Create SplayTree class, with all tests passed.

thu_dsa/chp7/AVL.h

@@ -9,8 +9,6 @@
 
 template <typename K, typename V>
 class AVL: public BST<K, V>{
-protected:
-
 public:
 	BinNodePosi(T) insert(K const &key, V const &value);
 	bool           remove(K const &key);

thu_dsa/chp8/SplayTree.h

@@ -0,0 +1,213 @@
+#ifndef SPLAYTREE_H_
+#define SPLAYTREE_H_
+
+#include "../chp7/BST.h"
+
+#define T entry<K, V>
+template <typename K, typename V>
+class SplayTree: public BST<K, V>{
+protected:
+	BinNodePosi(T) splay(BinNodePosi(T) x);
+	BinNodePosi(T) zig(BinNodePosi(T) p);						//right rotation
+	BinNodePosi(T) zag(BinNodePosi(T) p);						//left  rotation
+	BinNodePosi(T) zigzig(BinNodePosi(T) g);
+	BinNodePosi(T) zagzag(BinNodePosi(T) g);
+
+public:
+	BinNodePosi(T)& search(K const &key);
+	BinNodePosi(T)  insert(K const &key, V const &value);
+	bool            remove(K const &key);
+};
+
+//implementations
+
+//protected methods
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::splay(BinNodePosi(T) x){
+	BinNodePosi(T) p;
+	BinNodePosi(T) g;
+	BinNodePosi(T) hot;
+	while(x != __root){
+		p = x->parent, g = p->parent;
+		if (!g) {
+			hot = p->parent;
+			x = (x == p->leftChild ? zig(p) : zag(p));
+			x->parent = hot;
+			if (hot) (p == hot->leftChild)? hot->leftChild : hot->rightChild = x;
+		}
+		else {
+			if (p == g->leftChild) {
+				if (x == p->leftChild) {							//zig-zig
+					hot       = g->parent;
+					x         = zigzig(g);
+					x->parent = hot;
+					if (hot) (g == hot->leftChild ? hot->leftChild : hot->rightChild) = x;
+				}
+				else {												//zig-zag
+					hot       = g->parent;
+					x         = connect34(p, x, g, p->leftChild, x->leftChild, x->rightChild, g->rightChild);
+					x->parent = hot;
+					if (hot) g == hot->leftChild ? hot->leftChild : hot->rightChild = x;
+				}
+			}
+			else {
+				if (x == p->leftChild) {							//zag-zig
+					hot       = g->parent;
+					x         = connect34(g, x, p, g->leftChild, x->leftChild, x->rightChild, p->rightChild);
+					x->parent = hot;
+					if (hot) g == hot->leftChild ? hot->leftChild : hot->rightChild = x;
+				}
+				else {												//zag-zag
+					hot       = g->parent;
+					x         = zagzag(g);
+					x->parent = hot;
+					if (hot) g == hot->leftChild ? hot->leftChild : hot->rightChild = x;
+				}
+			}
+		}
+		if (!x->parent) __root = x;
+	}
+	return x;
+}
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::zig(BinNodePosi(T) p){
+	BinNodePosi(T) x = p->leftChild;
+	p->leftChild = x->rightChild;
+	if (x->rightChild) x->rightChild->parent = p;
+
+	x->rightChild = p;
+	p->parent = x;
+
+	updateHeight(p);
+	updateHeight(x);
+	return x;
+}
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::zag(BinNodePosi(T) p) {
+	BinNodePosi(T) x = p->rightChild;
+	p->rightChild = x->leftChild;
+	if (x->leftChild) x->leftChild->parent = p;
+
+	x->leftChild = p;
+	p->parent = x;
+
+	updateHeight(p);
+	updateHeight(x);
+	return x;
+}
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::zigzig(BinNodePosi(T) g) {
+	BinNodePosi(T) p = g->leftChild;
+	BinNodePosi(T) x = p->leftChild;
+
+	p->leftChild = x->rightChild;
+	if (x->rightChild) x->rightChild->parent = p;
+
+	x->rightChild = p;
+	p->parent = x;
+
+	g->leftChild = p->rightChild;
+	if (p->rightChild) p->rightChild->parent = g;
+
+	p->rightChild = g;
+	g->parent = p;
+
+	updateHeight(g);
+	updateHeight(p);
+	updateHeight(x);
+
+	return x;
+}
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::zagzag(BinNodePosi(T) g) {
+	BinNodePosi(T) p = g->rightChild;
+	BinNodePosi(T) x = p->rightChild;
+
+	p->rightChild = x->leftChild;
+	if (x->leftChild) x->leftChild->parent = p;
+
+	x->leftChild = p;
+	p->parent = x;
+
+	g->rightChild = p->leftChild;
+	if (p->leftChild) p->leftChild->parent = g;
+
+	p->leftChild = g;
+	g->parent = p;
+
+	updateHeight(g);
+	updateHeight(p);
+	updateHeight(x);
+
+	return x;
+}
+
+//public interfaces
+
+template <typename K, typename V>
+BinNodePosi(T)& SplayTree<K, V>::search(K const &key){
+	BinNodePosi(T) x = searchIn(__root, key, __hot = nullptr);
+	if (x) splay(x);
+	else if(__hot) splay(__hot);
+	return __root;
+}
+
+template <typename K, typename V>
+BinNodePosi(T) SplayTree<K, V>::insert(K const &key, V const &value) {
+	BinNodePosi(T) x = search(key);
+	if (x && x->data.key == key) return x;
+	//else
+	__root = new BinNode<T>(entry<K, V>(key, value));
+	++__size;
+	if (!x) return __root;
+
+	if(key < x->data.key){
+		__root->leftChild  = x->leftChild;
+		__root->rightChild = x;
+		x->leftChild       = nullptr;
+		x->parent          = __root;
+	}else{
+		__root->leftChild  = x;
+		__root->rightChild = x->rightChild;
+		x->rightChild      = nullptr;
+		x->parent          = __root;
+	}
+	updateHeight(x);
+	updateHeight(__root);
+	return __root;
+}
+
+template <typename K, typename V>
+bool SplayTree<K, V>::remove(K const &key){
+	BinNodePosi(T) x = search(key);
+	if (!x || x->data.key != key) return false;
+	//else
+	if(!__root->leftChild){
+		__root = __root->rightChild;
+		if(__root) __root->parent = nullptr;
+		search(key);
+	}
+	else if(!__root->rightChild){
+		__root = __root->leftChild;
+		__root->parent = nullptr;
+		search(key);
+	}
+	else {
+		__root = x->rightChild;
+		__root->parent = nullptr;
+		search(key);						//move x's succ to root, and __root has no left child(for succ has the smallest key
+		__root->leftChild = x->leftChild;
+		x->leftChild->parent = __root;
+		updateHeight(__root);
+	}
+	--__size;
+	delete x;
+	return true;
+}
+
+#endif

