Selection sort
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Selection sort is an algorithm that sorts data in place by iteratively finding the minimum value from an unsorted portion of an array and moving it to the beginning. It has a quadratic time complexity of O(n^2) and is only suitable for sorting small lists. The algorithm works by making multiple passes over the array, finding the minimum value on each pass and swapping it into place.
![Session 4Ver. 1.0
Selection Sort
Pass 1
n = 5
Search the minimum value in the array, arr[0] to arr[n – 1].
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 10 200105 20
min](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-4-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 1
n = 5
Search the minimum value in the array, arr[0] to arr[n – 1].
Swap the minimum value with the value at index 0.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 10 200105 20
min
Swap
10510](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-5-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 1
n = 5
Search the minimum value in the array, arr[0] to arr[n – 1].
Swap the minimum value with the value at index 0.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 105 20010 20
The smallest value is placed at its correct location after Pass 1](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-6-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 2
n = 5
Search the minimum value in the array, arr[1] to arr[n – 1].
Swap the minimum value with the value at index 1.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 105 20010 20
min
20 120
Swap](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-7-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 2
n = 5
Search the minimum value in the array, arr[1] to arr[n – 1].
Swap the minimum value with the value at index 1.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 200 2010510arr
210 43
20 200 120
The second smallest value is placed at its correct location after
Pass 2
10510](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-8-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 3
n = 5
Search the minimum value in the array, arr[2] to arr[n – 1].
Swap the minimum value with the value at index 2.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 200 2010510arr
210 43
20 200
min
10 120105](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-9-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 3
n = 5
Search the minimum value in the array, arr[2] to arr[n – 1].
Swap the minimum value with the value at index 2.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 200 2010510arr
210 43
20 200
minThe third smallest value is placed at its correct location after Pass 3
12010510](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-10-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 4
n = 5
Search the minimum value in the array, arr[3] to arr[n – 1].
Swap the minimum value with the value at index 3.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 200 2010510arr
210 43
20 200 12010 105
min
120 200
Swap](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-11-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Pass 4
n = 5
Search the minimum value in the array, arr[3] to arr[n – 1].
Swap the minimum value with the value at index 3.
Implementing Selection Sort Algorithm (Contd.)
arr
210 43
120 200 2010510arr
210 43
20
The fourth smallest value is placed at its correct location after Pass 4
120 20010 105](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-12-320.jpg)
![Session 4Ver. 1.0
Selection Sort
Write an algorithm to implement selection sort.
Algorithm for selection sort:
1. Repeat steps 2 and 3 varying j from 0 to n – 2
2. Find the minimum value in arr[j] to arr[n – 1]:
a. Set min_index = j
b. Repeat step c varying i from j + 1 to n – 1
c. If arr[i] < arr[min_index]:
i. min_index = i
3. Swap arr[j] with arr[min_index]
Implementing Selection Sort Algorithm (Contd.)](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-14-320.jpg)
![Session 4Ver. 1.0
Selection Sort
public void selectionSort()
{
int out,in,min;
for(out=0;out<nElems;out++)
{
min=out;
for(in=out+1;in<nElems-1;in++)
{
if(A[in]<a[min])
min=in;
}
swap(out,min);
}
}
Selection Sort Method](https://image.slidesharecdn.com/selectionsort-181004165141/85/Selection-sort-15-320.jpg)
Selection sort
- 1. Session 4Ver. 1.0 Selection Sort Selection sort algorithm: Has a quadratic order of growth and is therefore suitable for sorting small lists only Scans through the list iteratively, selects one item in each scan, and moves the item to its correct position in the list Sorting Data by Using Selection Sort
- 2. Session 4Ver. 1.0 Selection Sort To understand the implementation of selection sort algorithm, consider an unsorted list of numbers stored in an array. Implementing Selection Sort Algorithm arr 210 43 120 10 200105 20
- 3. Session 4Ver. 1.0 Selection Sort Let us sort this unsorted list. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 10 200105 20
- 4. Session 4Ver. 1.0 Selection Sort Pass 1 n = 5 Search the minimum value in the array, arr[0] to arr[n – 1]. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 10 200105 20 min
