块状链表(unrolled Linked List)

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195

/**************************************************************** 
 * 代码作者: Alex Li
 * 创建时间: 2026-03-03 16:49:46
 * 最后修改: 2026-03-03 18:05:28
 * 文件描述: 块状链表(unrolled linked list)功能：
    1. 插入元素
    2. 删除元素
    3. 查询第 k 个元素
    4. 自动分裂块
    5. 自动简单合并块

  时间复杂度：
    单次操作 O(√n)

  设计思想：
    - 每个节点存储一个小数组
    - 节点之间用链表连接
    - 当块过大 -> 分裂
    - 当块过小 -> 尝试合并

****************************************************************/


#include <bits/stdc++.h>
using namespace std;

int BLOCK_SIZE;   // 不再是常量，根据 n 决定

struct Node {
    vector<int> data;
    Node* next;
};

Node* head = nullptr;

// 创建新节点
Node* newNode() {
    Node* node = new Node;
    node->next = nullptr;
    return node;
}

// 分裂
void split(Node* cur) {
    Node* newnode = newNode();

    // 把 BLOCK_SIZE 之后的元素移到新块
    newnode->data.assign(cur->data.begin() + BLOCK_SIZE,
                         cur->data.end());

    cur->data.erase(cur->data.begin() + BLOCK_SIZE,
                    cur->data.end());

    newnode->next = cur->next;
    cur->next = newnode;
}

// 合并
void merge(Node* cur) {
    if (!cur || !cur->next) return;

    if (cur->data.size() + cur->next->data.size() <= BLOCK_SIZE) {
        Node* nxt = cur->next;

        cur->data.insert(cur->data.end(),
                         nxt->data.begin(),
                         nxt->data.end());

        cur->next = nxt->next;
        delete nxt;
    }
}

// 插入（1-index）
void insert(int pos, int x) {
    if (!head) head = newNode();

    Node* cur = head;
    int cnt = 0;

    while (cur) {
        if (cnt + cur->data.size() >= pos) {
            cur->data.insert(cur->data.begin() + (pos - cnt - 1), x);

            if (cur->data.size() > BLOCK_SIZE)
                split(cur);
            return;
        }

        cnt += cur->data.size();

        if (!cur->next) break;
        cur = cur->next;
    }

    // 插入到末尾
    cur->data.push_back(x);
    if (cur->data.size() > BLOCK_SIZE)
        split(cur);
}

// 删除
void erase_pos(int pos) {
    Node* cur = head;
    Node* prev = nullptr;
    int cnt = 0;

    while (cur) {
        if (cnt + cur->data.size() >= pos) {
            cur->data.erase(cur->data.begin() + (pos - cnt - 1));

            if (cur->data.size() < BLOCK_SIZE / 2)
                merge(cur);

            if (cur->data.empty()) {
                if (prev)
                    prev->next = cur->next;
                else
                    head = cur->next;
                delete cur;
            }

            return;
        }

        cnt += cur->data.size();
        prev = cur;
        cur = cur->next;
    }
}

// 查询
int query(int pos) {
    Node* cur = head;
    int cnt = 0;

    while (cur) {
        if (cnt + cur->data.size() >= pos)
            return cur->data[pos - cnt - 1];

        cnt += cur->data.size();
        cur = cur->next;
    }

    return -1;
}

// 打印块结构
void print_blocks() {
    Node* cur = head;
    int id = 1;

    while (cur) {
        cout << "Block " << id++
             << " (size=" << cur->data.size() << "): ";

        for (int x : cur->data)
            cout << x << " ";

        cout << endl;

        cur = cur->next;
    }

    cout << "----------------------\n";
}

int main() {
    int n;
    cout << "输入元素个数: ";
    cin >> n;

    // 根据 n 自动设块大小
    int s = (int)sqrt(n);
    if (s * s == n)
        BLOCK_SIZE = s;
    else
        BLOCK_SIZE = s + 1;

    cout << "BLOCK_SIZE = " << BLOCK_SIZE << endl;

    cout << "输入元素:\n";

    for (int i = 1; i <= n; i++) {
        int x;
        cin >> x;
        insert(i, x);   // 插入到末尾
    }

    cout << "\n初始分块结果:\n";
    print_blocks();
    //erase_pos(13);
    //print_blocks();
    return 0;
}