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Sorting of linked list data through python.ppt

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The document introduces common sorting algorithms used to arrange lists in order, focusing on selection sort, insertion sort, and bubble sort. It describes the selection sort algorithm in detail, illustrating how it repeatedly finds and moves the smallest element to the sorted side of the array. Additionally, it explains the insertion sort process and briefly outlines the mechanics of the bubble sort algorithm, emphasizing the comparison and swapping of array entries.

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Sorting
Introduction • Common problem: sort a list of values, starting from lowest to highest. – List of exam scores – Words of dictionary in alphabetical order – Students names listed alphabetically – Student records sorted by ID# • Generally, we are given a list of records that have keys. These keys are used to define an ordering of the items in the list.
Quadratic Sorting Algorithms • We are given n records to sort. • There are a number of simple sorting algorithms whose worst and average case performance is quadratic O(n2): – Selection sort – Insertion sort – Bubble sort
Sorting an Array of Integers • Example: we are given an array of six integers that we want to sort from smallest to largest 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Start by finding the smallest entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap the smallest entry with the first entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap the smallest entry with the first entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Part of the array is now sorted. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Find the smallest element in the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap with the front of the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • We have increased the size of the sorted side by one element. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side Smallest from unsorted [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side Sorted side is bigger [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process keeps adding one more number to the sorted side. • The sorted side has the smallest numbers, arranged from small to large. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • We can stop when the unsorted side has just one number, since that number must be the largest number. [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The array is now sorted. • We repeatedly selected the smallest element, and moved this element to the front of the unsorted side. [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The Insertion Sort algorithm also views the array as having a sorted side and an unsorted side. [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The sorted side starts with just the first element, which is not necessarily the smallest element. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The sorted side grows by taking the front element from the unsorted side... 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • ...and inserting it in the place that keeps the sorted side arranged from small to large. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • Sometimes we are lucky and the new inserted item doesn't need to move at all. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertionsort Algorithm • Sometimes we are lucky twice in a row. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Copy the new element to a separate location. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Shift elements in the sorted side, creating an open space for the new element. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Shift elements in the sorted side, creating an open space for the new element. [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Continue shifting elements... [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Continue shifting elements... [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element ...until you reach the location for the new element. [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Copy the new element back into the array, at the correct location. [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element [2] [3] [4] [5] [6] • The last element must also be inserted. Start by copying it... [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] Sorted Result [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5]
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Continue looping, until done. [0] [1] [2] [3] [4] [5] Swap? Yes.

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Sorting of linked list data through python.ppt

  • 2. Introduction • Common problem: sort a list of values, starting from lowest to highest. – List of exam scores – Words of dictionary in alphabetical order – Students names listed alphabetically – Student records sorted by ID# • Generally, we are given a list of records that have keys. These keys are used to define an ordering of the items in the list.
  • 3. Quadratic Sorting Algorithms • We are given n records to sort. • There are a number of simple sorting algorithms whose worst and average case performance is quadratic O(n2): – Selection sort – Insertion sort – Bubble sort
  • 4. Sorting an Array of Integers • Example: we are given an array of six integers that we want to sort from smallest to largest 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 5. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Start by finding the smallest entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 6. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap the smallest entry with the first entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 7. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap the smallest entry with the first entry. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 8. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Part of the array is now sorted. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 9. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Find the smallest element in the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 10. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • Swap with the front of the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 11. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • We have increased the size of the sorted side by one element. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 12. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side Smallest from unsorted [0] [1] [2] [3] [4] [5]
  • 13. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 14. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process continues... Sorted side Unsorted side Sorted side is bigger [0] [1] [2] [3] [4] [5]
  • 15. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The process keeps adding one more number to the sorted side. • The sorted side has the smallest numbers, arranged from small to large. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]
  • 16. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • We can stop when the unsorted side has just one number, since that number must be the largest number. [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
  • 17. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Selection Sort Algorithm • The array is now sorted. • We repeatedly selected the smallest element, and moved this element to the front of the unsorted side. [0] [1] [2] [3] [4] [5]
  • 18. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The Insertion Sort algorithm also views the array as having a sorted side and an unsorted side. [0] [1] [2] [3] [4] [5]
  • 19. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The sorted side starts with just the first element, which is not necessarily the smallest element. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 20. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • The sorted side grows by taking the front element from the unsorted side... 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 21. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • ...and inserting it in the place that keeps the sorted side arranged from small to large. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 22. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 23. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertion Sort Algorithm • Sometimes we are lucky and the new inserted item doesn't need to move at all. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 24. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Insertionsort Algorithm • Sometimes we are lucky twice in a row. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 25. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Copy the new element to a separate location. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted side
  • 26. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Shift elements in the sorted side, creating an open space for the new element. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 27. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Shift elements in the sorted side, creating an open space for the new element. [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 28. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Continue shifting elements... [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 29. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Continue shifting elements... [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 30. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element ...until you reach the location for the new element. [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] [0] [1] [2] [3] [4] [5]
  • 31. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element Copy the new element back into the array, at the correct location. [3] [4] [5] [6] [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
  • 32. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] How to Insert One Element [2] [3] [4] [5] [6] • The last element must also be inserted. Start by copying it... [0] [1] [2] [3] [4] [5] Sorted side Unsorted sid
  • 33. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] Sorted Result [0] [1] [2] [3] [4] [5]
  • 34. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5]
  • 35. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
  • 36. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
  • 37. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
  • 38. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] No.
  • 39. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
  • 40. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] No.
  • 41. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
  • 42. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
  • 43. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Swap?
  • 44. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. [0] [1] [2] [3] [4] [5] Yes!
  • 45. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
  • 46. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
  • 47. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 48. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 49. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 50. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 51. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Repeat. [0] [1] [2] [3] [4] [5] Swap? No.
  • 52. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
  • 53. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 54. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 55. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 56. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? Yes.
  • 57. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
  • 58. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Loop over array n-1 times, swapping pairs of entries as needed. [0] [1] [2] [3] [4] [5] Swap? No.
  • 59. 0 10 20 30 40 50 60 70 [1] [2] [3] [4] [5] [6] The Bubble Sort Algorithm • Continue looping, until done. [0] [1] [2] [3] [4] [5] Swap? Yes.

