Building Java Programs, Study notes of Java Programming

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Building Java Programs

Binary Search Trees

reading: 17.3 – 17.

contains

91 60

87 29

55

42

overallRoot

private boolean contains(IntTreeNode root,

int value) {

if (root == null) {

return false;

} else if (root.data == value) {

return true;

} else {

return contains(root.left, value)

|| contains(root.right, value);

}

}

root

1

root

2

root

3

root

5

root

4

root

6

F F

F T

T

Case study: contains w/ arrays

 What is the Big-O efficiency to see if a value is contained in

an unsorted array?

 What about if the array is sorted?

-3 87 42 55 91 29 60

-3 29 42 55 60 87 91

BST examples

 Which of the trees shown are legal binary search trees?

k x

g q

m

e

b

10 18

5 11

8

4

2 7

20

18

42

-1 -

8.1 21.

1.9 9.

Searching a BST

 Describe an algorithm for searching a binary search tree.

 Try searching for the value 31, then 6.

 What is the maximum

number of nodes you

would need to examine

to perform any search?

12

18

7

4 15

overall root

-2 16 13

35

31

22 58

19 87 40

Exercise solution

// Returns whether this BST contains the given integer.

public boolean contains(int value) {

return contains(overallRoot, value);

private boolean contains(IntTreeNode node, int value) {

if (node == null) {

return false; // base case: not found here

} else if (node.data == value) {

return true; // base case: found here

} else if (node.data > value) {

return contains(node.left, value);

} else { // root.data < value

return contains(node.right, value);

Adding to a BST

 Suppose we want to add new values to the BST below.

 Where should the value 14 be added?

 Where should 3 be added? 7?

 If the tree is empty, where

should a new value be added?

 What is the general algorithm?

10 19

5 11

8

4

2 7

25

22

overall root

Exercise

 Add a method add to the SearchTree class that adds a

given integer value to the BST.

 Add the new value in the proper place to maintain BST

ordering.

 tree.add(49);

60 91

29 87

55

-3 42

overall root

49

An incorrect solution

// Adds the given value to this BST in sorted order.

public void add(int value) {

add(overallRoot, value);

private void add(IntTreeNode node, int value) {

if (node == null) {

node = new IntTreeNode(value);

} else if (node.data > value) {

add(node.left, value);

} else if (node.data < value) {

add(node.right, value);

// else node.data == value, so

// it's a duplicate (don't add)

 Why doesn't this solution work?

60 91

29 87

55

-3 42

overallRoot

A tangent: Change a point

 What is the state of the object referred to by p after this

code?

public static void main(String[] args) {

Point p = new Point(1, 2);

change(p);

System.out.println(p);

public static void change(Point thePoint) {

thePoint.x = 3;

thePoint.y = 4;

// answer: (3, 4)

y 1

x p

Change point, version 2

 What is the state of the object referred to by p after this

code?

public static void main(String[] args) {

Point p = new Point(1, 2);

change(p);

System.out.println(p);

public static void change(Point thePoint) {

thePoint = new Point(3, 4);

// answer: (1, 2)

y 1

x p

y 3

x

Change point, version 3

 What is the state of the object referred to by p after this

code?

public static void main(String[] args) {

Point p = new Point(1, 2);

change(p);

System.out.println(p);

public static Point change(Point thePoint) {

thePoint = new Point(3, 4);

return thePoint;

// answer: (1, 2)

y 1

x p

y 3

x

Change point, version 4

 What is the state of the object referred to by p after this

code?

public static void main(String[] args) {

Point p = new Point(1, 2);

p = change(p);

System.out.println(p);

public static Point change(Point thePoint) {

thePoint = new Point(3, 4);

return thePoint;

// answer: (3, 4)

y 1

p x

y 3

x