[标程]: 二叉搜索树和平衡二叉搜索树

贴一个二叉搜索树(BST)和平衡二叉搜索树的标程(BBST).

 

#include <iostream> #include <algorithm> using namespace std; /************************************************************************/ /*二叉搜索树标程 */ /************************************************************************/ struct BSTNode{ int data; BSTNode* left; BSTNode* right; }; typedef BSTNode* BSTree; //p返回访问的最后一个节点 //father为传入的当前树的父节点 bool SearchBST(BSTree tree, int t, BSTree father, BSTree& p) { if(!tree) { p = father; return false; } else if(t == tree->data) { p = tree; return true; } else if(t < tree->data) return SearchBST(tree->left, t, tree, p); else return SearchBST(tree->right, t, tree, p); } bool InsertBST(BSTree& tree, int t) { BSTree p, new_node; if(!SearchBST(tree, t, NULL, p)) //当树中没有此节点时,插入 { new_node = new BSTNode; new_node->data = t; new_node->left = new_node->right = NULL; if(!p) //空树 tree = new_node; else if(t < p->data) p->left = new_node; else p->right = new_node; return true; } return false; } bool Delete(BSTree& p) { BSTree tmp; if(!p->right) { tmp = p; p = p->left; delete tmp; } else if(!p->left) { tmp = p; p = p->right; delete tmp; } else { tmp = p->left; BSTree father = p; while (tmp->right) { father = tmp; tmp = tmp->right; } p->data = tmp->data; if(p != father) father->right = tmp->left; else p->left = tmp->left; delete tmp; } return true; } bool DeleteBST(BSTree& tree, int t, BSTree father) { if(!tree) return false; else if(t < tree->data) return DeleteBST(tree->left, t, tree); else if(t > tree->data) return DeleteBST(tree->right, t, tree); else return Delete(tree); } void Travel(BSTree tree) { if(tree) { Travel(tree->left); cout << tree->data << ' '; Travel(tree->right); } } /************************************************************************/ /*二叉平衡搜索树标程 */ /************************************************************************/ typedef struct BBSTNode{ int data; int bf; BBSTNode* lchild, *rchild; }*BBSTree; void RightRotate(BBSTree& p) //右旋 { BBSTree tmp = p->lchild; p->lchild = tmp->rchild; tmp->rchild = p; p = tmp; } void LeftRotate(BBSTree& p) //左旋 { BBSTree tmp = p->rchild; p->rchild = tmp->lchild; tmp->lchild = p; p = tmp; } #define LH 1 #define EH 0 #define RH -1 void LeftBalance(BBSTree& p) //平衡左树 { BBSTree tmp = p->lchild; switch(tmp->bf) { case LH: p->bf = tmp->bf = EH; RightRotate(p); break; case RH: BBSTree tmp2 = tmp->rchild; switch(tmp2->bf) { case LH: tmp->bf = EH; p->bf = RH; break; case EH: p->bf = tmp->bf = EH; break; case RH: tmp->bf = LH; p->bf = EH; break; } tmp2->bf = EH; LeftRotate(tmp); RightRotate(p); break; } } void RightBalance(BBSTree& p) //平衡右树 { BBSTree tmp = p->rchild; switch(tmp->bf) { case RH: p->bf = tmp->bf = EH; LeftRotate(p); break; case LH: BBSTree tmp2 = tmp->lchild; switch(tmp2->bf) { case LH: p->bf = EH; tmp->bf = RH; break; case EH: p->bf = tmp->bf = EH; break; case RH: p->bf = LH; tmp->bf = EH; break; } tmp2->bf = EH; RightRotate(tmp); LeftRotate(p); break; } } bool InsertAVL(BBSTree& p, int t, bool &taller) //将值插入AVL树 { if(!p) { p = new BBSTNode; p->data = t; p->lchild = p->rchild = NULL; p->bf = EH; taller = true; } else { if(t == p->data) { taller = false; return false; } else if(t < p->data) { if(!InsertAVL(p->lchild, t, taller)) return false; if(taller) { switch(p->bf) { case LH: LeftBalance(p); taller = false; break; case EH: p->bf = LH; taller = true; break; case RH: p->bf = EH; taller = false; break; } } } else { if(!InsertAVL(p->rchild, t, taller)) return false; if(taller) { switch(p->bf) { case LH: p->bf = EH; taller = false; break; case EH: p->bf = RH; taller = true; break; case RH: RightBalance(p); taller = false; break; } } } } return true; } int main() { //BSTree test { BSTree tree = NULL; int arr[] = {0,1,2,3,4,5,6,7,8,9}; random_shuffle(arr, arr+10); for(int i = 0; i < 10; ++i) InsertBST(tree, arr[i]); Travel(tree);cout << endl; for (int i = 2; i < 7; ++i) DeleteBST(tree, arr[i], NULL); Travel(tree);cout << endl; } { BSTree tree = NULL; int arr[] = {45,12,53,3,37,100,24,61,90,78}; for(int i = 0; i < 10; ++i) InsertBST(tree, arr[i]); Travel(tree);cout << endl; DeleteBST(tree, arr[2], NULL); Travel(tree);cout << endl; } //AVL tree test //... return 0; }