tree/tree_query_weighted.hpp

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• Last update: 2024-07-01 23:39:10+09:00
• Include: #include "tree/tree_query_weighted.hpp"

Depends on

• template/const.hpp
• template/inout_old.hpp
• template/template.hpp
• template/utils.hpp

Verified with

• test/tree/Tree_Diameter_hld.test.cpp

Code

#pragma once

#include"../template/template.hpp"

namespace noya2{

struct Tree_weighted {
    Tree_weighted (int n_ = 0, int root_ = 0) : n(n_), root(root_), inner_edge_id(0), es(n-1), start(n+1,0){
        if (n == 1) build();
    }
    void add_edge(int u, int v, ll w){
        es[inner_edge_id] = {u,w}, start[inner_edge_id] = v;
        if (++inner_edge_id == n-1) build();
    }
    void input(int indexed = 1){
        rep(i,n-1){
            int u, v; ll w; cin >> u >> v >> w;
            u -= indexed, v -= indexed;
            add_edge(u,v,w);
        }
    }
    void input_parents(int indexed = 1){
        rep(i,n-1){
            int p; ll w; cin >> p >> w;
            p -= indexed;
            add_edge(p,i+1,w);
        }
    }
    int degree(int v){
        assert(0 <= v && v < n);
        return start[v+1] - start[v];
    }
    int parent(int v){
        assert(0 <= v && v < n);
        if (v == root) return -1;
        return es[start[v]].first;
    }
    int subtree_size(int v){
        assert(0 <= v && v < n);
        return sub[v];
    }
    int depth(int v){
        assert(0 <= v && v < n);
        return dep[v];
    }
    ll depth_weighted(int v){
        assert(0 <= v && v < n);
        return wdep[v];
    }
    int la(int v, int d){
        assert(0 <= v && v < n);
        while (v != -1){
            int u = nxt[v];
            if (down[v] - d >= down[u]){
                v = tour[down[v] - d];
                break;
            }
            d -= down[v] - down[u] + 1;
            v = parent(u);
        }
        return v;
    }
    pair<int,ll> la_weighted(int v, ll d){
        assert(0 <= v && v < n);
        if (d > wdep[v]) return make_pair(-1,0LL);
        if (d == wdep[v]) return make_pair(root,0LL);
        while (v != -1){
            int u = nxt[v];
            if (d < wdep[v] - wdep[u]) break;
            d -= wdep[v] - wdep[u];
            if (d < es[start[u]].second){
                return make_pair(u,d);
            }
            d -= es[start[u]].second;
            v = parent(u);
        }
        int le = down[nxt[v]], ri = down[v];
        while (ri - le > 1){
            int md = (le + ri) / 2;
            if (d >= wdep[v] - wdep[tour[md]]) ri = md;
            else le = md;
        }
        return make_pair(tour[ri],d-(wdep[v]-wdep[tour[ri]]));
    }
    int lca(int u, int v){
        assert(0 <= v && v < n && 0 <= u && u < n);
        while (nxt[u] != nxt[v]){
            if (down[u] < down[v]) swap(u,v);
            u = es[start[nxt[u]]].first;
        }
        return dep[u] < dep[v] ? u : v;
    }
    int jump(int from, int to, int d){
        int l = lca(from,to);
        if (d <= dep[from] - dep[l]){
            return la(from,d);
        }
        d -= dep[from] - dep[l];
        if (d <= dep[to] - dep[l]){
            return la(to,dep[to]-dep[l]-d);
        }
        return -1;
    }
    pair<int,ll> jump_weighted(int from, int to, ll d){
        int l = lca(from,to);
        if (d <= wdep[from] - wdep[l]){
            return la_weighted(from,d);
        }
        d -= wdep[from] - wdep[l];
        if (d <= wdep[to] - wdep[l]){
            return la_weighted(to,wdep[to]-wdep[l]-d);
        }
        return make_pair(-1,0LL);
    }
    int dist(int u, int v){ return dep[lca(u,v)]*(-2) + dep[u] + dep[v]; }
    ll dist_weighted(int u, int v){ return wdep[lca(u,v)]*(-2) + wdep[u] + wdep[v]; }
    vector<int> path(int from, int to){
        int l = lca(from,to);
        const int sizf = dep[from]-dep[l], sizt = dep[to]-dep[l];
        vector<int> pf = {from}, pt;
        pf.reserve(sizf+1); pt.reserve(sizt);
        for (int i = 0; i < sizf; i++){
            from = parent(from);
            pf.push_back(from);
