Data Structures and Algorithms

Data Structures and Algorithms

• 1.
  GROUP 4
• 2.
  Objectives Define sorting. Types ofsorting. Selection Sort Exchange Sort Insertion Sort
• 3.
  What is Sorting? is the process of placing elements from a collection in some kind of order. refers to ordering data in an increasing or decreasing fashion according to some linear relationship among the data items. can be done on names, numbers and records. For example, it is relatively easy to look up the phone number of a friend from a telephone dictionary because the names in the phone book have been sorted into alphabetical order.
• 4.
  Types of Sorting SelectionSort Exchange Sort Insertion Sort
• 5.
  SELECTION SORT In thismethod, sorting is done by inserting elements into an existing sorted list. Initially, the sorted list has only one element. Other elements are gradually added into the list in the proper position. In this technique, the first element is selected and compared with all other elements. If any other element is less than the first element swapping should take place. By the end of this comparison, the least element most top position in the array.
• 6.
  This is knownas pass1. In pass II, the second element is selected and compared with all other elements. Swapping takes place if any other element is less than selected element. This process continuous until array is sorted.
• 7.
  EXAMPLE : 9 25 7 4 8 on pass 1 look for smallest in 1st to 6th swap 2nd with first giving 2 9 5 7 4 8 on pass 2 look for smallest in 2nd to 6th swap 5th with second giving 2 4 5 7 9 8 on pass 3 look for smallest in 3rd to 6th swap 3rd with third giving 2 4 5 7 9 8 on pass 4 look for smallest in 4th to 6th swap 4th with fourth giving 2 4 5 7 9 8 on pass 5 look for smallest in 5th to 6th swap 5th with 6th giving 2 4 5 7 8 9 sorted.
• 8.
  EXCHANGE SORT The exchangesort is almost similar as the bubble sort. In fact some people refer to the exchange sort as just a different bubble sort. The exchange sort compares each element of an array and swap those elements that are not in their proper position, just like a bubble sort does. The only difference between the two sorting algorithms is the manner in which they compare the elements. The exchange sort compares the first element with each element of the array, making a swap where is necessary.
• 9.
  EXAMPLE : 9 25 4 7 8 compare 1st & 2nd -> 2 9 5 4 7 8 compare 2nd & 3rd -> 2 5 9 4 7 8 compare 3rd & 4th -> 2 5 4 9 7 8 compare 4th & 5th -> 2 5 4 7 9 8 compare 5th & 6th -> 254789
• 10.
  1. Compare thefirst pair of numbers (positions 0 and 1) and reverse them if they are not in the correct order. 2. Repeat for the next pair (positions 1 and 2). 3. Continue the process until all pairs have been checked. 4. Repeat steps 1 through 3 for positions 0 through n - 1 to i (for i = 1, 2, 3, ...) until no pairs remain to be checked. 5. The list is now sorted.
• 11.
  INSERTION SORT is anefficient algorithm for sorting a small number of elements. Insertion sort works the same way as one would sort a bridge or gin rummy hand, i.e. starting with an empty left hand and the cards face down on the table. One card at a time is then removed from the table and inserted into the correct position in the left hand. To find the correct position for a card, it is compared with each of the cards already in the hand, from right to left.
• 12.
  12 Insertion Sort To insert12, we need to make room for it by moving first 36 and then 24.
• 13.
  13 Insertion Sort
• 14.
  14 Insertion Sort