程序是建立一颗二叉排序树,查找节点找到了返回其父节点,失败的时候返回NULL,删除节点分为四种情况:1、左子树和右子树都为空;2、左子树为空,右子树不为空;3、左子树不为空,右子树为空;4、左子树和右子树都不为空。
C语言版本(利用结构体实现):
#include <stdio.h> #include <stdlib.h> typedef int DataType; typedef struct BTree{ DataType data; struct BTree *Tleft; struct BTree *Tright; }*BTree; BTree CreateTree(); //建树 BTree insert(BTree root, DataType data);//插入节点 void InBTree(BTree root); //中序遍历 void PreBTree(BTree root); //先序遍历 void PostBTree(BTree root);//后序遍历 BTree findPostion(BTree root, int deleteNode, int *flags);//寻找合适的插入点 BTree delNode(BTree root, BTree parent, int flags); //删除树节点 int main(){ BTree root = NULL; int flags = 0; int deleteNode = 0; BTree parent = NULL;//所删除节点的父节点 char choiceAgain = 'Y'; root = CreateTree(); printf("\n中序遍历: "); InBTree(root); printf("\n前序遍历: "); PreBTree(root); printf("\n后序遍历: "); PostBTree(root); printf("\n"); do{ printf("需要删掉的节点: "); scanf("%d", &deleteNode); parent = findPostion(root, deleteNode, &flags); root = delNode(root, parent, flags); printf("删除后的结果: "); printf("\n中序遍历: "); InBTree(root); printf("\n前序遍历: "); PreBTree(root); printf("\n后序遍历: "); PostBTree(root); choiceAgain = 'N'; printf("\nDelete Again(Y) or N?: "); getchar(); scanf("%c", &choiceAgain); }while(choiceAgain == 'Y' || choiceAgain == 'y'); printf("\nDone!\n"); return 0; } BTree CreateTree(){ BTree root = NULL; DataType temp = 0; printf("请输入节点,以0结尾:\n"); scanf("%d", &temp); while(temp != 0){ root = insert(root, temp); scanf("%d", &temp); } return root; } BTree insert(BTree root, DataType data){ BTree ptr = root; BTree tempNode; BTree newNode = (BTree)malloc(sizeof(struct BTree)); newNode->data = data ; newNode->Tleft = NULL; newNode->Tright = NULL; if(ptr == NULL){ return newNode; }else{ while(ptr != NULL){ tempNode = ptr; if(ptr->data >= data){ ptr = ptr->Tleft; }else{ ptr = ptr->Tright; } } if(tempNode->data >= data){ tempNode->Tleft = newNode; }else{ tempNode->Tright = newNode; } } return root; } BTree findPostion(BTree root, int deleteNode, int *flags){ BTree parentNode = root; BTree temp = root; *flags = 0; while(temp != NULL){ if(temp->data == deleteNode){ return parentNode; }else{ parentNode = temp; if(temp->data > deleteNode){ temp = temp->Tleft; *flags = -1; }else{ temp = temp->Tright; *flags = 1; } } } return NULL; } BTree delNode(BTree root, BTree parent, int flags){ BTree deleteNode = NULL; if(parent == NULL){ printf("未找到删除的节点!\n"); return root; } switch(flags){ case -1: deleteNode = parent->Tleft; break; case 0: deleteNode = parent; break; case 1: deleteNode = parent->Tright; break; default: printf("ERROR!\n"); exit(1); } if(deleteNode->Tleft == NULL && deleteNode->Tright == NULL){ if(parent->Tleft == deleteNode){ parent->Tleft = NULL; }else if(parent->Tright == deleteNode){ parent->Tright = NULL; }else{ parent = NULL; } free(deleteNode); }else if(deleteNode->Tleft == NULL && deleteNode->Tright != NULL){ if(deleteNode->data == root->data){ root = deleteNode->Tright; }else{ if(parent->Tleft->data == deleteNode->data){ parent->Tleft = deleteNode->Tright; }else{ parent->Tright = deleteNode->Tright; } } free(deleteNode); }else if(deleteNode->Tleft != NULL && deleteNode->Tright == NULL){ if(deleteNode->data == root->data){ root = deleteNode->Tleft; }else{ if(parent->Tleft->data == deleteNode->data){ parent->Tleft = deleteNode->Tleft; }else{ parent->Tright = deleteNode->Tleft; } } free(deleteNode); }else{ BTree temp = deleteNode->Tleft; BTree