平衡二叉树
#include<iostream> #include<cstdio> #include<cstring> #include<math.h> #include<stack> #include<queue> #include<algorithm> using namespace std; const int maxn=107; typedef struct node { node():height(0), lchild(NULL), rchild(NULL) {} int data; int height; struct node* lchild; struct node* rchild; } AVLTreeNode, *AVLTree; int Getheight(AVLTree &T) { if(T) return T->height; else return -1; } ///查找最大元素 AVLTree FindMax(AVLTree T) { if(T) { while(T->rchild) T=T->rchild; } return T; } ///查找最小元素 AVLTree FindMin(AVLTree T) { if(T) { while(T->lchild) T=T->lchild; } return T; } AVLTree SingleLeftRotate(AVLTree &A) { AVLTree B=A->lchild; A->lchild=B->rchild; B->rchild=A; A->height=max(Getheight(A->lchild), Getheight(A->rchild))+1; B->height=max(Getheight(B->lchild), A->height)+1; return B; } AVLTree SingleRightRotate(AVLTree &A) { AVLTree B=A->rchild; A->rchild=B->lchild; B->lchild=A; A->height=max(Getheight(A->lchild), Getheight(A->rchild))+1; B->height=max(Getheight(B->rchild), A->height)+1; return B; } AVLTree DoubleLeftRightRotate(AVLTree &A) { A->lchild=SingleRightRotate(A->lchild); return SingleLeftRotate(A); } AVLTree DoubleRightLeftRotate(AVLTree &A) { A->rchild=SingleLeftRotate(A->rchild); return SingleRightRotate(A); } ///插入函数 AVLTree AVLInsert(AVLTree &T, int x) { if(!T)/**若插入空树, 则新建包含一个结点的树*/ { T=new AVLTreeNode(); T->data=x; T->height=0; T->lchild=NULL; T->rchild=NULL; } else if(x < T->data)/**插入T的左子树*/ { T->lchild=AVLInsert(T->lchild, x); if(Getheight(T->lchild)-Getheight(T->rchild)==2)/**需要左旋*/ { if(x < T->lchild->data) T=SingleLeftRotate(T);///左单旋 else T=DoubleLeftRightRotate(T);///左-右双旋 } } else if(x > T->data)/**插入T的右子树*/ { T->rchild=AVLInsert(T->rchild, x); if(Getheight(T->lchild)-Getheight(T->rchild)==-2) { if(x > T->rchild->data) T=SingleRightRotate(T);///右单旋 else T=DoubleRightLeftRotate(T);///右-左双旋 } } T->height=max(Getheight(T->lchild), Getheight(T->rchild))+1; return T; } ///删除函数 bool AVLDelete(AVLTree &T, int x) { if(T==NULL) return false; if(T->data==x) { if(T->lchild!=NULL && T->rchild!=NULL) { if(Getheight(T->lchild) > Getheight(T->rchild)) { AVLTree p=FindMax(T->lchild); T->data=p->data; AVLDelete(T->lchild, T->data); } else { AVLTree p=FindMin(T->rchild); T->data=p->data; AVLDelete(T->rchild, T->data); } } else { AVLTree p=T; if(T->lchild!=NULL) T=T->lchild; else T=T->rchild; delete p; } } else if(x < T->data) { AVLDelete(T->lchild, x); if(Getheight(T->rchild)-Getheight(T->lchild)>1) { if(Getheight(T->rchild->lchild)>Getheight(T->rchild->rchild)) T=DoubleRightLeftRotate(T); else T=SingleRightRotate(T); } else T->height=max(Getheight(T->lchild), Getheight(T->rchild))+1; } else { AVLDelete(T->rchild, x); if(Getheight(T->lchild)-Getheight(T->rchild)>1) { if(Getheight(T->lchild->rchild)>Getheight((T->lchild->lchild))) T=DoubleLeftRightRotate(T); else T=SingleLeftRotate(T); } else T->height=max(Getheight(T->lchild), Getheight(T->rchild))+1; } return true; } ///查找函数 AVLTree IterFind(AVLTree T, int x) { while(T) { if(x > T->data) T=T->rchild; else if(x < T->data) T=T->lchild; else return T; } return NULL; } void InOrder(AVLTree T) { if(T) { InOrder(T->lchild); printf("%d ", T->data); InOrder(T->rchild); } } void LevelOrder(AVLTree T) { queue<AVLTree>Q; Q.push(T); while(!Q.empty()) { T=Q.front(); Q.pop(); printf("%d ", T->data); if(T->lchild!=NULL) Q.push(T->lchild); if(T->rchild!=NULL) Q.push(T->rchild); } } int main() { AVLTree T=NULL; int a[11]= {3, 2, 1, 4, 5, 6, 7, 10, 9, 8}; for(int i=0; i<10; i++) AVLInsert(T, a[i]); InOrder(T); printf("\n"); LevelOrder(T); printf("\n"); if(AVLDelete(T, 6)) { puts("Delete Success"); InOrder(T); printf("\n"); } else puts("Delete Failed"); AVLTree x=IterFind(T, 6); if(!x) puts("NotFound"); else puts("Found"); return 0; }