        }
        for (int i = 0; i < sizt; i++){
            pt.push_back(to);
            to = parent(to);
        }
        pf.insert(pf.end(),pt.rbegin(),pt.rend());
        return pf;
    }
    // dist, v1, v2
    tuple<int,int,int> diameter(){
        int v1 = max_element(dep.begin(),dep.end()) - dep.begin();
        vector<int> dist_from_v1(n,numeric_limits<int>::max());
        queue<int> que;
        que.push(v1);
        dist_from_v1[v1] = 0;
        while (!que.empty()){
            int p = que.front(); que.pop();
            for (int i = start[p]; i < start[p+1]; i++){
                if (chmin(dist_from_v1[es[i].first],dist_from_v1[p]+1)){
                    que.push(es[i].first);
                }
            }
        }
        int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
        return make_tuple(dist_from_v1[v2],v1,v2);
    }
    // dist, v1, v2
    tuple<ll,int,int> diameter_weighted(){
        int v1 = max_element(wdep.begin(),wdep.end()) - wdep.begin();
        vector<ll> dist_from_v1(n,numeric_limits<ll>::max());
        queue<int> que;
        que.push(v1);
        dist_from_v1[v1] = 0;
        while (!que.empty()){
            int p = que.front(); que.pop();
            for (int i = start[p]; i < start[p+1]; i++){
                if (chmin(dist_from_v1[es[i].first],dist_from_v1[p]+es[i].second)){
                    que.push(es[i].first);
                }
            }
        }
        int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
        return make_tuple(dist_from_v1[v2],v1,v2);
    }
    const auto operator[](int idx){ return ranges::subrange(es.begin()+start[idx],es.begin()+start[idx+1]); }
  private:
    void build(){
        vector<pair<int,ll>> nes(2*(n-1));
        vector<int> fs = start;
        fill(start.begin(),start.end(),0);
        for (int i = 0; i < n-1; i++) start[es[i].first+1]++, start[fs[i]+1]++;
        for (int i = 0; i < n; i++) start[i+1] += start[i];
        auto geta = start;
        for (int i = 0; i < n-1; i++){
            nes[geta[es[i].first]++] = {fs[i],es[i].second};
            nes[geta[fs[i]]++] = es[i];
        }
        swap(es,nes);
        init_bfs();
        init_dfs();
    }
    void init_bfs(){
        dep.resize(n,numeric_limits<int>::max());
        wdep.resize(n);
        queue<int> que;
        que.push(root);
        dep[root] = 0;
        vector<int> order; order.reserve(n);
        while (!que.empty()){
            int p = que.front(); que.pop();
            order.push_back(p);
            for (int i = start[p]; i < start[p+1]; i++){
                auto [q, w] = es[i];
                if (chmin(dep[q],dep[p]+1)){
                    wdep[q] = wdep[p] + w;
                    que.push(q);
                }
                else {
                    swap(es[start[p]],es[i]);
                }
            }
        }
        sub.resize(n,0);
        for (int v : order | views::reverse){
            sub[v] = 1;
            int stv = start_skip_parent(v);
            for (int i = stv; i < start[v+1]; i++){
                sub[v] += sub[es[i].first];
                if (sub[es[stv].first] < sub[es[i].first]) swap(es[stv],es[i]);
            }
        }
    }
    void init_dfs(){
        down.resize(n);
        tour.resize(n);
        nxt.resize(n);
        nxt[root] = root;
        int nowtime = 0;
        auto dfs = [&](auto sfs, int v) -> void {
            down[v] = nowtime++;
            tour[down[v]] = v;
            int stv = start_skip_parent(v);
            if (stv >= start[v+1]) return ;
            nxt[es[stv].first] = nxt[v];
            sfs(sfs,es[stv].first);
            for (int i = stv+1; i < start[v+1]; i++){
                nxt[es[i].first] = es[i].first;
                sfs(sfs,es[i].first);
            }
        };
        dfs(dfs,root);
    }
    inline int start_skip_parent(int v) const { return start[v]+int(v != root); }
    int n, root, inner_edge_id;
    vector<pair<int,ll>> es;
    vector<int> start, dep, sub, down, tour, nxt;
    vector<ll> wdep;
};

