目录
舒展树（splay tree）是1种搜索2叉树，它能在
（1）舒展树满足搜索2叉树的性质，左子节点小于根节点，右子节点大于等于根节点。
（2）舒展树独有特点：当某个节点被访问时，舒展树会通过旋转使该节点成为树的根。
舒展树的动身点是这样的：斟酌到局部性原理（刚被访问的内容下次更大的可能仍会被访问）和28原则（80%的时间只会访问20%的节点）,为了使全部查找时间更小，被查找频率高的节点应当常常处于靠近根的位置。
因而提出以下方案：在每次查找以后对树进行重构，把查找到的节点移到离树根更近些。舒展树应运而生，它是1种自调剂情势的2叉搜索树，它会沿着从某个节点到树根的路径，通过1系列的旋转把这个节点搬到树根上去。
因此相对“2叉搜索树”和“AVL树”，对舒展树重点关注如何旋转的
以下舒展树的实现思想来源于2叉搜索树的根插法（先插入节点到叶子，然后递归旋转到根），我们将查找到的节点旋转到根，等价于将被查找节点插入到根部：
typedef SplayTreeNode* SplayTree;
struct SplayTreeNode {
Item key;
SplayTree left;
SplayTree right;
};舒展树不需要记录额外甚么值（如AVL的高度）来保护树的信息，节省了内存。
引入两种基本的旋转：左旋和右旋
- 当被查找节点在根节点的左子树上时，以根为轴，右旋，将该节点提升到根上
//右旋--k2是根，k1是k2的左子树，将k1旋转成根 -- 以k2为原点向右旋
SplayTree rotR(SplayTree k2)
{
SplayTree k1 = k2->left;
k2->left = k1->right;
k1->right = k2;
return k1;
}//左旋---k2是根，k1是k2的右子树，(k1的右子树非空)将k1旋转成根 -- 以k2为原点向左旋
SplayTree rotL(SplayTree k2)
{
SplayTree k1 = k2->right;
k2->right = k1->left;
k1->left = k2;
return k1;
}
<注>该算法实现没有经过严格的验证，自创；
如有疑问可参考经典算法：
舒展树(1)之 图文解析 和 C语言的实现：http://www.cnblogs.com/skywang12345/p/3604238.html
设被查找节点为 x , 当查找到 x 的先驱节点时：
（1） x 在当前根的左边，那末右旋，将和 x 接近的节点向上提升1步；
（2） x 在当前根的右边，那末左旋，将和 x 接近的节点向上提升1步；
（3） x 的值等于当前根的值，查找结束，在上述两步递归进程中完成旋转；
先驱节点不存在时，查找结束。
递归实现进程是自底向上的，当查找节点命中后，以它的父节点为轴旋转，提升查找节点为根；向上递归，在根与查找节点的路径上每步都旋转1次，直至原树根。
//舒展进程：将key对应的节点舒展到根上，并返回根节点
SplayTree Splay(SplayTree tree, Item key)
{
if (tree == NULL)
return tree;
if (key == tree->key) //命中
return tree;
if (key < tree->key) { //左边
if (tree->left == NULL)
return tree;
tree->left = Splay(tree->left, key);
tree = rotR(tree);
} else { //右边
if (tree->right == NULL)
return tree;
tree->right = Splay(tree->right, key);
tree = rotL(tree);
}
return tree;
}SplayTree SplayTreeSearch(SplayTree tree, Item key)
{
if (tree == NULL || tree->key == key)
return tree;
if (key < tree->key)
return SplayTreeSearch(tree->left, key);
else
return SplayTreeSearch(tree->right, key);
}（1）插入：和搜索2叉树的插入相同，省略
（2）删除: 删除舒展树中键值为key的节点。
先在舒展树中查找键值为key的节点：如果没找到，则直接返回；如果找到的话则将该节点旋转成根节点，然后在删除该节点，然后将该节点的两个子树连接到1起（根节点选用和key邻近的节点）；
/*
*删除舒展树中键值为key的节点
*参数说明：
* tree: 根节点
* key: 待删除节点的键值
*返回：
* 根节点
*/
SplayTree SplayTreeDelete(SplayTree tree, Item key)
{
SplayTree x = NULL;
if (tree == NULL)
return tree;
tree = Splay(tree, key);
if (tree == NULL)
return tree;
if (tree->left != NULL) {
//将根的左边，邻近key的节点旋转成根
x = Splay(tree->left, key);
x->right = tree->right;
} else {
//tree->left == NULL
x = tree->right;
}
delete tree;
return x;
}#include <stdio.h>
#include <stdlib.h>
#define MAX(A, B) ((A > B) ? A : B)
typedef int Item;
typedef struct SplayTreeNode SplayTreeNode;
typedef SplayTreeNode* SplayTree;
struct SplayTreeNode {
Item key;
SplayTree left;
SplayTree right;
};
static int g_error = 0; //毛病代码
