lmori's Library

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:heavy_check_mark: Persistent Union Find
(data-structure/union-find/PersistentUnionFind.hpp)

概要

todo

計算量

todo

Depends on

Verified with

Code

#include "../others/PersistentArray.hpp"

struct PersistentUnionfind {
 public:
  using Node = PersistentArray<int>::Node;
  PersistentUnionfind() : _n(0) {}
  explicit PersistentUnionfind(int n) : _n(n), parent_or_size(n, -1) {
    root = parent_or_size.get_root();
  }

  Node *get_root() {
    return root;
  }

  Node *merge(Node *p, int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    int x = leader(p, a), y = leader(p, b);
    if (x == y) return p;
    int px = parent_or_size.get(p, x);
    int py = parent_or_size.get(p, y);
    if (-px < -py) std::swap(x, y);
    // Node *ret = parent_or_size.set(p, x, px + py);
    return parent_or_size.set(parent_or_size.set(p, x, px + py), y, x);
  }

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

  int leader(Node *p, int a) {
    assert(0 <= a && a < _n);
    if (parent_or_size.get(p, a) < 0) return a;
    return leader(p, parent_or_size.get(p, a));
  }

  int size(Node *p, int a) {
    assert(0 <= a && a < _n);
    return -parent_or_size.get(p, leader(p, a));
  }

  std::vector<std::vector<int>> groups(Node *p) {
    std::vector<int> leader_buf(_n), group_size(_n);
    for (int i = 0; i < _n; i++) {
      leader_buf[i] = leader(p, 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

  PersistentArray<int> parent_or_size;
  Node *root;
};
#line 1 "data-structure/others/PersistentArray.hpp"

template <class T>
class PersistentArray {
 public:
  struct Node {
    Node *l, *r;
    T val;
    Node() : l(nullptr), r(nullptr) {
    }
  };
  PersistentArray() {}
  PersistentArray(int siz) {
    n = siz;
    vector<T> v(n);
    root = new Node();
    for (int i = 0; i < n; i++) {
      init_set(root, i, v[i], 0, n);
    }
  }

  PersistentArray(int siz, T x) {
    n = siz;
    root = new Node();
    for (int i = 0; i < n; i++) {
      init_set(root, i, x, 0, n);
    }
  }

  PersistentArray(const vector<T> &v) {
    n = int(v.size());
    root = new Node();
    for (int i = 0; i < n; i++) {
      init_set(root, i, v[i], 0, n);
    }
  }

  T get(Node *ptr, int p) {
    return get(ptr, p, 0, n)->val;
  }

  Node *get_root() {
    return root;
  }

  Node *set(Node *ptr, int p, T x) {
    Node *new_root = new Node();
    Node *cur = new_root;
    int l = 0;
    int r = n;
    while (r - l > 1) {
      int m = (l + r) >> 1;
      if (l <= p and p < m) {
        if (!cur->l) cur->l = new Node();
        cur->r = ptr->r;
        cur = cur->l;
        ptr = ptr->l;
        r = m;
      } else {
        if (!cur->r) cur->r = new Node();
        cur->l = ptr->l;
        cur = cur->r;
        ptr = ptr->r;
        l = m;
      }
    }
    cur->val = x;
    return new_root;
  }

 private:
  int n;

  Node *root;

  void init_set(Node *cur, int p, T x, int l, int r) {
    while (r - l > 1) {
      int m = (l + r) >> 1;
      if (l <= p and p < m) {
        if (!cur->l) cur->l = new Node();
        cur = cur->l;
        r = m;
      } else {
        if (!cur->r) cur->r = new Node();
        cur = cur->r;
        l = m;
      }
    }
    cur->val = x;
  }

  Node *get(Node *cur, int p, int l, int r) {
    while (r - l > 1) {
      int m = (l + r) >> 1;
      if (l <= p and p < m) {
        cur = cur->l;
        r = m;
      } else {
        cur = cur->r;
        l = m;
      }
    }
    return cur;
  }
};
#line 2 "data-structure/union-find/PersistentUnionFind.hpp"

struct PersistentUnionfind {
 public:
  using Node = PersistentArray<int>::Node;
  PersistentUnionfind() : _n(0) {}
  explicit PersistentUnionfind(int n) : _n(n), parent_or_size(n, -1) {
    root = parent_or_size.get_root();
  }

  Node *get_root() {
    return root;
  }

  Node *merge(Node *p, int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    int x = leader(p, a), y = leader(p, b);
    if (x == y) return p;
    int px = parent_or_size.get(p, x);
    int py = parent_or_size.get(p, y);
    if (-px < -py) std::swap(x, y);
    // Node *ret = parent_or_size.set(p, x, px + py);
    return parent_or_size.set(parent_or_size.set(p, x, px + py), y, x);
  }

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

  int leader(Node *p, int a) {
    assert(0 <= a && a < _n);
    if (parent_or_size.get(p, a) < 0) return a;
    return leader(p, parent_or_size.get(p, a));
  }

  int size(Node *p, int a) {
    assert(0 <= a && a < _n);
    return -parent_or_size.get(p, leader(p, a));
  }

  std::vector<std::vector<int>> groups(Node *p) {
    std::vector<int> leader_buf(_n), group_size(_n);
    for (int i = 0; i < _n; i++) {
      leader_buf[i] = leader(p, 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

  PersistentArray<int> parent_or_size;
  Node *root;
};
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