thu_dsa/chp8/SplayTree.md

@@ -0,0 +1,18 @@
+伸展树知识总结
+=============
+
+> 相对于AVL树的比较。
+AVL树更像是循规蹈矩，如履薄冰。而伸展树则更加潇洒，不顾小节。
+
+> 局部性原理(locality)
+类比于列表
+
+> 逐层伸展策略与最坏情况
+
+双层伸展策略
++ 描述
++ 效果
++ 时间复杂度
+
+> 伸展树的实现
+为了保证局部性，插入结点也需要插入到根节点。删除结点后，需要将被删除结点附近的结点移到根节点。这两个操作都可以通过伸展树的查找快速实现。

thu_dsa/chp8/test_SplayTree.cpp

@@ -0,0 +1,89 @@
+#include "SplayTree.h"
+#include <time.h>
+#include <iostream>
+#include <cassert>
+
+using std::cout;
+using std::endl;
+
+void test_insert_and_search();
+void test_remove();
+
+int main(){
+	cout << "Running tests." << endl;
+
+	test_insert_and_search();
+	test_remove();
+
+	cout << "All tests passed." << endl;
+	system("pause");
+	return 0;
+}
+
+void test_insert_and_search(){
+	SplayTree<int, int> sTree;
+
+	//orderly insert
+	for (int ix = 0; ix != 32; ++ix)
+		sTree.insert(ix, ix);
+	assert(sTree.size() == 32);
+	assert(sTree.root()->data.key == 31);
+	assert(sTree.root()->height == 31);
+
+	//test search
+	assert(sTree.search(0)->data.key == 0);
+	assert(sTree.root()->data.key == 0);
+	assert(sTree.root()->height == 17);
+	assert(sTree.root()->rightChild->data.key = 31);
+	assert(sTree.root()->leftChild == nullptr);
+	assert(sTree.root()->rightChild->height == 16);
+
+	assert(sTree.search(1)->data.key == 1);
+	assert(sTree.root()->data.key == 1);
+	assert(sTree.root()->height == 10);
+	assert(sTree.root()->rightChild->data.key = 31);
+	assert(sTree.root()->leftChild->data.key  == 0);
+	assert(sTree.root()->rightChild->height == 9);
+
+	assert(sTree.search(2)->data.key == 2);
+	assert(sTree.root()->data.key == 2);
+	assert(sTree.root()->height == 7);
+	assert(sTree.root()->rightChild->data.key = 27);
+	assert(sTree.root()->leftChild->data.key == 1);
+	assert(sTree.root()->rightChild->height == 6);
+}
+
+void test_remove(){
+	SplayTree<int, int> sTree;
+	//orderly insert
+	for (int ix = 0; ix != 32; ++ix)
+		sTree.insert(ix, ix);
+	assert(sTree.size() == 32);
+	assert(sTree.root()->data.key == 31);
+	assert(sTree.root()->height == 31);
+
+	assert(!sTree.remove(33));
+	assert(!sTree.remove(35));
+	assert(sTree.size() == 32);
+
+	assert(sTree.remove(31));
+	assert(sTree.size() == 31);
+	assert(sTree.root()->data.key == 30);
+	assert(sTree.root()->height == 30);
+
+	assert(sTree.remove(0));
+	assert(sTree.size() == 30);
+	assert(sTree.root()->data.key == 1);
+	assert(sTree.root()->height == 9);
+	assert(sTree.root()->rightChild->data.key == 27);
+	assert(sTree.root()->rightChild->height == 8);
+	assert(sTree.root()->leftChild == nullptr);
+
+	assert(sTree.remove(27));
+	assert(sTree.size() == 29);
+	assert(sTree.root()->data.key == 28);
+	assert(sTree.root()->leftChild->data.key == 1);
+	assert(sTree.root()->rightChild->data.key == 29);
+	assert(sTree.root()->height == 9);
+	assert(sTree.root()->leftChild->height == 8);
+}