} // namespace noya2

#line 2 "tree/tree_query_weighted.hpp"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 4 "tree/tree_query_weighted.hpp"

namespace noya2{

struct Tree_weighted {
    Tree_weighted (int n_ = 0, int root_ = 0) : n(n_), root(root_), inner_edge_id(0), es(n-1), start(n+1,0){
        if (n == 1) build();
    }
    void add_edge(int u, int v, ll w){
        es[inner_edge_id] = {u,w}, start[inner_edge_id] = v;
        if (++inner_edge_id == n-1) build();
    }
    void input(int indexed = 1){
        rep(i,n-1){
            int u, v; ll w; cin >> u >> v >> w;
            u -= indexed, v -= indexed;
            add_edge(u,v,w);
        }
    }
    void input_parents(int indexed = 1){
        rep(i,n-1){
            int p; ll w; cin >> p >> w;
            p -= indexed;
            add_edge(p,i+1,w);
        }
    }
    int degree(int v){
        assert(0 <= v && v < n);
        return start[v+1] - start[v];
    }
    int parent(int v){
        assert(0 <= v && v < n);
        if (v == root) return -1;
        return es[start[v]].first;
    }
    int subtree_size(int v){
        assert(0 <= v && v < n);
        return sub[v];
    }
    int depth(int v){
        assert(0 <= v && v < n);
        return dep[v];
    }
    ll depth_weighted(int v){
        assert(0 <= v && v < n);
        return wdep[v];
    }
    int la(int v, int d){
        assert(0 <= v && v < n);
        while (v != -1){
            int u = nxt[v];
            if (down[v] - d >= down[u]){
                v = tour[down[v] - d];
                break;
            }
            d -= down[v] - down[u] + 1;
            v = parent(u);
        }
        return v;
    }
    pair<int,ll> la_weighted(int v, ll d){
        assert(0 <= v && v < n);
        if (d > wdep[v]) return make_pair(-1,0LL);
        if (d == wdep[v]) return make_pair(root,0LL);
        while (v != -1){
            int u = nxt[v];
            if (d < wdep[v] - wdep[u]) break;
            d -= wdep[v] - wdep[u];
            if (d < es[start[u]].second){
                return make_pair(u,d);
            }
            d -= es[start[u]].second;
            v = parent(u);
        }
        int le = down[nxt[v]], ri = down[v];
        while (ri - le > 1){
            int md = (le + ri) / 2;
            if (d >= wdep[v] - wdep[tour[md]]) ri = md;
            else le = md;
        }
        return make_pair(tour[ri],d-(wdep[v]-wdep[tour[ri]]));
    }
    int lca(int u, int v){
        assert(0 <= v && v < n && 0 <= u && u < n);
        while (nxt[u] != nxt[v]){
            if (down[u] < down[v]) swap(u,v);
            u = es[start[nxt[u]]].first;
        }
        return dep[u] < dep[v] ? u : v;
    }
    int jump(int from, int to, int d){
        int l = lca(from,to);
        if (d <= dep[from] - dep[l]){
            return la(from,d);
        }
        d -= dep[from] - dep[l];
        if (d <= dep[to] - dep[l]){
            return la(to,dep[to]-dep[l]-d);
        }
        return -1;
    }
    pair<int,ll> jump_weighted(int from, int to, ll d){
        int l = lca(from,to);
        if (d <= wdep[from] - wdep[l]){
            return la_weighted(from,d);
        }
        d -= wdep[from] - wdep[l];
        if (d <= wdep[to] - wdep[l]){
            return la_weighted(to,wdep[to]-wdep[l]-d);
        }
        return make_pair(-1,0LL);
    }
    int dist(int u, int v){ return dep[lca(u,v)]*(-2) + dep[u] + dep[v]; }
    ll dist_weighted(int u, int v){ return wdep[lca(u,v)]*(-2) + wdep[u] + wdep[v]; }
    vector<int> path(int from, int to){
        int l = lca(from,to);
        const int sizf = dep[from]-dep[l], sizt = dep[to]-dep[l];
        vector<int> pf = {from}, pt;
        pf.reserve(sizf+1); pt.reserve(sizt);
        for (int i = 0; i < sizf; i++){
            from = parent(from);
            pf.push_back(from);
        }
        for (int i = 0; i < sizt; i++){
            pt.push_back(to);
            to = parent(to);
        }
        pf.insert(pf.end(),pt.rbegin(),pt.rend());
