各种平衡树Treap/SBT/Avl/Splay tree

看了这么久的平衡树，是时候做个总结了。

以poj 3481为例，敲了四份代码，分别是Treap ，Size Balance Tree，Avl Tree，splay tree。

唯独少了红黑树T_T。。。

总的来说每种平衡树各有各的优点吧：

Treap写起来简单上手也快如果熟练的话不到十分种可以敲完。

SBT速度快名不虚传。。。

Avl树高度平衡吧，不过实际的效果不尽如人意，可能是我实现的姿势不对吧/(ㄒoㄒ)/~~

splay tree各方面比较均衡，特别的伸展树在维护序列方面相对其它几种树优势明显。

可持久化的Treap除外(因为没比较过故不好妄下结论)。

总之，只要理解了旋转操作和建树的思想，每种树实现起来都很方便。。。

好了少扯淡了代码如下：

Treap：

#include
#include
#include
#define Max_N 110000
#define size(_) ((_)==NULL ? 0 : (_)->size)
typedef struct _trp{
	int client, key, size, fix;
	struct _trp *ch[2];
}treap, *Treap;
treap stack[Max_N];
int sz = 0;
int run(){
	static int x = 1840828537;
	x += (x << 2) | 1;
	return x;
}
void update(Treap x){
	if (x == NULL) return;
	x->size = size(x->ch[0]) + size(x->ch[1]) + 1;
}
void rotate(Treap *x, int d){
	Treap k = (*x)->ch[!d];
	(*x)->ch[!d] = k->ch[d];
	k->ch[d] = *x;
	k->size = (*x)->size;
	update(*x);
	*x = k;
}
void insert(Treap *x, int client, int key){
	if (*x == NULL){
		*x = &stack[sz++];
		(*x)->ch[0] = (*x)->ch[1] = NULL;
		(*x)->key = key, (*x)->size = 1, (*x)->client = client, (*x)->fix = run();
	} else {
		int d = key > (*x)->key;
		insert(&((*x)->ch[d]), client, key);
		update(*x);
		if ((*x)->ch[d]->fix < (*x)->fix) rotate(x, !d);
	}
}
void _delete(Treap *x, int key){
	if (*x == NULL) return;
	if ((*x)->key == key){
		if (!(*x)->ch[0] || !(*x)->ch[1]){
			*x = (*x)->ch[0] ? (*x)->ch[0] : (*x)->ch[1];
		} else {
			int d = (*x)->ch[0]->fix < (*x)->ch[1]->fix;
			rotate(x, d);
			_delete(&((*x)->ch[d]), key);
		}
	} else {
		_delete(&((*x)->ch[key>(*x)->key]), key);
	}
	if (*x != NULL) update(*x);
}
Treap find_kth(Treap x, int k){
	int t = 0;
	for (; x != NULL;){
		t = size(x->ch[0]);
		if (k == t + 1) break;
		else if (k <= t) x = x->ch[0];
		else k -= t + 1, x = x->ch[1];
	}
	return x;
}
int main(){
#ifdef LOCAL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w+", stdout);
#endif
	int n, a, b;
	Treap root = NULL, ret = NULL;
	while (~scanf("%d", &n) && n){
		ret = NULL;
		if (2 == n || 3 == n){
			if (2 == n && root) ret = find_kth(root, root->size);
			else if (3 == n && root) ret = find_kth(root, 1);
			if (!ret || !root) printf("0\n");
			else printf("%d\n", ret->client), _delete(&root, ret->key);
		} else {
			scanf("%d %d", &a, &b);
			insert(&root, a, b);
		}

