noya2_Library

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:heavy_check_mark: test/tree/Lowest_Common_Ancestor.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/lca"

#include"../../template/template.hpp"
#include"../../tree/heavy_light_decomposition.hpp"

int main(){
    int n, q; in(n,q);
    hld_tree g(n);
    g.input_parents<0>();
    while (q--){
        int u, v; in(u,v);
        out(g.lca(u,v));
    }
}
#line 1 "test/tree/Lowest_Common_Ancestor.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"

#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 2 "tree/heavy_light_decomposition.hpp"

#line 6 "tree/heavy_light_decomposition.hpp"
#include <ranges>
#line 9 "tree/heavy_light_decomposition.hpp"

// #include "data_structure/csr.hpp"

namespace noya2 {

struct hld_tree {
    int n, root;
    std::vector<int> down, nxt, sub, tour;
	// noya2::internal::csr<int> childs;

    // default constructor (nop)
    hld_tree () {}

    // tree with _n node
    // after construct, call input_edges / input_parents / add_edge _n - 1 times
    hld_tree (int _n, int _root = 0) : n(_n), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
        if (n == 1){
            nxt[0] = -1;
            down[0] = -1;
            build_from_parents();
        }
    }

    // par[i] < i, par[0] == -1
    hld_tree (const std::vector<int> &par) : n(par.size()), root(0), down(n, -1), nxt(par), sub(n, 1), tour(n){
        build_from_parents();
    }

    // par[i] < i, par[0] == -1
    hld_tree (std::vector<int> &&par) : n(par.size()), root(0), down(n, -1), sub(n, 1), tour(n) {
        nxt.swap(par);
        build_from_parents();
    }

    // distinct unweighted undirected n - 1 edges of tree 
    hld_tree (const std::vector<std::pair<int, int>> &es, int _root = 0) : n(es.size() + 1), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
        for (auto &[u, v] : es){
            down[u]++;
            down[v]++;
            nxt[u] ^= v;
            nxt[v] ^= u;
        }
        build_from_edges();
    }

    // input parents from cin
    template<int indexed = 1>
    void input_parents(){
        // using std::cin;
        nxt[0] = -1;
        for (int u = 1; u < n; u++){
            cin >> nxt[u];
            nxt[u] -= indexed;
        }
        build_from_parents();
    }

    // input n - 1 edges from cin
    template<int indexed = 1>
    void input_edges(){
        // using std::cin;
        for (int i = 1; i < n; i++){
            int u, v; cin >> u >> v;
            u -= indexed;
            v -= indexed;
            down[u]++;
            down[v]++;
            nxt[u] ^= v;
            nxt[v] ^= u;
        }
        build_from_edges();
    }

    void add_edge(int u, int v){
        down[u]++;
        down[v]++;
        nxt[u] ^= v;
        nxt[v] ^= u;
        // use tour[0] as counter
        if (++tour[0] == n - 1){
            build_from_edges();
        }
    }

    size_t size() const {
        return n;
    }

    // top vertex of heavy path which contains v
    int leader(int v) const {
        return nxt[v] < 0 ? v : nxt[v];
    }

    // level ancestor
    // ret is ancestor of v, dist(ret, v) == d
    // if d > depth(v), return -1
    int la(int v, int d) const {
        while (v != -1){
            int u = leader(v);
            if (down[v] - d >= down[u]){
                v = tour[down[v] - d];
                break;
            }
            d -= down[v] - down[u] + 1;
            v = (u == root ? -1 : ~nxt[u]);
        }
        return v;
    }

    // lowest common ancestor of u and v
    int lca(int u, int v) const {
        int du = down[u], dv = down[v];
        if (du > dv){
            std::swap(du, dv);
            std::swap(u, v);
        }
        if (dv < du + sub[u]){
            return u;
        }
        while (du < dv){
            v = ~nxt[leader(v)];
            dv = down[v];
        }
        return v;
    }

    // distance from u to v
    int dist(int u, int v) const {
        int _dist = 0;
        while (leader(u) != leader(v)){
            if (down[u] > down[v]) std::swap(u, v);
            _dist += down[v] - down[leader(v)] + 1;
            v = ~nxt[leader(v)];
        }
        _dist += std::abs(down[u] - down[v]);
        return _dist;
    }

