資料結構與演算法問題 AVL二叉平衡樹

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AVL樹本質上還是一棵二叉搜尋樹，它的特點是：

1. 本身首先是一棵二叉搜尋樹。

2. 帶有平衡條件：每個結點的左右子樹的高度之差的絕對值（平衡因子）最多為1

#include <iostream>using namespace std;const int LH = 1;const int EH = 0;const int RH = -1;bool TRUE = 1;bool FALSE = 0;typedef struct BSTNode{int key;int bf;BSTNode *lchild, *rchild;}BSTNode;//中序遍曆void inordertree(BSTNode * &root){if (root){inordertree(root->lchild);cout << root->key<<",";inordertree(root->rchild);}}//前序走訪void preordertree(BSTNode * &root){if (root){cout << root->key<<",";preordertree(root->lchild);preordertree(root->rchild);}}//右旋void R_Rotate(BSTNode * &p){BSTNode *lc = p->lchild;p->lchild = lc->rchild;lc->rchild = p;p = lc;}//左旋void L_Rotate(BSTNode *& p){BSTNode *rc = p->rchild;p->rchild = rc->lchild;rc->lchild = p;p = rc;}void LeftBalance(BSTNode * &T){BSTNode *lc = T->lchild;switch (lc->bf){case LH:T->bf = lc->bf = EH;R_Rotate(T);break;case RH:BSTNode *rd = lc->rchild;switch (rd->bf){case LH:T->bf = RH;lc->bf = EH;break;case EH:T->bf = lc->bf = EH;lc->bf = LH;break;}rd->bf = EH;L_Rotate(T->lchild);//先左旋R_Rotate(T);break;}}void RightBalance(BSTNode *& T){BSTNode *rc = T->rchild;switch (rc->bf){case RH:T->bf = rc->bf = EH;L_Rotate(T);break;case LH:BSTNode *ld = rc->lchild;switch (ld->bf){case RH:T->bf = LH;rc->bf = EH;break;case EH:T->bf = rc->bf = EH;break;case LH:T->bf = EH;rc->bf = RH;break;}ld->bf = EH;R_Rotate(T->rchild);L_Rotate(T);break;}}int insertAVL(BSTNode *& t, int e, bool &taller){if (!t){t = new BSTNode;t->key = e;t->lchild = t->rchild = NULL;t->bf = EH;taller = TRUE;}else{if (e == t->key){taller = FALSE;return 0;}if (e < t->key){if (!insertAVL(t->lchild, e,taller))return 0;if (taller){switch (t->bf){case LH:LeftBalance(t);taller = FALSE;break;case EH:t->bf = LH;taller = TRUE;break;case RH:t->bf = EH;taller = FALSE;break;}}}else{if (!insertAVL(t->rchild, e, taller))return 0;if (taller){switch (t->bf){case RH:RightBalance(t);taller = FALSE;break;case EH:t->bf = RH;taller = TRUE;break;case LH:t->bf = EH;taller = FALSE;break;}}}}return 1;}BSTNode *search(BSTNode *t, int key){BSTNode *p = t;while (p){if (p->key == key)return p;else if (p->key < key)p = p->rchild;elsep = p->lchild;}return p;}int main(){BSTNode *root = NULL;BSTNode *r;bool taller = FALSE;int array[] = { 13, 24, 37, 90, 53 };for (int i = 0; i < 5; i++)insertAVL(root, array[i], taller);cout << "inorder traverse..." << endl;inordertree(root);cout << endl;cout << "preorder traverse..." << endl;preordertree(root);cout << endl;cout << "search key..." << endl;r = search(root, 37);if (r){cout << r->key << endl;}else{cout << "not find" << endl;}system("pause");return 0;}

資料結構與演算法問題 AVL二叉平衡樹