	}
	return 0;
}

SBT：

#include
#include
#include
#define Max_N 110000
#define size(_) ((_)==NULL ? 0 : (_)->size)
typedef struct _sbt{
	int client, key, size;
	struct _sbt *ch[2];
}SBTNode, *SBT;
SBTNode stack[Max_N];
int sz = 0;
void rotate(SBT *x, int d){
	SBT k = (*x)->ch[!d];
	(*x)->ch[!d] = k->ch[d];
	k->ch[d] = *x;
	k->size = (*x)->size;
	(*x)->size = size((*x)->ch[0]) + size((*x)->ch[1]) + 1;
	*x = k;
}
void Maintain(SBT *x, int d){
	if ((*x)->ch[d] == NULL) return;
	if (size((*x)->ch[d]->ch[d]) > size((*x)->ch[!d])) rotate(x, !d);
	else if (size((*x)->ch[d]->ch[!d]) > size((*x)->ch[!d]))
		rotate(&((*x)->ch[d]), d), rotate(x, !d);
	else return;
	Maintain(&((*x)->ch[d]), 0);
	Maintain(&((*x)->ch[!d]), 1);
	Maintain(x, 0), Maintain(x, 1);
}
void insert(SBT *x, int client, int key){
	if (*x == NULL){
		*x = &stack[sz++];
		(*x)->ch[0] = (*x)->ch[1] = NULL;
		(*x)->key = key, (*x)->size = 1, (*x)->client = client;
	} else {
		(*x)->size++;
		insert(&((*x)->ch[key > (*x)->key]), client, key);
		Maintain(x, key >= (*x)->key);
	}
}
void _delete(SBT *x, int key){
	if (*x == NULL) return;
	(*x)->size--;
	if ((*x)->key == key){
		if (!(*x)->ch[0] || !(*x)->ch[1]){
			*x = (*x)->ch[0] ? (*x)->ch[0] : (*x)->ch[1];
		} else {
			SBT ret = (*x)->ch[1];
			for (; ret->ch[0] != NULL; ret = ret->ch[0]);
			_delete(&((*x)->ch[1]), (*x)->key = ret->key);
		}
	} else {
		_delete(&((*x)->ch[key > (*x)->key]), key);
	}
}
SBT find_kth(SBT x, int k){
	int t = 0;
	for (; x != NULL;){
		t = size(x->ch[0]);
		if (k == t + 1) break;
		else if (k <= t) x = x->ch[0];
		else k -= t + 1, x = x->ch[1];
	}
	return x;
}
int main(){
#ifdef LOCAL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w+", stdout);
#endif
	int n, a, b;
	SBT root = NULL, ret = NULL;
	while (~scanf("%d", &n) && n){
		ret = NULL;
		if (2 == n || 3 == n){
			if (2 == n && root) ret = find_kth(root, root->size);
			else if (3 == n && root) ret = find_kth(root, 1);
			if (!ret || !root) printf("0\n");
			else printf("%d\n", ret->client), _delete(&root, ret->key);
		} else {
			scanf("%d %d", &a, &b);
			insert(&root, a, b);
		}

	}
	return 0;
}

Avl:

#include
#include
#include
#define Max_N 200000
#define _max(a,b) ((a)>(b)?(a):(b))
#define size(_) ((_)==NULL ? 0 : (_)->size)
#define Height(_) ((_)==NULL ? -1 : (_)->Height)
typedef struct _avl{
	int client, key, size, Height;
	struct _avl *ch[2];
}AvlTree, *Avl;
AvlTree stack[Max_N];
int sz = 0;
void update(Avl x){
	if (x == NULL) return;
	x->size = size(x->ch[0]) + size(x->ch[1]) + 1;
	x->Height = _max(Height(x->ch[0]), Height(x->ch[1])) + 1;
}
void rotate(Avl *x, int d){
	Avl k = (*x)->ch[!d];
	(*x)->ch[!d] = k->ch[d];
	k->ch[d] = *x;
	update(*x);
	update(k);
	*x = k;
}
void Maintain(Avl *x, int d){
	if (Height((*x)->ch[d]) - Height((*x)->ch[!d]) == 2){
		if (Height((*x)->ch[d]->ch[d]) - Height((*x)->ch[d]->ch[!d]) == 1) rotate(x, !d);
		else if (Height((*x)->ch[d]->ch[d]) - Height((*x)->ch[d]->ch[!d]) == -1){
			rotate(&((*x)->ch[d]), d), rotate(x, !d);
		}
	}
}
void insert(Avl *x, int client, int key){
	if (*x == NULL){
		*x = &stack[sz++];
		(*x)->ch[0] = (*x)->ch[1] = NULL;
		(*x)->key = key, (*x)->Height = 0, (*x)->size = 1, (*x)->client = client;
	} else {
		int d = key > (*x)->key;
		insert(&((*x)->ch[d]), client, key);
		update(*x);
		Maintain(x, d);
	}
}
void _delete(Avl *x, int key){
	if (*x == NULL) return;
	if ((*x)->key == key){
		if (!(*x)->ch[0] || !(*x)->ch[1]){
			*x = (*x)->ch[0] ? (*x)->ch[0] : (*x)->ch[1];
		} else {
			Avl ret = (*x)->ch[1];
			for (; ret->ch[0] != NULL; ret = ret->ch[0]);
			_delete(&((*x)->ch[1]), (*x)->key = ret->key);
		}
	} else {
		_delete(&((*x)->ch[key > (*x)->key]), key);
	}
	if (*x != NULL){
		update(*x);
		Maintain(x, 0), Maintain(x, 1);
	}
}
Avl find_kth(Avl x, int k){
	int t = 0;
	for (; x != NULL;){
		t = size(x->ch[0]);
		if (k == t + 1) break;
		else if (k <= t) x = x->ch[0];
		else k -= t + 1, x = x->ch[1];
	}
	return x;
}
int main(){
#ifdef LOCAL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w+", stdout);
#endif
	int n, a, b;
	Avl root = NULL, ret = NULL;
	while (~scanf("%d", &n) && n){
		ret = NULL;
		if (2 == n || 3 == n){
			if (2 == n && root) ret = find_kth(root, root->size);
			else if (3 == n && root) ret = find_kth(root, 1);
			if (!ret || !root) printf("0\n");
			else printf("%d\n", ret->client), _delete(&root, ret->key);
		} else {
			scanf("%d %d", &a, &b);
			insert(&root, a, b);
		}

