CSPC/ PPS Sorting methods

CSPC/ PPS Sorting methods

• 1.
  SORTING PPS
• 2.
  DEFINATION • A SortingAlgorithm is used to rearrange a given array or list elements according to a comparison operator on the elements. • The comparison operator is used to decide the new order of element in the respective data structure.
• 3.
  Example: • The belowlist of characters is sorted in increasing order of their ASCII values. That is, the character with lesser ASCII value will be placed first than the character with higher ASCII value.
• 4.
  TYPES OF SORTING •Selection Sort • Insertion Sort • Bubble Sort
• 5.
  Selection Sort • Theselection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from unsorted part and putting it at the beginning. • The algorithm maintains two subarrays in a given array. • 1) The subarray which is already sorted. 2) Remaining subarray which is unsorted.
• 6.
  Example arr[] = 6425 12 22 11 // Find the minimum element in arr[0...4] // and place it at beginning 11 25 12 22 64 // Find the minimum element in arr[1...4] // and place it at beginning of arr[1...4] 11 12 25 22 64 // Find the minimum element in arr[2...4] // and place it at beginning of arr[2...4] 11 12 22 25 64 // Find the minimum element in arr[3...4] // and place it at beginning of arr[3...4] 11 12 22 25 64
• 7.
  Example
• 8.
  Insertion Sort • Insertionsort is a simple sorting algorithm that works the way we sort playing cards in our hands. • Algorithm // Sort an arr[] of size n insertionSort(arr, n) Loop from i = 1 to n-1. ……a) Pick element arr[i] and insert it into sorted sequence arr[0…i-1]
• 9.
  Example:
• 10.
  Another Example: • 12, 11,13, 5, 6 • Let us loop for i = 1 (second element of the array) to 4 (last element of the array) • i = 1. Since 11 is smaller than 12, move 12 and insert 11 before 12 11, 12, 13, 5, 6 • i = 2. 13 will remain at its position as all elements in A[0..I-1] are smaller than 13 11, 12, 13, 5, 6 • i = 3. 5 will move to the beginning and all other elements from 11 to 13 will move one position ahead of their current position. 5, 11, 12, 13, 6 • i = 4. 6 will move to position after 5, and elements from 11 to 13 will move one position ahead of their current position. 5, 6, 11, 12, 13
• 11.
  Bubble Sort • BubbleSort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order. • Example: First Pass: ( 5 1 4 2 8 ) –> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. ( 1 5 4 2 8 ) –> ( 1 4 5 2 8 ), Swap since 5 > 4 ( 1 4 5 2 8 ) –> ( 1 4 2 5 8 ), Swap since 5 > 2 ( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them.
• 12.
  Contd… • Second Pass: (1 4 2 5 8 ) –> ( 1 4 2 5 8 ) ( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) Now, the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted.
• 13.
  Contd… • Third Pass: (1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
• 14.
  Example: