AVL平衡树(二叉搜索树 c++实现)

参考博客:数据结构 AVL      

                Treap平衡树  

                平衡查找树

代码:

指针实现

/*仿一个博客的AVL*/#include<iostream>#include<cstdlib>#include<cstdio>#include<algorithm>#include<cmath>#include<map>#include<stack>#include<queue>#include<ctime>#include<cstring>#include<string>#define LL __int64#define INF 0x3f3f3f3f3fusing namespace std;struct node{int val;int height;node* l;node* r;};node root;int max(int a, int b){return a>b;}int height(node *p){if(p) return p->height;return 0;}node* maximum(node* p){if(p){while(p->r) p=p->r;return p;}return NULL;}node* minimum(node* p){if(p){while(p->l) p=p->l;return p;}return NULL;}node* LeftRotation(node* p){node *q = p->r;p->r = q->l;q->l = p;p->height = max(height(p->l), height(p->r)) + 1;q->height = max(height(q->l), height(q->r)) + 1;return q;}node* RightRotation(node* p){node *q = p->l;p->l = q->r;q->r = p;p->height = max(height(p->l), height(p->r)) + 1;q->height = max(height(q->l), height(q->r)) + 1;return q;}node* RLeftRotation(node* p){p->r = RightRotation(p->r);return LeftRotation(p);}node* LRightRotation(node* p){p->l = LeftRotation(p->l);return RightRotation(p);}node* InsertNode(node* &p, int val){if(!p){p = new node;p->height=0;p->l=NULL;p->r=NULL;p->val=val;}else if(val > p->val){p->r = InsertNode(p->r, val);if(height(p->r) - height(p->l)==2) //插入失衡 {if(val > p->r->val) p = LeftRotation(p);else  p = RLeftRotation(p);}}else if(val < p->val){p->l = InsertNode(p->l, val);if(height(p->l) - height(p->r)==2) //插入失衡 {if(val < p->l->val) p = RightRotation(p);else  p = LRightRotation(p);}}p->height = max(height(p->l), height(p->r)) + 1;return p;}node* del(node* &p, int val){if(p){if(val == p->val){if(p->l && p->r)//左右都不为空 {if(height(p->l) > height(p->r)){node* q = maximum(p->l);p->val = q->val;p->l = del(p->l, q->val);}else{node* q = minimum(p->r);p->val = q->val;p->r = del(p->r, q->val);}}else{node* q = p;if(p->l) p=p->l;else if(p->r)p=p->r;return NULL;}}else if(val > p->val){p->r = del(p->r, val);if(height(p->l) - height(p->r) == 2){if(height(p->l->r)>height(p->l->l)){ p = LRightRotation(p);}else p = RightRotation(p);}}else if(val < p->val){p->l = del(p->l, val);if(height(p->r) - height(p->l) ==2){if(height(p->r->l)>height(p->r->r)){p=RLeftRotation(p);}else p = LeftRotation(p);}}return p;}return NULL;}int query(int x){node *p=root.l;int k=0;stack<node*>S;if(!p)  return false;while(p || !S.empty()){while(p){S.push(p);p=p->l;}p=S.top();S.pop();k++;if(k==x){return p->val;break;}p=p->r;}return false;}int main(){//freopen("in.txt","r",stdin);      //freopen("out.txt","w",stdout);  int n,x;char c[4];scanf("%d", &n);root.l=root.r=NULL;while(n--){scanf("%s", c);if(c[0]=='Y') printf("Single dog!\n");else{scanf("%d", &x);if(c[0]=='J')      InsertNode(root.l, x);else if(c[0]=='W') printf("%d\n", query(x));else if(c[0]=='X')del(root.l, x);}}return 0;}

数组实现:

/***************Problem from :数据结构 Problem describe :平衡树的应用 ****************/#include<iostream>#include<cstdlib>#include<cstdio>#include<algorithm>#include<cmath>#include<map>#include<stack>#include<queue>#include<ctime>#include<cstring>#include<string>#define LL __int64#define INF 0x3f3f3f3f3fusing namespace std;struct Tree{int key, l, r, size;}node[111111];int root=0, top=0;void left_rotation(int &x){int y = node[x].r;node[x].r = node[y].l;node[y].l = x;node[y].size = node[x].size;node[x].size = node[node[x].l].size + node[node[x].r].size+1;x = y;}void right_rotation(int &x){int y = node[x].l;node[x].l = node[y].r;node[y].r = x;node[y].size = node[x].size;node[x].size = node[node[x].l].size + node[node[x].r].size+1;x = y;}void maintain(int &root, bool flag){if(flag == false)//false => 左 {// root 的左儿子的左儿子的size>root的右儿子的size if(node[node[node[root].l].l].size > node[node[root].r].size){right_rotation(root);}// root 的左儿子的右儿子的size>root的右儿子的size else if(node[node[node[root].l].r].size > node[node[root].r].size){left_rotation(node[root].l);right_rotation(root);}else return ;}else {// root 的右儿子的右儿子的size>root的左儿子的size if(node[node[node[root].r].r].size > node[node[root].l].size){left_rotation(root);}// root 的右儿子的左儿子的size>root的右儿子的size else if(node[node[node[root].r].l].size > node[node[root].l].size){right_rotation(node[root].r);left_rotation(root);}else return ;}maintain(node[root].l,false);maintain(node[root].r,true);maintain(root,true);maintain(root,false);}void insert(int &root, int key){if(root==0){root=++top;node[root].l = node[root].r = 0;node[root].size = 1;node[root].key = key;}else{node[root].size ++;if(key < node[root].key) insert(node[root].l, key);else insert(node[root].r, key);maintain(root, key>=node[root].key);}return ;}int remove(int &root, int key){int d_key;node[root].size--;if( key == node[root].key || (key > node[root].key&& node[root].r==0) || (key < node[root].key&& node[root].l==0)){d_key = node[root].key;        if(node[root].l && node[root].r)        {            node[root].key = remove(node[root].l,node[root].key+1);        }        else        {            root = node[root].l + node[root].r;         }}else if(key > node[root].key){d_key = remove(node[root].r, key);}else{d_key = remove(node[root].l, key);}return d_key;}int select(int &root,int k)//求第k小数{    int r = node[node[root].l].size + 1;    if(r == k) return node[root].key;    else if(r < k) return select(node[root].r,k - r);    else return select(node[root].l,k);}int main(){ //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);int n,cnt=0,x;          char c[4];      scanf("%d", &n);     while(n--)      {          scanf("%s", c);          if(c[0]=='Y') printf("Single dog!\n");          else          {              scanf("%d", &x);              if(c[0]=='J')       insert(root, x), cnt++;              else if(c[0]=='W')  printf("%d\n", (x>cnt)?0:select(root, x));              else if(c[0]=='X')  remove(root, x), cnt--;          }      }  return 0;}