Searching and Sorting

1
Searching and Sorting
Chapter 14
2
Outline

• Search
• Linear Search
• Binary Search
• Sort
• Selection Sort
• Bubble Sort
• Insertion Sort
• Template Functions for Sorting and Searching

3
Sorting and Searching

• Sorting Arranging a list of values in order
• Searching Locating a particular item in a list
• Searching a sorted list is faster
• but sorting could be time consuming
• Linear (sequential) search
• used on any list
• Binary search
• used on sorted list only

4
Linear Search

• Using a bounded number of tries
• use the variables found and index to control the
  search loop

use a mid-loop exit
5
Binary Search

• Given a sorted list
• keep narrowing the search by eliminating half of
  the remaining list
• Example search for the name Gil

• Compare the name Gil to the contents of the
  middle cell v5
• Because Gil is alphabetically less than Jan, Gil
  (if exits) must be in the left half

If there are even number of cells ? take the
middle cell to be that cell just to the left of
the middle line
6
Binary Search

• Compare the name Gil to the contents of the
  current middle cell v2
• Because Gil is greater than Fay, Gil (if exits)
  must be in the right half

7
Binary Search Function

• We want the binary_search function to return
  either the subscript of the cell containing the
  desired item or -1 if the item is not in the
  vector
• use variables first, last, and mid
• the segment still under consideration is changed
  to the left half segment by last mid -1or to
  the right half segment by first mid 1

8
Binary Search Function

• Page 322
• Trace to-find 48
• Trace to-find 82 (not in the Vector)

first mid 1
9
Selection Sort

• Idea 1) find the smallest number and swap it
  with the number in position 02) from the
  remaining numbers, find the next smallest number
  and swap it with the number in position 13)
  continue this fashion until the last position

10
Selection Sort

• for cell 0, we make a pass through v0 .. v6
  to locate the smallest number, 12, and swap it
  with the number in cell 0

• for cell 1, we make a pass through v1 .. v6
  to locate the smallest number, 30, and swap it
  with the number in cell 1

11
Selection Sort

• A vector with N numbers
• ctf cell to fill

• suppose v0 through vctf-1 are sorted
• we need to pass through subvector vctf ..
  vN-1to find the index_min of the smallest
  element in this subvector
• then swap the contends of vctf and vindex_min

12
Selection Sort

• outer loop vctf..vN-2
• inner loop vctf1..vN-1
• index_min is initialized with ctf
• how many passes? N-1

13
Bubble Sort

• Idea 1) During each pass of bubble sort, the
  contents of successive pairs of adjacent cells
  are compared and, if out of order, switched2)
  bubble sort will correctly fill cells, starting
  at the right end with the last cell

Pass 1
Comparison Result Action v0 gt v1 true
switchv1 gt v2 false none v2 gt
v3 true switch
After Pass 1 the largest number is in v3
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Bubble Sort
Pass 2
Comparison Result Action v0 gt v1 false
nonev1 gt v2 true switch
After Pass 2 the two largest numbers are in
v2, v3
Pass 3
Comparison Result Action v0 gt v1 true
switch
After Pass 3 the vector, v0 .. vsize-1, is
sorted
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Bubble Sort function

• The smaller numbers bubble to the top, while
  larger ones sink into place, one by one, at the
  bottom.

• Version 1 of the bubble sort
• for (pass 1 pass lt size, pass)
• ctf size pass
• for (i0 iltctf i)
• if (vi gt vi1
• swap(vi, vi1)

16
Bubble Sort function - Version 2

• As pass goes from 1 to size ? cft goes from
  size-1 down to 0
• If no swap occurs during a pass ? the vector is
  already sorted

for (ctf size-1 ctf gt 0, ctf--)
swaps 0 for (i0 iltctf i)
if (vi gt vi1 swap(vi,
vi1) swaps if
(swaps0) return
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Bubble Sort function - Version 2
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Inserting into a sorted vector

• insert function inserts one new entry into a
  sorted vector so that the new vector is also
  sorted
• use a for loop
• 1) after the loop, the value of i will be the
  index of the cell immediately to the left of the
  cell into which the new entry is to be inserted
• 2) the loop shifts some elements to the right
  to make room for the new entry.

19
Inserting into a sorted vector
e.g. entry 55
20
Insertion Sort

• Idea making repeated calls to the insert function