1. Tree 기�� 개��
2. Binary Tree
3. Binray Tree ��
4. Binary Tree Traversal
5. Binary Search Trees (�� )
6. Insert x
7. Delete x(�� 금 ��)
8. Tree�� (Cross Reference �� 거 ��간 ��. C++�� -.-)

1. Tree 기�� 개�� ¶

Node : ��
Root : �� 꼭��기 ��
Edge : ��
Degree : �� Edge��
Parent : ��
Child : ��
Level : ��?
Sibling : ��(�� ) ��
Height : Maximum Level

2. Binary Tree ¶

�� 0 - 2개
�� , �� 구��
깊�� k�� = 2^k - 1
�� i�� = 2^(i-1)
n0�� 갯��, n2�� Degree�� 2�� 갯��고 �� n0 = n2 + 1 �� 공�� .

3. Binray Tree �� ¶

��
- 그�� . ��, �� , �� .. �� 깐��.
- �� 근��
  - Left Child : �� * 2
  - Right Child : �� * 2 + 1
  - Parent : ��/2 -> ��
Linked List
- �� , �� 구��.

4. Binary Tree Traversal ¶

PreOrder : Root -> Left Child -> Right Child : ��

~cpp 
PreOrder(a) 
{
    if(a)
    {
        visit a
        Preorder(a->left)
        Preorder(a->right)
    }
}

InOrder : Left Child -> Root -> Right Child : ��게 ��

~cpp 
InOrder(a) 
{
    if(a)
    {
        InOrder(a->left)
        visit a
        InOrder(a->right)
    }
}

PostOrder : Left Child -> Right Child -> Root

~cpp 
PostOrder(a) 
{
    if(a)
    {
        PostOrder(a->left)
        PostOrder(a->right)
        visit a
    }
}

LevelOrder : ��

~cpp 
AddQ(Root)
while(1)
{
    a = DeleteQ();
    Visit a;
    if(!a) break;
    if(a->left) AddQ(a->left)
    if(a->right) AddQ(a->right)
}

5. Binary Search Trees (�� ) ¶

�� 고�� .(��?--;)
- �� : θ(n)
- �� : θ(log2 n) - 2�� . �� ?--;
- n�� 2048�� 고 �� 2048�� 걸�� 11�� 걸��
- but, �� . �� . ��간�� 꼬�� ..--;
��
- Binray Search Tree ��까 �� Binary Tree �� .
- Keys in Left Subtree < Keys of Node
- Keys in Right Subtree > Keys of Node(고�� .)
��고��
- Search x => Compare with Root
  - if x = Root's Key then ��까 ��고��
  - else if x > Root's Key Root�� Right Subtree�� Root�� . 거기��
  - else if x < Root's Key Root를 Left Subtree의 Root로 셋팅. 거기서부터 검색 다시 시작

6. Insert x ¶

�� 기�� 기�� .

7. Delete x(�� 금 ��) ¶

Search x
- �� x�� leaf(�� ) - 그�� ..--;
- x�� Child�� 1개 �� 경�� - 그 �� 고 그 �� . 고�� .(�� ?--;)
- x�� Child�� 2개 �� 경�� - 그 �� Left Subtree�� 값�� . ��값�� y��고 �� y�� Child�� . y�� x�� 갖�� 고 ��기��
  - y�� Child �� - 그�� .
  - y�� Child �� - 그 �� 계 ��.. 고��

8. Tree�� (Cross Reference �� 거 ��간 ��. C++�� -.-) ¶

~cpp 
// ��������� ������ ���������

void init(Node** node,char* ch)			// ���기���
{
	(*node)->pLeft = (*node)->pRight = NULL;	// ������ ��������� ������ NULL���
	(*node)->Data = new char[strlen(ch) + 1];	// ��������� 길��������� ������
	strcpy((*node)->Data,ch);			// ��������� ��������� ������
}

void PrintandDelete(Node* root)			// ��� ������������ ������(Preorder�����?)
{
    if( root->pLeft )		
        Print( root->pLeft );

    cout << root->Data << endl;

    if( root->pRight )
        Print( root->pRight );

    delete root;					// ��������� ������ ���거
}

int Add(Node** root,char* ch)
{
    if(!(*root))					// ����������� ���������
    {
        *root = new Node;				// ������
        init(root,ch);		   	         // ���기���
        return 1;
    }
	
    else if(strcmp((*root)->Data,ch)>0)		// �������� ������������ ������ ��������� �����
	return add(&((*root)->pLeft),ch);
    else if(strcmp((*root)->Data,ch)<0)		// �������� ������������ ��������� ������������ �����
	return add(&((*root)->pRight),ch);
    else if(strcmp((*root)->Data,ch)==0)		// �������� ��������� �����
	return 1;
}

DataStructure

Data Structure/Tree

Contents

1. Tree 기�� 개�� ¶

2. Binary Tree ¶

3. Binray Tree �� ¶

4. Binary Tree Traversal ¶

5. Binary Search Trees (�� ) ¶

6. Insert x ¶

7. Delete x(�� 금 ��) ¶

8. Tree�� (Cross Reference �� 거 ��간 ��. C++�� -.-) ¶

Data Structure/Tree

Contents

1. Tree 기��� 개������ ¶

2. Binary Tree ¶

3. Binray Tree ��� ������ ¶

4. Binary Tree Traversal ¶

5. Binary Search Trees (������������ ������ ������ ������) ¶

6. Insert x ¶

7. Delete x(����� ���금 ���������) ¶

8. Tree��� ��������� ������ ��������(Cross Reference ������ ������거 ���간 ���������������. C++������������ ���������-.-) ¶

1. Tree 기�� 개�� ¶

3. Binray Tree �� ¶

5. Binary Search Trees (�� ) ¶

7. Delete x(�� 금 ��) ¶

8. Tree�� (Cross Reference �� 거 ��간 ��. C++�� -.-) ¶