SplayTree NewNode(Item key, SplayTree left, SplayTree right)
{
SplayTree x = (SplayTree)malloc(sizeof(*x));
if (x == NULL) {
g_error = 1;
exit(-1);
}
x->key = key;
x->left = left;
x->right = right;
return x;
}
SplayTree SplayTreeInit()
{
return NewNode(10, NULL, NULL);
}
//左旋---k2是根，k1是k2的右子树，(k1的右子树非空)将k1旋转成根 -- 以k2为原点向左旋
SplayTree rotL(SplayTree k2)
{
SplayTree k1 = k2->right;
k2->right = k1->left;
k1->left = k2;
return k1;
}
//右旋--k2是根，k1是k2的左子树，将k1旋转成根 -- 以k2为原点向右旋
SplayTree rotR(SplayTree k2)
{
SplayTree k1 = k2->left;
k2->left = k1->right;
k1->right = k2;
return k1;
}
SplayTree Splay(SplayTree tree, Item key)
{
if (tree == NULL)
return tree;
if (key == tree->key)
return tree;
if (key < tree->key) { //左边
if (tree->left == NULL)
return tree;
tree->left = Splay(tree->left, key);
tree = rotR(tree);
} else { //右边
if (tree->right == NULL)
return tree;
tree->right = Splay(tree->right, key);
tree = rotL(tree);
}
return tree;
}
SplayTree SplayTreeSearch(SplayTree tree, Item key)
{
if (tree == NULL || tree->key == key)
return tree;
if (key < tree->key)
return SplayTreeSearch(tree->left, key);
else
return SplayTreeSearch(tree->right, key);
}
SplayTree SplayTreeInsert(SplayTree tree, Item key)
{
if (tree == NULL)
return NewNode(key, NULL, NULL);
if(key < tree->key)
tree->left = SplayTreeInsert(tree->left, key);
else
tree->right = SplayTreeInsert(tree->right, key);
return tree;
}
void traversal(SplayTree tree)
{
if (tree == NULL) {
printf("NIL ");
return;
}
printf("%d ", tree->key);
traversal(tree->left);
traversal(tree->right);
return;
}
SplayTree SplayTreeDelete(SplayTree tree, Item key)
{
SplayTree x = NULL;
if (tree == NULL)
return tree;
tree = Splay(tree, key);
if (tree == NULL)
return tree;
if (tree->left != NULL) {
x = Splay(tree->left, key);
x->right = tree->right;
} else {
//tree->left == NULL
x = tree->right;
}
delete tree;
return x;
}
int main()
{
SplayTree splay_tree = NULL;
//for (int i = 0; i < 10; i++) {
// int key = rand()%100;
// splay_tree = SplayTreeInsert(splay_tree, key);
// printf("%d ", key);
//}
splay_tree = SplayTreeInsert(splay_tree, 1);
splay_tree = SplayTreeInsert(splay_tree, 5);
splay_tree = SplayTreeInsert(splay_tree, 4);
splay_tree = SplayTreeInsert(splay_tree, 2);
splay_tree = SplayTreeInsert(splay_tree, 6);
printf("
Traversal
");
traversal(splay_tree);
splay_tree = Splay(splay_tree, 6);
splay_tree = SplayTreeDelete(splay_tree, 4);
printf("
Deleted Traversal
");
traversal(splay_tree);
getchar();
}参考资料：
舒展树-维基百科：https://zh.wikipedia.org/wiki/%E4%BC%B8%E5%B1%95%E6%A0%91
舒展树(1)之 图文解析 和 C语言的实现：http://www.cnblogs.com/skywang12345/p/3604238.html
2叉搜索树的实现：http://blog.csdn.net/quzhongxin/article/details/45038399