    // d times move from to its neighbor (direction of to)
    // if d > dist(from, to), return -1
    int jump(int from, int to, int d) const {
        int _from = from, _to = to;
        int dist_from_lca = 0, dist_to_lca = 0;
        while (leader(_from) != leader(_to)){
            if (down[_from] > down[_to]){
                dist_from_lca += down[_from] - down[leader(_from)] + 1;
                _from = ~nxt[leader(_from)];
            }
            else {
                dist_to_lca += down[_to] - down[leader(_to)] + 1;
                _to = ~nxt[leader(_to)];
            }
        }
        if (down[_from] > down[_to]){
            dist_from_lca += down[_from] - down[_to];
        }
        else {
            dist_to_lca += down[_to] - down[_from];
        }
        if (d <= dist_from_lca){
            return la(from, d);
        }
        d -= dist_from_lca;
        if (d <= dist_to_lca){
            return la(to, dist_to_lca - d);
        }
        return -1;
    }

    // parent of v (if v is root, return -1)
    int parent(int v) const {
        if (v == root) return -1;
        return (nxt[v] < 0 ? ~nxt[v] : tour[down[v] - 1]);
    }

    // visiting time in euler tour
    // usage : seg.set(index(v), X[v])
    int index(int vertex) const {
        return down[vertex];
    }
    // usage : seg.set(index_edge(e.u, e.v), e.val)
    int index(int vertex1, int vertex2) const {
        return std::max(down[vertex1], down[vertex2]);
    }

    // subtree size of v
    int subtree_size(int v) const {
        return sub[v];
    }

    // prod in subtree v : seg.prod(subtree_l(v), subtree_r(v))
    int subtree_l(int v) const {
        return down[v];
    }
    int subtree_r(int v) const {
        return down[v] + sub[v];
    }

    // v is in subtree r
    bool is_in_subtree(int r, int v) const {
        return subtree_l(r) <= subtree_l(v) && subtree_r(v) <= subtree_r(r);
    }
    
    // distance table from s
    std::vector<int> dist_table(int s) const {
        std::vector<int> table(n, -1);
        table[s] = 0;
        while (s != root){
            table[parent(s)] = table[s] + 1;
            s = parent(s);
        }
        for (int v : tour){
            if (table[v] == -1){
                table[v] = table[parent(v)] + 1;
            }
        }
        return table;
    }

    // dist, v1, v2
    std::tuple<int, int, int> diameter() const {
        std::vector<int> dep = dist_table(root);
        int v1 = std::ranges::max_element(dep) - dep.begin();
        std::vector<int> fromv1 = dist_table(v1);
        int v2 = std::ranges::max_element(fromv1) - fromv1.begin();
        return {fromv1[v2], v1, v2};
    }

    // vertex array {from, ..., to}
    std::vector<int> path(int from, int to) const {
        int d = dist(from, to);
        std::vector<int> _path(d + 1);
        int front = 0, back = d;
        while (from != to){
            if (down[from] > down[to]){
                _path[front++] = from;
                from = parent(from);
            }
            else {
                _path[back--] = to;
                to = parent(to);
            }
        }
        _path[front] = from;
        return _path;
    }

    // path decomposition and query (vertex weighted)
    // if l < r, decsending order tour[l, r)
    // if l > r, acsending order tour(l, r]
    template<bool vertex = true>
    void path_query(int u, int v, auto f) const {
        while (leader(u) != leader(v)){
            if (down[u] < down[v]){
                f(down[leader(v)], down[v] + 1);
                v = ~nxt[leader(v)];
            }
            else {
                f(down[u] + 1, down[leader(u)]);
                u = ~nxt[leader(u)];
            }
        }
        if constexpr (vertex){
            if (down[u] < down[v]){
                f(down[u], down[v] + 1);
            }
            else {
                f(down[u] + 1, down[v]);
            }
        }
        else {
            if (down[u] != down[v]){
                f(down[u] + 1, down[v] + 1);
            }
        }
    }

    // {parent, mapping} : cptree i is correspond to tree mapping[i]. parent[i] is parent of i in cptree.
    // parent[i] < i, parent[0] == -1
	std::pair<std::vector<int>, std::vector<int>> compressed_tree(std::vector<int> vs) const {
        if (vs.empty()){
            return {{},{}};
        }
        auto comp = [&](int l, int r){
            return down[l] < down[r];
        };
		std::ranges::sort(vs, comp);
		int sz = vs.size(); vs.reserve(2*sz);
        for (int i = 0; i < sz-1; i++){
            vs.emplace_back(lca(vs[i], vs[i+1]));
        }
        std::sort(vs.begin() + sz, vs.end(), comp);
        std::ranges::inplace_merge(vs, vs.begin() + sz, comp);
        auto del = std::ranges::unique(vs);
        vs.erase(del.begin(), del.end());
        sz = vs.size();
        std::stack<int> st;
        std::vector<int> par(sz);
        par[0] = -1;
        st.push(0);
        for (int i = 1; i < sz; i++){
            while (!is_in_subtree(vs[st.top()], vs[i])) st.pop();
            par[i] = st.top();
            st.push(i);
        }
        return {par, vs};
	}