        return pf;
    }
    // dist, v1, v2
    tuple<int,int,int> diameter(){
        int v1 = max_element(dep.begin(),dep.end()) - dep.begin();
        vector<int> dist_from_v1(n,numeric_limits<int>::max());
        queue<int> que;
        que.push(v1);
        dist_from_v1[v1] = 0;
        while (!que.empty()){
            int p = que.front(); que.pop();
            for (int i = start[p]; i < start[p+1]; i++){
                if (chmin(dist_from_v1[es[i].first],dist_from_v1[p]+1)){
                    que.push(es[i].first);
                }
            }
        }
        int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
        return make_tuple(dist_from_v1[v2],v1,v2);
    }
    // dist, v1, v2
    tuple<ll,int,int> diameter_weighted(){
        int v1 = max_element(wdep.begin(),wdep.end()) - wdep.begin();
        vector<ll> dist_from_v1(n,numeric_limits<ll>::max());
        queue<int> que;
        que.push(v1);
        dist_from_v1[v1] = 0;
        while (!que.empty()){
            int p = que.front(); que.pop();
            for (int i = start[p]; i < start[p+1]; i++){
                if (chmin(dist_from_v1[es[i].first],dist_from_v1[p]+es[i].second)){
                    que.push(es[i].first);
                }
            }
        }
        int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
        return make_tuple(dist_from_v1[v2],v1,v2);
    }
    const auto operator[](int idx){ return ranges::subrange(es.begin()+start[idx],es.begin()+start[idx+1]); }
  private:
    void build(){
        vector<pair<int,ll>> nes(2*(n-1));
        vector<int> fs = start;
        fill(start.begin(),start.end(),0);
        for (int i = 0; i < n-1; i++) start[es[i].first+1]++, start[fs[i]+1]++;
        for (int i = 0; i < n; i++) start[i+1] += start[i];
        auto geta = start;
        for (int i = 0; i < n-1; i++){
            nes[geta[es[i].first]++] = {fs[i],es[i].second};
            nes[geta[fs[i]]++] = es[i];
        }
        swap(es,nes);
        init_bfs();
        init_dfs();
    }
    void init_bfs(){
        dep.resize(n,numeric_limits<int>::max());
        wdep.resize(n);
        queue<int> que;
        que.push(root);
        dep[root] = 0;
        vector<int> order; order.reserve(n);
        while (!que.empty()){
            int p = que.front(); que.pop();
            order.push_back(p);
            for (int i = start[p]; i < start[p+1]; i++){
                auto [q, w] = es[i];
                if (chmin(dep[q],dep[p]+1)){
                    wdep[q] = wdep[p] + w;
                    que.push(q);
                }
                else {
                    swap(es[start[p]],es[i]);
                }
            }
        }
        sub.resize(n,0);
        for (int v : order | views::reverse){
            sub[v] = 1;
            int stv = start_skip_parent(v);
            for (int i = stv; i < start[v+1]; i++){
                sub[v] += sub[es[i].first];
                if (sub[es[stv].first] < sub[es[i].first]) swap(es[stv],es[i]);
            }
        }
    }
    void init_dfs(){
        down.resize(n);
        tour.resize(n);
        nxt.resize(n);
        nxt[root] = root;
        int nowtime = 0;
        auto dfs = [&](auto sfs, int v) -> void {
            down[v] = nowtime++;
            tour[down[v]] = v;
            int stv = start_skip_parent(v);
            if (stv >= start[v+1]) return ;
            nxt[es[stv].first] = nxt[v];
            sfs(sfs,es[stv].first);
            for (int i = stv+1; i < start[v+1]; i++){
                nxt[es[i].first] = es[i].first;
                sfs(sfs,es[i].first);
            }
        };
        dfs(dfs,root);
    }
    inline int start_skip_parent(int v) const { return start[v]+int(v != root); }
    int n, root, inner_edge_id;
    vector<pair<int,ll>> es;
    vector<int> start, dep, sub, down, tour, nxt;
    vector<ll> wdep;
};

} // namespace noya2

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