1. The document introduces binary trees, including common tree terminology like nodes, edges, root, parent, child, leaf, and subtree. 2. It explains different ways to traverse a binary tree, including in-order, pre-order, and post-order traversal. 3. It also covers level order traversal using a queue, where nodes are added level by level from left to right.

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Introduction to
Tree/Binary Tree

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차수: 3
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15. typedef struct TreeNode {
int data;
struct TreeNode *left, *right;
} TreeNode;
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16. 이진 트리 순회

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+ 3
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20. W RS ObS O
6
6

21. W RS ObS O
d
inOrder (x) {
if (x != NULL) {
inOrder (x->left);
print x;
inOrder (x->right);
}
}

22. W RS ObS O
d
inOrder (x) {
if (x != NULL) {
inOrder (x->left);
print x;
inOrder (x->right);
}
}
@ A : B = C 9 D > ; ?

23. S RS ObS O
* 3
+ LD 3 D
, LJ 3 J
2.
1.
3.

24. S RS ObS O
d
preOrder (x) {
if (x != NULL) {
print x;
preOrder (x->left);
preOrder (x->right);
}
}

25. S RS ObS O
d
preOrder (x) {
if (x != NULL) {
print x;
preOrder (x->left);
preOrder (x->right);
}
}
9 : @ A = B C ; > D ?

26. RS ObS O
* LD 3 D
+ LJ 3 J
, 3
2.1.
3.

27. RS ObS O
d
postOrder (x) {
if (x != NULL) {
postOrder (x->left);
postOrder (x->right);
print x;
}
}

28. RS ObS O
d
postOrder (x) {
if (x != NULL) {
postOrder (x->left);
postOrder (x->right);
print x;
}
}
@ A B C = : D > ? ; 9

29. SbS RS ObS O
…

30. SbS RS ObS O
…
9 : ; = > ? @ A B C D

31. level_order(x) {
if (x == NULL) return;
}
NULL NULL NULL NULL NULL NULL NULL NULL
SbS RS ObS O

32. level_order(x) {
if (x == NULL) return;
}
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

33. level_order(x) {
if (x == NULL) return;
}
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

34. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

35. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

36. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

37. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

38. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

39. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

40. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

41. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

42. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

43. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
x = A;
SbS RS ObS O

44. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
x = A;
SbS RS ObS O

45. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
D
x = A;
SbS RS ObS O

46. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DE
x = A;
SbS RS ObS O

47. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DE
x = A;
SbS RS ObS O

48. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DE
x = A;
SbS RS ObS O

49. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DE
C
x = A;
SbS RS ObS O

50. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEF
C
x = A;
SbS RS ObS O

51. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C
x = A;
SbS RS ObS O

52. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C
x = A;
SbS RS ObS O

53. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C
x = A;
SbS RS ObS O

54. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D
x = A;
SbS RS ObS O

55. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D
x = A;
SbS RS ObS O

56. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D
x = A;
SbS RS ObS O

57. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E
x = A;
SbS RS ObS O

58. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E
x = A;
SbS RS ObS O

59. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E
x = A;
SbS RS ObS O

60. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E F
x = A;
SbS RS ObS O

61. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E F
x = A;
SbS RS ObS O

62. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E F G
x = A;
SbS RS ObS O

63. level_order(x) {
if (x == NULL) return;
}
enQueue(queue, x);
A
while (!isEmpty(queue)) {
}
x = deQueue(queue);
print x->data;
if (x->left != NULL)
enQueue(queue, x->left);
B
if (x->right != NULL)
enQueue(queue, x->right);
C
A
NULL NULL NULL NULL NULL NULL NULL NULL
B
DEFG
C D E F G
x = A;
SbS RS ObS O

64. Binary Search Tree

65. N O W O SO Q 7
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l
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v
L S SQ R T SdO S O O S ORR S aRS WRS WTWQO W
a PS O R QWO SQa W e a PS S Q 3
L S Se W O TWS R a SR T RW Q W W O W U SQ R 9 O SdO S
QWO SQa W e a PS aRS WRS WTWQO W a PS QO PS
a SR O Se 3 v
KSO Q 3 k
KSO Q

66. y v
Se
Se Se
Se Se
s
:KL 3 k
:W O e KSO Q L SS
ST
aP SS aP SS
WU

67. KSO Q 3
A S 3
S S S3
KSO Q A S S S S h
SWU
h 3 h
:KL3
:W O e KSO Q L SS

68. y
Se is Se is u
Se is Se i
Se i Se i
Se i Se i
:KL 3 k
:KL KSO Q G S O W
*1
0
, *+
+/
,*
+0

69. y
Se is Se is u
Se is Se i
Se i Se i
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:KL 3 k
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, *+
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+0
I* *+

70. y
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Se is Se i
Se i Se i
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71. y
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72. y
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Se i Se i
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73. y
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74. y
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75. y
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76. y
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77. y
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78. y
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79. y
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80. y
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81. y
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82. y
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83. y
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84. :KL 3
i a a S a
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85. :KL 3
i a a S a
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86. :KL 3
i a a S a
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87. :KL 3
i a a S a
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88. :KL 3
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89. :KL 3
:KL KSO Q G S O W
3 L SSF RS
3 SO Q F RS L SSF RS W Se 4
+ 3 RS Se i
TreeNode* searchNode(TreeNode *root, int key) {
if (root == NULL) return NULL;
if (root->data == key) return root;
else if (root->data > key)
return searchNode(root->left, key);
else
return searchNode(root->right, key);
}
typedef struct TreeNode {
int data;
struct TreeNode *left, *right;
}TreeNode;

