项目介绍
- 本项目通过分解各大厂的常见笔面试题，追本溯源至数据结构和算法的底层实现原理，知其然知其所以然；
- 建立知识结构体系，方便查找，欢迎更多志同道合的朋友加入项目AlgorithmPractice，（欢迎提issue和pull request）。
一、题目描述
-
跳表是什么：跳表是一种可以进行对半查找的链表，其通过在源链表上插入标记指针，再将标记指针也串成链表，这样通过查找标记指针达到快速查找数值的目的。同理，标记指针过长，可以同样对标记指针再次进行标记，类似多级缓存。
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代码实现：SkipList
二、解题思路
首先准备一个Node结点的数据结构，我们假设这个快表的每一个链表数值都是从小到大排序，所有起点的值设置为 Integer.MIN_VALUE。
class SkipListNode {
int value;
SkipListNode next;
SkipListNode down;
public SkipListNode() {
this.value = Integer.MIN_VALUE;
next = null;
down = null;
}
public SkipListNode(int value) {
this.value = value;
next = null;
down = null;
}
}
1、initial()方法
每条链表初始化的时候，都需要头尾两个结点，注意到头结点和尾结点的值设置为（从小到大）：public static final int HEAD_KEY = Integer.MIN_VALUE;
public static final int TAIL_KEY = Integer.MAX_VALUE;
每次初始化的时候都需要交换新老头结点和尾结点的链接。
public SkipListNode initial() {
SkipListNode phead = new SkipListNode();
SkipListNode ptail = new SkipListNode();
phead.value = HEAD_KEY;
ptail.value = TAIL_KEY;
phead.next = ptail;
return phead;
}
2、add()方法
add方法首先判断节点时都存在，存在的话直接return，不存在的话，首先判断是否需要在源链表的基础上新建一层标记指针。public void add(int Value) {
if (find(Value)) {
return;
}
SkipListNode insertKey;
SkipListNode fathersln = null;
/* 经过实验证明：查找 耗时 比 插入 更加耗时。
层数越高，整个数据备份越多，越臃肿，但是查找快、插入和删除慢
层数越低，整个数据备份越少， 但是查找慢、插入和删除快
综合考虑，建议层数高
*/
//无需新建层数
if (SkipListnum <= (2 << SkipListlevel - 1)) {
int k = randomLevel();
insertKey = head;
for (int i = 0; i < k; i++) {
insertKey = insertKey.down;
}
} else {
//需要新建层数
SkipListNode phead = initial();
phead.down = head;
phead.next.down = tail;
head = phead;
tail = phead.next;
insertKey = head;
SkipListlevel++;
}
//向下补全所有的插入节点
while (insertKey != null) {
while (insertKey.next.value < Value) {
insertKey = insertKey.next;
}
SkipListNode sln = new SkipListNode(Value);
if (fathersln != null) {
fathersln.down = sln;
}
sln.next = insertKey.next;
insertKey.next = sln;
insertKey = insertKey.down;
fathersln = sln;
}
SkipListnum++;
}
3、delete()方法
删除方法需要注意三点：1、表层数降级，2、横向查找数值，3、纵向查找数值。public boolean delete(int x) {
//快表层高降级
if (head.next == tail && head.down != null) {
head = head.down;
tail = tail.down;
this.SkipListlevel--;
}
//注意顺序：先降级、再判断不然会出现最后一个元素删除了，但是表级仍然不为1
if (!find(x)) {
return false;
}
SkipListNode point = head;
SkipListNode prepoint = point;
//横向查找
while (point.value != x) {
while (point.next.value <= x) {
prepoint = point;
point = point.next;
}
if (point.value == x) {
break;
}
point = point.down;
prepoint = prepoint.down;
if (point.equals(prepoint)) {
continue;
}
while (prepoint.next != point) {
prepoint = prepoint.next;
}
}
//纵向删除
while (prepoint != null) {
point = point.down;
prepoint.next = prepoint.next.next;
prepoint = prepoint.down;
//循环至最低点结束
while (prepoint != null && prepoint.next != point) {
prepoint = prepoint.next;
}
}
this.SkipListnum--;
return true;
}
4、find()方法
public boolean find(int x) {
SkipListNode point = head;
while (true) {
while (point.next.value <= x) {
point = point.next;
}
if (point.value == x) {
return true;
}
if (point.down == null) {
//到达最底层
return false;
}
point = point.down;
}
}
5、print()方法
输出的是链表的从上到下整体结构。public void print() {
//输出链表的整体结构
SkipListNode point;
SkipListNode headpoint = head;
while (headpoint != null) {
point = headpoint;
while (point.value != TAIL_KEY) {
if (point.value != HEAD_KEY) {
System.out.print(point.value + "-");
}
point = point.next;
}
System.out.println();
headpoint = headpoint.down;
}
}