/*  CSR

	// build csr for using operator()
	void build_csr(){
		childs = noya2::internal::csr<int>(n, n - 1);
		for (int v = 0; v < n; v++){
			if (v == root) continue;
			childs.add(parent(v), v);
		}
		childs.build();
	}
	const auto operator()(int v) const {
		return childs[v];
	}
	auto operator()(int v){
		return childs[v];
	}
*/

    // hld_tree g;
    // euler tour order : `for (int v : g)`
    // with range_adaptor : `for (int v : g | std::views::reverse)`
    // bottom-up DP : `for (int v : g | std::views::drop(1) | std::views::reverse){ update dp[g.parent(v)] by dp[v] }`
    auto begin() const {
        return tour.begin();
    }
    auto end() const {
        return tour.end();
    }

  private:
    // nxt[v] : parent of v, nxt[0] == -1
    void build_from_parents(){
        for (int u = n - 1; u >= 1; u--){
            int v = nxt[u];
            sub[v] += sub[u];
            down[v] = std::max(down[v], sub[u]);
        }
        for (int u = n - 1; u >= 1; u--){
            int v = nxt[u];
            if (down[v] == sub[u]){
                sub[u] = ~sub[u];
                down[v] = ~down[v];
            }
        }

        sub[0] = ~down[0] + 1;
        down[0] = 0;
        for (int u = 1; u < n; u++){
            int v = nxt[u];
            int nsub = ~down[u] + 1;
            if (sub[u] < 0){
                down[u] = down[v] + 1;
                nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
            }
            else {
                down[u] = down[v] + sub[v];
                sub[v] += sub[u];
                nxt[u] = ~v;
            }
            sub[u] = nsub;
        }

        for (int u = 0; u < n; u++){
            tour[down[u]] = u;
        }
    }

    // down[v] : degree of v
    // nxt[v] : xor prod of neighbor of v
    void build_from_edges(){
        // use tour as queue
        int back = 0;
        for (int u = 0; u < n; u++){
            if (u != root && down[u] == 1){
                tour[back++] = u;
            }
        }
        for (int front = 0; front < n - 1; front++){
            int u = tour[front];
            down[u] = -1;
            int v = nxt[u]; // parent of v
            nxt[v] ^= u;
            if (--down[v] == 1 && v != root){
                tour[back++] = v;
            }
        }
        // check : now, tour is reverse of topological order

        tour.pop_back();

        // check : now, down[*] <= 1
        for (int u : tour){
            int v = nxt[u];
            // subtree size (initialized (1,1,...,1))
            sub[v] += sub[u];
            // heaviest subtree of its child
            down[v] = std::max(down[v], sub[u]);
        }
        for (int u : tour){
            int v = nxt[u];
            // whether u is not the top of heavy path
            if (down[v] == sub[u]){
                sub[u] = ~sub[u];
                down[v] = ~down[v];
            }
        }

        // after appearing v as u (or v == root), 
        // down[v] is the visiting time of euler tour
        // nxt[v] is the lowest vertex of heavy path which contains v
        //   (if v itself, nxt[v] is ~(parent of v))
        // sub[v] + down[v] is the light child's starting time of euler tour
        // note : heavy child's visiting time of euler tour is (the time of its parent) + 1
        sub[root] = ~down[root] + 1;
        down[root] = 0;
        nxt[root] = -1;
        for (int u : tour | std::views::reverse){
            int v = nxt[u];
            int nsub = ~down[u] + 1;
            // heavy child
            if (sub[u] < 0){
                down[u] = down[v] + 1;
                nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
            }
            // light child
            else {
                down[u] = down[v] + sub[v];
                sub[v] += sub[u];
                nxt[u] = ~v;
            }
            sub[u] = nsub;
        }

        // tour is inverse permutation of down
        tour.push_back(0);
        for (int u = 0; u < n; u++){
            tour[down[u]] = u;
        }
    }
};

} // namespace noya2
#line 5 "test/tree/Lowest_Common_Ancestor.test.cpp"

int main(){
    int n, q; in(n,q);
    hld_tree g(n);
    g.input_parents<0>();
    while (q--){
        int u, v; in(u,v);
        out(g.lca(u,v));
    }
}
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