Binary Search Tree

Introduction:

The nature of the binary tree to become a binary search tree is: For each node X in the tree, all the key values in its left subtree are less than the key value of X, all the keyword values in its right subtree are greater than those of X.

Binary Search Tree statement

struct TreeNode;typedef struct TreeNode *Position;typedef struct TreeNode *SearchTree;struct TreeNode{ElementType Element;SearchTree  Left;SearchTree  Right;};

Create an empty tree routine

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

Find operation of Binary Search Tree

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;}

Recursive and non-Recursive Implementation of the findmin of the Binary Search Tree

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;}

Recursive and non-Recursive Implementation of the findmax of the Binary Search Tree

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;}

Routine for inserting elements into a binary search tree

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;}

Binary Search tree deletion routine

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;}