tree/lca_sparse_table.hpp

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• Last update: 2021-09-12 23:20:08-04:00
• Include: #include "tree/lca_sparse_table.hpp"

Depends on

• template.hpp

Verified with

• tests/tree/lca_sparse_table.test.cpp

Code

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

// Due to some limitations with the current format of the templates, I cannot use the sparse_table.hpp template here
template <typename GraphType, typename EdgeType> struct LCASparseTable {
    EdgeType E;
    vector<int> dep, tour, fst;
    vector<vector<int>> tb;
    int N, lg;
    int minByDep(int a, int b) { return dep[a] < dep[b] ? a : b; }
    void init(int N, GraphType &g, int rt) {
        dep.assign(N+1, 0); fst.assign(N+1, 0); tour.clear();
        function<void(int, int)> dfs = [&] (int c, int p) {
            tour.push_back(c);
            fst[c] = tour.size();
            for (auto to : g[c]) {
                int v = E.v(to);
                if (v != p) {
                    dep[v] = dep[c] + 1;
                    dfs(v, c);
                    tour.push_back(c);
                }
            }
        };
        dfs(rt, -1);

        N = tour.size(); lg = __lg(N);
        tb.assign(lg+1, vector<int>(N+1));
        copy(tour.begin(), tour.end(), tb[0].begin()+1);
        for (auto i = 1; i <= lg; i++) {
            int jmp = 1 << (i-1), end = N - (1<<i) + 1;
            for (auto j = 1; j <= end; j++)
                tb[i][j] = minByDep(tb[i-1][j], tb[i-1][j+jmp]);
        }
    }
    int lca(int a, int b) {
        a = fst[a]; b = fst[b];
        if (a > b) swap(a, b);
        int bit = __lg(b-a+1);
        return minByDep(tb[bit][a], tb[bit][b-(1<<bit)+1]);
    }
};

#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_sparse_table.hpp"

// Due to some limitations with the current format of the templates, I cannot use the sparse_table.hpp template here
template <typename GraphType, typename EdgeType> struct LCASparseTable {
    EdgeType E;
    vector<int> dep, tour, fst;
    vector<vector<int>> tb;
    int N, lg;
    int minByDep(int a, int b) { return dep[a] < dep[b] ? a : b; }
    void init(int N, GraphType &g, int rt) {
        dep.assign(N+1, 0); fst.assign(N+1, 0); tour.clear();
        function<void(int, int)> dfs = [&] (int c, int p) {
            tour.push_back(c);
            fst[c] = tour.size();
            for (auto to : g[c]) {
                int v = E.v(to);
                if (v != p) {
                    dep[v] = dep[c] + 1;
                    dfs(v, c);
                    tour.push_back(c);
                }
            }
        };
        dfs(rt, -1);

        N = tour.size(); lg = __lg(N);
        tb.assign(lg+1, vector<int>(N+1));
        copy(tour.begin(), tour.end(), tb[0].begin()+1);
        for (auto i = 1; i <= lg; i++) {
            int jmp = 1 << (i-1), end = N - (1<<i) + 1;
            for (auto j = 1; j <= end; j++)
                tb[i][j] = minByDep(tb[i-1][j], tb[i-1][j+jmp]);
        }
    }
    int lca(int a, int b) {
        a = fst[a]; b = fst[b];
        if (a > b) swap(a, b);
        int bit = __lg(b-a+1);
        return minByDep(tb[bit][a], tb[bit][b-(1<<bit)+1]);
    }
};

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