90. :KL 3
:KL KSO Q G S O W
3 L SSF RS
3 SO Q F RS L SSF RS W Se 4
+ 3 RS Se i
TreeNode* searchNode(TreeNode *root, int key) {
while (root != NULL) {
if (root->data == key) return root;
else if (root->data > key)
root = root->left;
else
root = root->right;
}
return NULL;
}

91. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0

92. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2

93. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
2

94. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
2

95. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
2

96. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
2

97. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
2

98. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2

99. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2
,,

100. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2
,,

101. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2
,,

102. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2 ,,

103. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
2 ,,

104. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
2 ,,

105. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
2 ,,
*2

106. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
2 ,,
*2

107. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
2 ,,
*2

108. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
2 ,,
*2

109. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2

110. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)

111. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)

112. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2 ,)

113. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)

114. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)

115. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)

116. :KL 3 k
:KL A S G S O W
y
g Se i
*1
0
, *+
+/
,*
+0
I* 2
I+ ,,
I, *2
Q4) 30 을 삽입
2 ,,
*2
,)
Q5) 29 를 삽입

117. :KL 3
:KL A S G S O W
Se i y
g g
[ RS Se L
FMDD l
L SSF RS
L SSF RS RO O o N Se L SSF RS 6 ST L SSF RS 6 WU
,,
L L SSF RS n

118. :KL 3
:KL A S G S O W
3 b WR
3 W S F RS L SSF RS W Se 4
+ 3 RS Se i
void insertNode(TreeNode **root, int key){
TreeNode *parentNode = NULL, *currentNode, *newNode;
currentNode = *root;
while (currentNode != NULL) {
if (currentNode->data == key) return;
parentNode = currentNode;
if (currentNode->data > key)
currentNode = currentNode->left;
else currentNode = currentNode->right;
}

119. :KL 3
:KL A S G S O W
3 b WR
3 W S F RS L SSF RS W Se 4
+ 3 RS Se i
void insertNode(TreeNode **root, int key){
TreeNode *parentNode = NULL, *currentNode, *newNode;
currentNode = *root;
while (currentNode != NULL) {
if (currentNode->data == key) return;
parentNode = currentNode;
if (currentNode->data > key)
currentNode = currentNode->left;
else currentNode = currentNode->right;
}
(( g
(( o
(( Seg s

120. :KL 3
newNode = (TreeNode *)malloc(sizeof(TreeNode));
if (newNode == NULL) return;
newNode->data = key;
newNode->left = newNode->right = NULL;
if (parentNode != NULL)
if (parentNode->data > key) parentNode->left = newNode;
else parentNode->right = newNode;
else
*root = newNode;
}
:KL A S G S O W
(( Se i o
(( o
L SSF RS rh s
n
n

121. :KL 3
:KL A S G S O W
,) -) +) *) +. ,.

122. :KL 3
:KL A S G S O W
,)
-)+)
*) +. ,.

123. y
,g o
] N L f ] N L U L 5314 6723 0
] N L f
] N L f
:KL 3 k
:KL S S S G S O W
*1
0
, *+
+/
,*
+0

124. y
,g o
] N L f ] N L U L 5314 6723 0
] N L f
] N L f
:KL 3 k
:KL S S S G S O W
*1
0
, *+
+/
,*
+0
I* +0
I+ +/
I, 0
Q4) 18 을 삽입

125. :KL 3
g ) * +
g * o
:KL S S S G S O W
g ) * + 7

126. :KL 3
g ) o
g * o
L ] L L ,, l n
] L a
:KL S S S G S O W
g + o
L ] ] L e [ L n
] L a
L ] L [ L ]
L
L ] L [ d L ]
L
] L a

127. :KL 3
:KL S S S G S O W
3 b WR
3 RS S SF RS L SSF RS W Se 4
+ 3 RS Se i
void deleteNode(TreeNode **root, int key){
TreeNode *pNode = NULL, *curNode, *newNode;
TreeNode *child, *succ; *succParent;
curNode = *root;
while (curNode != NULL && curNode->data != key) {
pNode = curNode;
if (curNode->data > key)
curNode = curNode->left;
else curNode = curNode->right;
}
if (curNode == NULL) {
printf(“key is not int the treen”);
return;
}

128. :KL 3
if (curNode->left == NULL && curNode->left == NULL){
if (pNode != NULL)
if (pNode->left == curNode)
pNode->left = NULL;
else
pNode->right = NULL;
else
*root = NULL;
}
else if (curNode->left == NULL || curNode->left == NULL){
child = (curNode->left != NULL) ? curNode->left : curNode->right;
if (pNode != NULL) {
if (pNode->left == curNode)
pNode->left = NULL;
else
pNode->right = NULL;
}
else
*root = NULL;
}
:KL S S S G S O W

129. :KL 3
else {
succParent = curNode;
succ = curNode->left;
while (succ->right != NULL) {
succParent = succ;
succ = succ->right;
}
if (succParent->right == succ)
succParent->right = succ->left;
else
succParent->left = succ->left;
curNode->data = succ->data;
curNode = succ;
}
free(curNode);
}
:KL S S S G S O W
(( g + o
(( aQQHO S
(( y
(( h
*1
0
, *+
+/
,*
*/*)
*,
*1
*0
2
+/
,*
1
aQQ
aQQ

130. :KL o
((
)(
(
6 82 35 01 4 9
)
((
)(
(
)

131. :KL g k o

132. :KL g +k o
((
)(
(
(
6 941 0 8
)
((
)(
(
(
5 32
)

133. :KL g +k o
((
)(
(
(
3 68 012
)
((
)(
(
(
5 64 9 2
)