- 5. Session 4Ver. 1.0 Selection Sort Pass 1 n = 5 Search the minimum value in the array, arr[0] to arr[n – 1]. Swap the minimum value with the value at index 0. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 10 200105 20 min Swap 10510
- 6. Session 4Ver. 1.0 Selection Sort Pass 1 n = 5 Search the minimum value in the array, arr[0] to arr[n – 1]. Swap the minimum value with the value at index 0. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 105 20010 20 The smallest value is placed at its correct location after Pass 1
- 7. Session 4Ver. 1.0 Selection Sort Pass 2 n = 5 Search the minimum value in the array, arr[1] to arr[n – 1]. Swap the minimum value with the value at index 1. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 105 20010 20 min 20 120 Swap
- 8. Session 4Ver. 1.0 Selection Sort Pass 2 n = 5 Search the minimum value in the array, arr[1] to arr[n – 1]. Swap the minimum value with the value at index 1. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 200 120 The second smallest value is placed at its correct location after Pass 2 10510
- 9. Session 4Ver. 1.0 Selection Sort Pass 3 n = 5 Search the minimum value in the array, arr[2] to arr[n – 1]. Swap the minimum value with the value at index 2. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 200 min 10 120105
- 10. Session 4Ver. 1.0 Selection Sort Pass 3 n = 5 Search the minimum value in the array, arr[2] to arr[n – 1]. Swap the minimum value with the value at index 2. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 200 minThe third smallest value is placed at its correct location after Pass 3 12010510
- 11. Session 4Ver. 1.0 Selection Sort Pass 4 n = 5 Search the minimum value in the array, arr[3] to arr[n – 1]. Swap the minimum value with the value at index 3. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 200 12010 105 min 120 200 Swap
- 12. Session 4Ver. 1.0 Selection Sort Pass 4 n = 5 Search the minimum value in the array, arr[3] to arr[n – 1]. Swap the minimum value with the value at index 3. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 The fourth smallest value is placed at its correct location after Pass 4 120 20010 105
- 13. Session 4Ver. 1.0 Selection Sort Pass 4 n = 5 The list is now sorted. Implementing Selection Sort Algorithm (Contd.) arr 210 43 120 200 2010510arr 210 43 20 20010 105 120
- 14. Session 4Ver. 1.0 Selection Sort Write an algorithm to implement selection sort. Algorithm for selection sort: 1. Repeat steps 2 and 3 varying j from 0 to n – 2 2. Find the minimum value in arr[j] to arr[n – 1]: a. Set min_index = j b. Repeat step c varying i from j + 1 to n – 1 c. If arr[i] < arr[min_index]: i. min_index = i 3. Swap arr[j] with arr[min_index] Implementing Selection Sort Algorithm (Contd.)
- 15. Session 4Ver. 1.0 Selection Sort public void selectionSort() { int out,in,min; for(out=0;out<nElems;out++) { min=out; for(in=out+1;in<nElems-1;in++) { if(A[in]<a[min]) min=in; } swap(out,min); } } Selection Sort Method
- 16. Session 4Ver. 1.0 Selection Sort In selection sort, there are n – 1 comparisons during Pass 1 to find the smallest element, n – 2 comparisons during Pass 2 to find the second smallest element, and so on. Total number of comparisons = (n – 1) + (n – 2) + (n – 3) + … + 3 + 2 + 1 = n(n – 1)/2 n(n – 1)/2 is of O(n2 ) order. Therefore, the selection sort algorithm is of the order O(n2 ). Determining the Efficiency of Selection Sort Algorithm
- 17. Session 4Ver. 1.0 Selection Sort Read the following statement and specify whether it is true or false: The efficiency of selection sort algorithm is same as that of the bubble sort algorithm. Just a minute Answer: True
- 18. Session 4Ver. 1.0 Selection Sort How many comparisons are performed in the second pass of the selection sort algorithm? Just a minute Answer: n – 2
Editor's Notes
- #2: Ask students to answer this question and then come to the given example.
- #3: Ask students to answer this question and then come to the given example.
- #4: Ask students to answer this question and then come to the given example.
- #5: Ask students to answer this question and then come to the given example.
- #6: Ask students to answer this question and then come to the given example.
- #7: Ask students to answer this question and then come to the given example.
- #8: Ask students to answer this question and then come to the given example.
- #9: Ask students to answer this question and then come to the given example.
- #10: Ask students to answer this question and then come to the given example.
- #11: Ask students to answer this question and then come to the given example.
- #12: Ask students to answer this question and then come to the given example.
- #13: Ask students to answer this question and then come to the given example.
- #14: Ask students to answer this question and then come to the given example.
- #15: Ask students to write an algorithm to implement bubble sorting. Given them 5-10 minutes to write the algorithm. Then show them the answer.
- #16: Ask students to write an algorithm to implement bubble sorting. Given them 5-10 minutes to write the algorithm. Then show them the answer.
- #17: In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.
- #18: In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.
- #19: In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.