二叉查找树

引言：

使二叉树成为二叉查找树的性质是：对于树中的每个节点X，它的左子树中所有关键字值小于X的关键字值，而它的右子树中所有关键字值大于X的关键字值。

二叉查找树声明

struct TreeNode;
typedef struct TreeNode *Position;
typedef struct TreeNode *SearchTree;

struct TreeNode{
ElementType Element;
SearchTree Left;
SearchTree Right;
};

建立一棵空树的例程

SearchTree MakeEmpty(SearchTree T)
{
if(T != NULL){
MakeEmpty(T->Left);
MakeEmpty(T->Right);
free(T);
}

return NULL;
}

二叉查找树的Find操作

Position Find(ElementType X, SearchTree T)
{
if(T == NULL)
return NULL;
if(X < T->Element)
return Find(X, T->Left);
else if(X > T->Element)
return Find(X, T->Right);
return T;
}

二叉查找树的FindMin递归与非递归实现

Position FindMin(SearchTree T)
{
if(T == NULL)
return NULL;
else if(T->Left == NULL)
return T;
else
return FindMin(T->Left);
}

Position FindMin(SearchTree T)
{
if(T != NULL)
while(T->Left != NULL)
T = T->Left;
return T;
}

二叉查找树的FindMax递归与非递归实现

Position FindMax(SearchTree T)
{
if(T == NULL)
return NULL;
else if(T->Right == NULL)
return T;
else
return FindMax(T->Right);
}

Position FindMax(SearchTree T)
{
if(T != NULL)
while(T->Right != NULL)
T = T->Right;
return T;
}

插入元素到二叉查找树的例程

SearchTree Insert(ElementType X, SearchTree T)
{
if(T == NULL){
T = (SearchTree)malloc(sizeof(struct TreeNode));
if(T == NULL){
printf("Out of space.\n");
return NULL;
}
}else if(X < T->Element){
T->Left = Insert(X, T->Left);
}else (X > T->Element){
T->Right = Insert(X, T->Right);
}

return T;
}

二叉查找树的删除例程

SearchTree Delete(ElementType X, SearchTree T)
{
Position TmpCell;

if(T == NULL){
fprintf(stderr,"Element not found.\n");
return NULL;
}else if(X < T->Element)
T->Left = Delete(X, T->Left);
else if(X > T->Element)
T->Right = Dlelte(X, T->Right);
else if(T->Left && T->Right){
TmpCell = FindMin(T->Right);
T->Element = TmpCell->Element;
T->Right = Delete(T->Element, T->Right);
}else{
TmpCell = T;
if(T->Left == NULL)
T = T->Right;
else if(T->Right == NULL)
T = T->Left;
free(TmpCell);
}

return T;
}