]; } return seg; } vector<P> point(int v) { vector<P> ret; int cur = v; while (cur != root) { int D = depth[v] + depth[base[cur]] - 2 * depth[hld.lca(v, base[cur])]; ret.push_back({cur, D}); cur = parent[cur]; } return ret; } vector<T> range(int v, int L, int R) { vector<T> ret; if (L <= 0 and 0 < R) ret.push_back({v, {0, 1}}); int cur = parent[v], pre = v; while (pre != root) { int bro = -1; for (auto &to : tree[cur]) if (to != parent[cur] and to != pre) { bro = to; break; } if (bro != -1) { int D = depth[v] + depth[base[bro]] - 2 * depth[hld.lca(v, base[bro])]; ret.push_back( {bro, {clamp(L - D, 0, seg[bro]), clamp(R - D, 0, seg[bro])}}); } pre = cur; cur = parent[cur]; } return ret; } private: int n, m, root; CentroidDecomposition cd; HLD hld; vector<vector<int>> tree; vector<int> depth, base, parent, buf, width, seg; int rec(int rt) { int cen = cd.find(rt); buf[cen] = 1; queue<P> que; auto cmp = [&](int u, int v) { return buf[u] > buf[v]; }; priority_queue<int, vector<int>, decltype(cmp)> pq{cmp}; pq.push(cen); depth[cen] = 0; base[cen] = cen; for (auto &to : cd.g[cen]) if (!cd.used[to]) { int v = rec(to); que.push({to, cen}); depth[to] = 1; while (!que.empty()) { auto [cur, par] = que.front(); que.pop(); width[v] = depth[cur] + 1; for (auto &nxt : cd.g[cur]) if (nxt != par and !cd.used[nxt]) { depth[nxt] = depth[cur] + 1; que.push({nxt, cur}); } } pq.push(v); base[v] = cen; } cd.used[cen] = 0; if (pq.size() > 1) { for (;;) { int v1 = pq.top(); pq.pop(); int v2 = pq.top(); pq.pop(); int extra = m++; tree[extra].push_back(v1); tree[extra].push_back(v2); tree[v1].push_back(extra); tree[v2].push_back(extra); buf[extra] = buf[v1] + buf[v2]; parent[v1] = parent[v2] = extra; if (pq.empty()) { return extra; } pq.push(extra); base[extra] = cen; width[extra] = max(width[v1], width[v2]); } } else { int extra = m++; tree[extra].push_back(cen); tree[cen].push_back(extra); buf[extra] = 1; parent[cen] = extra; return extra; } } void dfs(int v, int p) { for (auto &to : cd.g[v]) if (to != p) { depth[to] = depth[v] + 1; dfs(to, v); } } }; /** * @brief Contour Sum Query */ #line 2 "DataStructure/bit.hpp" template<typename T>struct BIT{ int n; T all=0; vector<T> val; BIT(int _n=0):n(_n),val(_n+10){} void clear(){val.assign(n+10,0); all=T();} void add(int i,T x){ for(i++;i<=n;i+=(i&-i))val[i]=val[i]+x; all+=x; } T sum(int i){ T res=0; for(;i;i-=(i&-i))res+=val[i]; return res; } T sum(int L,int R){return sum(R)-sum(L);} // [L,R) int lower_bound(T x){ int ret=0,len=1; while(2*len<=n)len<<=1; for(;len>=1;len>>=1){ if(ret+len<=n and val[ret+len]<x){ ret+=len; x-=val[ret]; } } return ret; } }; /** * @brief Binary Indexed Tree */ #line 9 "Verify/LC_vertex_add_range_contour_sum_on_tree.test.cpp" int main() { int n, q; read(n, q); vector<ll> a(n); read(a); ContourQuery buf(n); rep(_, 0, n - 1) { int u, v; read(u, v); buf.add_edge(u, v); } auto len = buf.run(); vector<BIT<ll>> seg(len.size()); rep(i, 0, len.size()) seg[i] = BIT<ll>(len[i]); rep(v, 0, n) { for (auto &[i, p] : buf.point(v)) seg[i].add(p, a[v]); } while (q--) { int t; read(t); if (t == 0) { int v, x; read(v, x); for (auto &[i, p] : buf.point(v)) seg[i].add(p, x); } else { int v, L, R; read(v, L, R); ll ret = 0; for (auto &[i, LR] : buf.range(v, L, R)) { auto [lb, rb] = LR; ret += seg[i].sum(lb, rb); } print(ret); } } return 0; }