tempParent = deleteNode; while(temp->Tright != NULL){ tempParent = temp; temp = temp->Tright; } deleteNode->data = temp->data; if(tempParent->Tleft == temp){ tempParent->Tleft = temp->Tleft; }else{ tempParent->Tright = temp->Tleft; } printf("temp = %d\n", temp->data); free(temp); } return root; } void InBTree(BTree root){ if(root != NULL){ InBTree(root->Tleft); printf("%d ", root->data); InBTree(root->Tright); } } void PreBTree(BTree root){ if(root != NULL){ printf("%d ", root->data); PreBTree(root->Tleft); PreBTree(root->Tright); } } void PostBTree(BTree root){ if(root != NULL){ PostBTree(root->Tleft); PostBTree(root->Tright); printf("%d ", root->data); } }
C++版本(利用类实现)
#include <iostream.h>
#include <cstring>
typedef int KeyType;
#define NUM 11
class BinStree;
class BinSTreeNode
{
public:
KeyType key;
BinSTreeNode *lchild;
BinSTreeNode *rchild;
BinSTreeNode()
{
lchild = NULL;
rchild = NULL;
}
};
class BinSTree
{
public:
BinSTreeNode *root;
BinSTree()
{
root = NULL;
}
~BinSTree()
{
//delete root;
}
BinSTreeNode *BSTreeSearch( BinSTreeNode *bt, KeyType k, BinSTreeNode *&p );
void BSTreeInsert( BinSTreeNode *&bt, KeyType k );
int BSTreeDelete( BinSTreeNode *&bt, KeyType k );
void BSTreePreOrder(BinSTreeNode *bt);
bool IsEmpty()
{
return root == NULL;
}
};
/**
* 二叉树排序查找算法
* 在根指针为bt的二叉排序树中查找元素k的节点,若查找成功,则返回指向该节点的指针
* 参数p指向查找到的结点,否则返回空指针,参数p指向k应插入的父结点
*/
BinSTreeNode* BinSTree::BSTreeSearch( BinSTreeNode *bt, KeyType k, BinSTreeNode *&p )
{
BinSTreeNode *q = NULL;
q = bt;
while(q)
{
p = q;
if( q->key == k )
{
return(p);
}
if( q->key > k )
q = q->lchild;
else
q = q->rchild;
}
return NULL;
}
/**
* 二叉排序树的插入节点算法
* bt指向二叉排序树的根结点,插入元素k的结点
*/
void BinSTree::BSTreeInsert( BinSTreeNode *&bt, KeyType k )
{
BinSTreeNode *p = NULL, *q;
q = bt;
if( BSTreeSearch( q, k, p ) == NULL )
{
BinSTreeNode *r = new BinSTreeNode;
r->key = k;
r->lchild = r->rchild = NULL;
if( q == NULL )
{
bt = r; //被插入节点做为树的根节点
}
if( p && k < p->key )
p->lchild = r;
else if( p )
p->rchild = r;
}
}
/**
* 中序遍历
*/
void BinSTree::BSTreePreOrder(BinSTreeNode *bt)
{
if(bt != NULL)
{
cout << bt->key << " ";
BSTreePreOrder(bt->lchild);
BSTreePreOrder(bt->rchild);
}
}
/**
* 二叉排序树的删除结点算法
* 在二叉排序树中删除元素为k的结点,*bt指向二叉排序树的根节点
* 删除成功返回1,不成功返回0.
*/
int BinSTree::BSTreeDelete( BinSTreeNode *&bt, KeyType k )
{
BinSTreeNode *f, *p, *q, *s;
p = bt;
f = NULL;
//查找关键字为k的结点,同时将此结点的双亲找出来
while( p && p->key != k )
{
f = p;
if( p->key > k )
p = p->lchild;
else
p = p->rchild;
}
if( p == NULL ) //找不到待删除的结点时返回
return 0;
if( p->lchild == NULL ) //待删除结点的左子树为空
{
if( f == NULL ) //待删除结点为根节点
bt = p->rchild;
else if( f->lchild == p ) //待删结点是其双亲结点的左节点
f->lchild = p->rchild;
else
f->rchild = p->rchild; //待删结点是其双亲结点的右节点
delete p;
}
else //待删除结点有左子树
{
q = p;
s = p->lchild;
while( s->rchild ) //在待删除结点的左子树中查找最右下结点
{
q = s;
s = s->rchild;
}
if( q == p )
q->lchild = s->lchild;
else
q->rchild = s->lchild;
p->key = s->key;
delete s;
}
return 1;
}
int main( void )
{
int a[NUM] = { 34, 18, 76, 13, 52, 82, 16, 67, 58, 73, 72 };
int i;
BinSTree bst;
BinSTreeNode *pBt = NULL, *p = NULL, *pT = NULL;
for( i = 0; i < NUM; i++ )
{
bst.BSTreeInsert( pBt, a[i] ); //创建二叉排序树
}
pT = bst.BSTreeSearch( pBt, 52, p ); //搜索排序二叉树
bst.BSTreePreOrder(pBt);
cout << endl;
bst.BSTreeDelete( pBt, 13 ); //删除无左孩子的情况
bst.BSTreePreOrder(pBt);
cout << endl;
bst.BSTreeDelete( pBt, 76 ); //删除有左孩子的情况
bst.BSTreePreOrder(pBt);
cout << endl;
return 0;
}