tree/lca_jump.hpp

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• Last update: 2021-09-12 23:20:08-04:00
• Include: #include "tree/lca_jump.hpp"
• Link: https://codeforces.com/blog/entry/74847

Depends on

• template.hpp

Verified with

• tests/tree/lca_jump.test.cpp

Code

#pragma once
#include "../template.hpp"

// Source: https://codeforces.com/blog/entry/74847
template <typename GraphType, typename EdgeType> struct LCAJump {
    EdgeType E;
    vector<int> dep, par, jmp;
    void init(int N, GraphType &g, int rt) {
        dep.assign(N+1, 0); par.assign(N+1, -1); jmp.assign(N+1, -1);
        function<void(int, int)> dfs = [&] (int c, int p) {
            par[c] = p;
            if (c != rt) {
                if (dep[p] - dep[jmp[p]] == dep[jmp[p]] - dep[jmp[jmp[p]]])
                    jmp[c] = jmp[jmp[p]];
                else
                    jmp[c] = p;
            }
            for (auto to : g[c]) {
                int v = E.v(to);
                if (v != p) {
                    dep[v] = dep[c] + 1;
                    dfs(v, c);
                }
            }
        };
        jmp[rt] = rt;
        dfs(rt, -1);
    }
    int findFirst(int u, function<bool(int)> check) {
        while (!check(u)) {
            if (!check(jmp[u])) u = jmp[u];
            else u = par[u];
        }
        return u;
    }
    int up(int u, int want) {
        while (dep[u] > want) {
            if (dep[jmp[u]] >= want) u = jmp[u];
            else u = par[u];
        }
        return u;
    }
    int lca(int a, int b) {
        if (dep[a] > dep[b]) swap(a, b);
        b = up(b, dep[a]);
        while (a != b) {
            if (jmp[a] != jmp[b]) {
                a = jmp[a];
                b = jmp[b];
            }
            else {
                a = par[a];
                b = par[b];
            }
        }
        return a;
    }
};

#line 2 "template.hpp"
#include <bits/stdc++.h>
#define DEBUG 1
using namespace std;

// Defines
#define fs first
#define sn second
#define pb push_back
#define eb emplace_back
#define mpr make_pair
#define mtp make_tuple
#define all(x) (x).begin(), (x).end()
// Basic type definitions
#if __cplusplus == 201703L // CPP17 only things
template <typename T> using opt_ref = optional<reference_wrapper<T>>; // for some templates
#endif
using ll = long long; using ull = unsigned long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<long long, long long>;
#ifdef __GNUG__
// PBDS order statistic tree
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T, class comp = less<T>> using os_tree = tree<T, null_type, comp, rb_tree_tag, tree_order_statistics_node_update>;
template <typename K, typename V, class comp = less<K>> using treemap = tree<K, V, comp, rb_tree_tag, tree_order_statistics_node_update>;
// HashSet
#include <ext/pb_ds/assoc_container.hpp>
template <typename T, class Hash> using hashset = gp_hash_table<T, null_type, Hash>;
template <typename K, typename V, class Hash> using hashmap = gp_hash_table<K, V, Hash>;
const ll RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash { ll operator()(ll x) const { return x ^ RANDOM; } };
#endif
// More utilities
int SZ(string &v) { return v.length(); }
template <typename C> int SZ(C &v) { return v.size(); }
template <typename C> void UNIQUE(vector<C> &v) { sort(v.begin(), v.end()); v.resize(unique(v.begin(), v.end()) - v.begin()); }
template <typename T, typename U> void maxa(T &a, U b) { a = max(a, b); }
template <typename T, typename U> void mina(T &a, U b) { a = min(a, b); }
const ll INF = 0x3f3f3f3f, LLINF = 0x3f3f3f3f3f3f3f3f;
#line 3 "tree/lca_jump.hpp"

// Source: https://codeforces.com/blog/entry/74847
template <typename GraphType, typename EdgeType> struct LCAJump {
    EdgeType E;
    vector<int> dep, par, jmp;
    void init(int N, GraphType &g, int rt) {
        dep.assign(N+1, 0); par.assign(N+1, -1); jmp.assign(N+1, -1);
        function<void(int, int)> dfs = [&] (int c, int p) {
            par[c] = p;
            if (c != rt) {
                if (dep[p] - dep[jmp[p]] == dep[jmp[p]] - dep[jmp[jmp[p]]])
                    jmp[c] = jmp[jmp[p]];
                else
                    jmp[c] = p;
            }
            for (auto to : g[c]) {
                int v = E.v(to);
                if (v != p) {
                    dep[v] = dep[c] + 1;
                    dfs(v, c);
                }
            }
        };
        jmp[rt] = rt;
        dfs(rt, -1);
    }
    int findFirst(int u, function<bool(int)> check) {
        while (!check(u)) {
            if (!check(jmp[u])) u = jmp[u];
            else u = par[u];
        }
        return u;
    }
    int up(int u, int want) {
        while (dep[u] > want) {
            if (dep[jmp[u]] >= want) u = jmp[u];
            else u = par[u];
        }
        return u;
    }
    int lca(int a, int b) {
        if (dep[a] > dep[b]) swap(a, b);
        b = up(b, dep[a]);
        while (a != b) {
            if (jmp[a] != jmp[b]) {
                a = jmp[a];
                b = jmp[b];
            }
            else {
                a = par[a];
                b = par[b];
            }
        }
        return a;
    }
};

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