Searching and Sorting

Topics

Linear and Binary SearchesSelection SortBubble Sort

ObjectivesAt the completion of this topic, students should be able to:

Explain the difference between a linear and a binary searchWrite a linear search routineWrite a binary search routineWrite a bubble sort routine

Find the person who is 23 years old.

Rules1. You may only talk to one person at a time2. You may only ask “How old are you?”3. The person must respond in years and months

Write down your algorithm

Searching an ArrayLinear SearchBinary Search

Linear SearchexamScores

0123456789

72985687648377916670

Problem: Determine which element in the arraycontains the score 87.

int thisOne = -1;

for (int index = 0; index < SIZE; index++){ if (examScores[index] == 87) thisOne = index;}

…

Binary SearchIn general, a binary search is much, much faster than a linear search, but requires that the array be sorted.

examScores

72

98

87

64

8377

91

6670

Start in the middle

Is this the one you are looking for (87)?If not, is this number smaller than 87?In this case it is. Therefore, we can elminatethe entire bottom half of the array. Why?Now try again, picking the middle of the remaining array elements.

Arrange the people in order of age – youngest to oldest

Rules1. You may only talk to one person at a time2. You may only ask “How old are you?”3. Responses will be in years and months.4. You are only allowed to keep track of two people’s ages at any one time.5. You may only ask two people to switch places at this time.6. A person cannot move unless asked to.

Write down your algorithm

SortingSorting means to put data into some specified order.

There are many, many algorithms that have been developedto sort data. In this section we will mention two of them:

Selection SortBubble Sort

Selection SortAlgorithm Development

Selection Sort

7 3 9 6 5 2

Step one:find the lowest cardin the hand

Selection sort

7 3 9 6 5 2

Step two:Swap the lowest card withthe left-most card

left-most card

Selection Sort

7 3 9 6 52

Selection Sort

3 9 6

7

52

Selection Sort

3 9 6752

Selection Sort

3 9 6752

Now … Make the second card The left-most card

left-most card

Selection Sort

3 9 6752

Find the lowest cardin the remaining cards

3 9 6752

Selection Sort

left-most card

It is already the left-most card, sono swap is required

Selection Sort

3 9 6752

Left-most card

Now make the thirdcard the left-most card

Selection Sort

3 9 6752

And find the lowest cardIn the remaining cards

Selection Sort

3 9 6

5

72

Swap it with the left-most card

Selection Sort

3 5 6972

Selection Sort

3 5 6972

Make the 4th cardthe left-most card

Selection Sort

3 5 6972

Find the lowest cardin the remaining cards

Selection Sort

3 5 6972

The lowest card is theleft-most card, so noswap is necessary

Selection Sort

3 5 6972

Make the next cardthe Leftmost-card

Selection Sort

3 5 6972

Lowest remaining cardis the left-most card sono swap is necessary

Selection Sort

3 5 6972

Make the next card the left-mostcard. It is the last card, so we aredone

Activity Diagram High Level View

Find lowest card in hand

Swap it with the left-most

card

Make the left-most card the card to the right of the current

left-most card

Is this the last card?

Find the lowest cardIn the set of cards to the right of the current left-most card

endyes

no

start

Study Lab #24 to see how a Bubble Sort works.