data_structure/range_parallel_dsu.hpp

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• Last update: 2024-07-28 16:18:08+09:00
• Include: #include "data_structure/range_parallel_dsu.hpp"

Depends on

• data_structure/dsu.hpp

Verified with

• test/data_structure/RangeParallelUnionfind.test.cpp

Code

#pragma once

#include"data_structure/dsu.hpp"

namespace noya2 {

struct range_parallel_dsu : dsu {
    using dsu::operator=;
    int n;
    std::vector<dsu> ds;
    range_parallel_dsu (int _n0) : n(_n0) {
        int msb = 31 - countl_zero((unsigned int)(n));
        ds.resize(msb, dsu(n));
        (*this) = dsu(n);
    }
    // for k = 0, 1, ... ,d-1
    // merge(i+k,j+k)
    std::vector<std::tuple<int,int,int>> merge_range(int i, int j, int d){
        assert(i + d <= n);
        assert(j + d <= n);
        if (d == 0) return {};
        int msb = std::bit_width((unsigned int)(d)) - 1;
        std::vector<std::tuple<int,int,int>> connected;
        inner_merge(i, j, msb, connected);
        inner_merge(i + d - (1<<msb), j + d - (1<<msb), msb, connected);
        return connected;
    }
  private:
    // d = 2^k
    void inner_merge(int i, int j, int k, std::vector<std::tuple<int,int,int>> &connected){
        // k >= 0
        if (k == 0){
            i = this->leader(i);
            j = this->leader(j);
            if (i == j) return ;
            int l = this->merge(i, j);
            connected.emplace_back(i, j, l);
        }
        else {
            k--;
            if (ds[k].same(i, j)) return ;
            ds[k].merge(i, j);
            inner_merge(i, j, k, connected);
            inner_merge(i + (1<<k), j + (1<<k), k, connected);
        }
    }
};

} // namespace noya2

#line 2 "data_structure/range_parallel_dsu.hpp"

#line 2 "data_structure/dsu.hpp"

#include <vector>
#include <cassert>
#include <algorithm>

namespace noya2{

struct dsu {
  public:
    dsu() : _n(0) {}
    dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};

} // namespace noya2
#line 4 "data_structure/range_parallel_dsu.hpp"

namespace noya2 {

struct range_parallel_dsu : dsu {
    using dsu::operator=;
    int n;
    std::vector<dsu> ds;
    range_parallel_dsu (int _n0) : n(_n0) {
        int msb = 31 - countl_zero((unsigned int)(n));
        ds.resize(msb, dsu(n));
        (*this) = dsu(n);
    }
    // for k = 0, 1, ... ,d-1
    // merge(i+k,j+k)
    std::vector<std::tuple<int,int,int>> merge_range(int i, int j, int d){
        assert(i + d <= n);
        assert(j + d <= n);
        if (d == 0) return {};
        int msb = std::bit_width((unsigned int)(d)) - 1;
        std::vector<std::tuple<int,int,int>> connected;
        inner_merge(i, j, msb, connected);
        inner_merge(i + d - (1<<msb), j + d - (1<<msb), msb, connected);
        return connected;
    }
  private:
    // d = 2^k
    void inner_merge(int i, int j, int k, std::vector<std::tuple<int,int,int>> &connected){
        // k >= 0
        if (k == 0){
            i = this->leader(i);
            j = this->leader(j);
            if (i == j) return ;
            int l = this->merge(i, j);
            connected.emplace_back(i, j, l);
        }
        else {
            k--;
            if (ds[k].same(i, j)) return ;
            ds[k].merge(i, j);
            inner_merge(i, j, k, connected);
            inner_merge(i + (1<<k), j + (1<<k), k, connected);
        }
    }
};

} // namespace noya2

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