Editor's Notes

  • #5: The picture shows a graphical representation of an array which we will sort so that the smallest element ends up at the front, and the other elements increase to the largest at the end. The bar graph indicates the values which are in the array before sorting--for example the first element of the array contains the integer 45.
  • #6: The first sorting algorithm that we'll examine is called Selectionsort. It begins by going through the entire array and finding the smallest element. In this example, the smallest element is the number 8 at location [4] of the array.
  • #7: Once we have found the smallest element, that element is swapped with the first element of the array...
  • #8: ...like this. The smallest element is now at the front of the array, and we have taken one small step toward producing a sorted array.
  • #9: At this point, we can view the array as being split into two sides: To the left of the dotted line is the "sorted side", and to the right of the dotted line is the "unsorted side". Our goal is to push the dotted line forward, increasing the number of elements in the sorted side, until the entire array is sorted.
  • #10: Each step of the Selectionsort works by finding the smallest element in the unsorted side. At this point, we would find the number 15 at location [5] in the unsorted side.
  • #11: This small element is swapped with the number at the front of the unsorted side, as shown here...
  • #12: ...and the effect is to increase the size of the sorted side by one element. As you can see, the sorted side always contains the smallest numbers, and those numbers are sorted from small to large. The unsorted side contains the rest of the numbers, and those numbers are in no particular order.
  • #13: Again, we find the smallest entry in the unsorted side...
  • #14: ...and swap this element with the front of the unsorted side.
  • #15: The sorted side now contains the three smallest elements of the array.
  • #16: Here is the array after increasing the sorted side to four elements.
  • #17: And now the sorted side has five elements. In fact, once the unsorted side is down to a single element, the sort is completed. At this point the 5 smallest elements are in the sorted side, and so the the one largest element is left in the unsorted side. We are done...
  • #18: ...The array is sorted. The basic algorithm is easy to state and also easy to program.
  • #19: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #20: ...like this. However, in the Selectionsort, the sorted side always contained the smallest elements of the array. In the Insertionsort, the sorted side will be sorted from small to large, but the elements in the sorted side will not necessarily be the smallest entries of the array. Because the sorted side does not need to have the smallest entries, we can start by placing one element in the sorted side--we don't need to worry about sorting just one element. But we do need to worry about how to increase the number of elements that are in the sorted side.
  • #21: The basic approach is to take the front element from the unsorted side...
  • #22: ...and insert this element at the correct spot of the sorted side. In this example, the front element of the unsorted side is 20. So the 20 must be inserted before the number 45 which is already in the sorted side.
  • #23: After the insertion, the sorted side contains two elements. These two elements are in order from small to large, although they are not the smallest elements in the array.
  • #24: Sometimes we are lucky and the newly inserted element is already in the right spot. This happens if the new element is larger than anything that's already in the array.
  • #25: Sometimes we are lucky twice in a row.
  • #26: The actual insertion process requires a bit of work that is shown here. The first step of the insertion is to make a copy of the new element. Usually this copy is stored in a local variable. It just sits off to the side, ready for us to use whenever we need it.
  • #27: After we have safely made a copy of the new element, we start shifting elements from the end of the sorted side. These elements are shifted rightward, to create an "empty spot" for our new element to be placed. In this example we take the last element of the sorted side and shift it rightward one spot...
  • #28: ...like this. Is this the correct spot for the new element? No, because the new element is smaller than the next element in the sorted section. So we continue shifting elements rightward...
  • #29: This is still not the correct spot for our new element, so we shift again...
  • #30: ...and shift one more time...
  • #31: Finally, this is the correct location for the new element. In general there are two situations that indicate the "correct location" has been found: 1. We reach the front of the array (as happened here), or 2. We reached an element that is less than or equal to the new element.
  • #32: Once the correct spot is found, we copy the new element back into the array. The number of elements in the sorted side has increased by one.
  • #33: The last element of the array also needs to be inserted. Start by copying it to a safe location.
  • #34: The new element is inserted into the array.
  • #35: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #36: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #37: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #38: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #39: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #40: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #41: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #42: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #43: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #44: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #45: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #46: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #47: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #48: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #49: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #50: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #51: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #52: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #53: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #54: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #55: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #56: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #57: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #58: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #59: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...
  • #60: Now we'll look at another sorting method called Insertionsort. The end result will be the same: The array will be sorted from smallest to largest. But the sorting method is different. However, there are some common features. As with the Selectionsort, the Insertionsort algorithm also views the array as having a sorted side and an unsorted side, ...