Definition

• 각 노드는 하나의 유니크한 키를 가짐
• 왼쪽 서브트리의 키는 루트 키보다 작음
• 오른쪽 서브트리 키는 루트 키보다 큼
• 왼쪽 오른쪽 서브트리도 binary search tree

Search

Code (recursive version)

element* search(treePointer root, int k) {
	/* return a pointer to the element whose key is k, if there is no such
	element, return NULL */
	if(!root) return NULL;
	if(k == root->data.key) return &(root->data);
	if(k < root->data.key) return search(root->leftChild, k);
	return search(root->rightChild, k);
}

Code (Iterative version)

element* iterSearch(treePointer tree, int k) {
/* return a pointer to the element whose key is k, if there is no such
element, return NULL */
while(tree) {
	if(k == tree->data.key) return &(tree->data);
	if(k < tree->data.key)
		tree = tree->leftChild;
	else
		tree = tree->rightChild;
	}
	return NULL;
}

Time complexity

O(h) = O(log n)

Insert

키가 이미 존재하면 삽입X

존재하지 않으면 search가 끝난 지점에 삽입

Code

void insertNode(treePointer *node, int k) {
	/* if the key k is already in the tree, do nothing; otherwise add a new
	node with key k */
	treePointer ptr, temp = modifiedSearch(*node, k); /* temp : 넣어야 할 위치의 부모 */
	if(temp) {
		/* k is not in the tree */
		ptr = (treePointer)malloc(sizeof(*ptr));
		ptr->data.key = k;
		ptr->leftChild = ptr->rightChild = NULL;
		if(*node) { /* not empty */
			if(k < temp->data.key) temp->leftChild = ptr;
			else temp->rightChild = ptr;
		}
		else *node = ptr; /* empty */
	}
}

modifiedSearch()

treePointer modifiedSearch(treePointer node, int k) {
    treePointer parent = NULL;
    while(node) {
        // if we found a node with key k, we return NULL
        if(k == node->data.key) return NULL;
        parent = node;
        if(k < node->data.key) node = node->leftChild;
        else node = node->rightChild;
    }
    return parent;
}

빈 트리거나 키가 존재하면 널 반환