	}
	return 0;
}

splay tree:

#include
#include
#include
#define Max_N 200000
#define size(_) ((_)==null ? 0 : (_)->size)
typedef struct _spt{
	int client, key, size;
	struct _spt *pre, *ch[2];
}splay;
splay *null, *root, stack[Max_N];
int sz = 0;
splay *_calloc(int client, int key){
	splay *p = &stack[sz++];
	p->pre = p->ch[0] = p->ch[1] = null;
	p->size = 1, p->key = key, p->client = client;
	return p;
}
void push_up(splay *x){
	if (x == null) return;
	x->size = size(x->ch[0]) + size(x->ch[1]) + 1;
}
void rotate(splay *x, int d){
	splay *y = x->pre;
	y->ch[!d] = x->ch[d];
	if (x->ch[d] != null) x->ch[d]->pre = y;
	x->pre = y->pre;
	if (y->pre != null) y->pre->ch[y->pre->ch[0] != y] = x;
	x->ch[d] = y;
	y->pre = x;
	push_up(y);
	if (y == root) root = x;
}
void splay_splay(splay *x, splay *f){
	for (; x->pre != f;){
		if (x->pre->pre == f){
			rotate(x, x->pre->ch[0] == x);
		} else {
			splay *y = x->pre, *z = y->pre;
			if (z->ch[0] == y){
				if (y->ch[0] == x) rotate(y, 1), rotate(x, 1);
				else rotate(x, 0), rotate(x, 1);
			} else {
				if (y->ch[1] == x)
					rotate(y, 0), rotate(x, 0);
				else rotate(x, 1), rotate(x, 0);
			}
		}
	}
	push_up(x);
}
void insert(int client, int key){
	splay *fp = null, *p = root;
	if (root == null){
		root = _calloc(client, key);
		return;
	}
	for (; p != null;){
		fp = p;
		if (key > p->key) p = p->ch[1];
		else p = p->ch[0];
	}
	p = _calloc(client, key);
	if (fp->key > key) fp->ch[0] = p;
	else fp->ch[1] = p;
	p->pre = fp;
	splay_splay(p, null);
	push_up(p);
}
void _delete(int key){
	splay *p = root, *rt = null;
	while (p != null && p->key != key) p = p->ch[key > p->key];
	if (p == null) return;
	splay_splay(p, null);
	rt = root->ch[0];
	if (rt == null){
		rt = root->ch[1];
	} else {
		splay *tmp = rt->ch[1];
		while (tmp != null && tmp->ch[1] != null) tmp = tmp->ch[1];
		if (tmp != null) splay_splay(tmp, root);
		rt = root->ch[0];
		rt->ch[1] = root->ch[1];
		root->ch[1]->pre = rt;
	}
	root = rt;
	root->pre = null;
	if (root != null) push_up(root);
}
void initialize(){
	null = _calloc(-1, -1);
	null->size = 0;
	root = null;
}
splay *find_kth(splay *x, int k){
	int t = 0;
	for (; x != null;){
		t = size(x->ch[0]);
		if (k == t + 1) break;
		else if (k <= t) x = x->ch[0];
		else k -= t + 1, x = x->ch[1];
	}
	if (x == null){
		return null;
	} else {
		splay_splay(x, null);
		return root;
	}
}
int main(){
#ifdef LOCAL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w+", stdout);
#endif
	int n, a, b;
	initialize();
	splay *ret = NULL;
	while (~scanf("%d", &n) && n){
		ret = NULL;
		if (2 == n || 3 == n){
			if (2 == n && root) ret = find_kth(root, root->size);
			else if (3 == n && root) ret = find_kth(root, 1);
			if (ret == null || root == null) printf("0\n");
			else printf("%d\n", ret->client), _delete(ret->key);
		} else {
			scanf("%d %d", &a, &b);
			insert(a, b);
		}

	}
	return 0;
}

最后上对比结果：从上到下依次是，splay tree， treap，sbt，avl。

其实蒟蒻只会用c语言不会c++，但提交代码的时候选了c++和gcc两种o(╯□╰)o。。。