CS157: Searching and Sorting arrays

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CS157 Searching and Sorting arrays
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Searching Sorting methodologies

• An array is a list of items (ints, floats,
  chars, structs, 2-D)
• Commonly, we want to search for an item in the
  list
• Is X in the list?
• What are the other values associated with X
• E.g. look up userid watti, what is his GPA?
• Usually we like to have our lists sorted in some
  way
• Ascending
• Descending
• By column
• By structure element
• Sorted lists are also helpful for more efficient
  search algorithms
• E.g., Binary search
• There are many ways to sort

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Search

• Easiest algorithm is a Linear Search
• Sequentially walk through the list
• If the key is found, then done
• Imagine searching through a phone book that was
  not in alphabetical order.

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Search

• Easiest algorithm is a Linear Search
• Sequentially walk through the list
• If the key is found, then done

define SIZE 7 int arrSIZE 1, 99, 25, 68,
92, 38, 74 int key 68 // searching for
value for (int i0 iltSIZE i ) if (
arri key ) printf( d FOUND! Position
d\n, key, i ) return // dont put return
if you want all dups printf( Sorry, d
not found in list\n, key )
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• Sorting

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Sorting

• Sorting is the process of arranging a list of
  items in a particular order
• The sorting process is based on specific value(s)
• sorting a list of test scores in ascending
  numeric order
• sorting a list of people alphabetically by last
  name
• There are many algorithms, which vary in
  efficiency, for sorting a list of items
• We will examine three specific algorithms
• Selection Sort
• Insertion Sort
• Bubble Sort

Slide from Lewis Loftus Java Software
Solutions
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• Sorting - Selection Sort

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Selection Sort

• The approach of Selection Sort
• select a value and put it in its final place into
  the list
• repeat for all other values
• In more detail
• find the smallest value in the list
• switch it with the value in the first position
• find the next smallest value in the list
• switch it with the value in the second position
• repeat until all values are in their proper places

Slide from Lewis Loftus Java Software
Solutions
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Selection Sort

• An example
• original 3 9 6 1 2
• smallest is 1 1 9 6 3 2
• smallest is 2 1 2 6 3 9
• smallest is 3 1 2 3 6 9
• smallest is 6 1 2 3 6 9
• Each time, the smallest remaining value is found
  and exchanged with the element in the "next"
  position to be filled

Slide from Lewis Loftus Java Software
Solutions
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Swapping

• The processing of the selection sort algorithm
  includes the swapping of two values
• Swapping requires three assignment statements and
  a temporary storage location
• temp first
• first second
• second temp

Slide from Lewis Loftus Java Software
Solutions
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• Sorting - Insertion Sort

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Insertion Sort

• The approach of Insertion Sort
• pick any item and insert it into its proper place
  in a sorted sublist
• repeat until all items have been inserted
• In more detail
• consider the first item to be a sorted sublist
  (of one item)
• insert the second item into the sorted sublist,
  shifting the first item as needed to make room to
  insert the new addition
• insert the third item into the sorted sublist (of
  two items), shifting items as necessary
• repeat until all values are inserted into their
  proper positions

Slide from Lewis Loftus Java Software
Solutions
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Insertion Sort

• An example
• original 3 9 6 1 2
• insert 9 3 9 6 1 2
• insert 6 3 6 9 1 2
• insert 1 1 3 6 9 2
• insert 2 1 2 3 6 9

Slide from Lewis Loftus Java Software
Solutions
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Comparing Sorts

• The Selection and Insertion sort algorithms are
  similar in efficiency
• They both have outer loops that scan all
  elements, and inner loops that compare the value
  of the outer loop with almost all values in the
  list
• Approximately n2 number of comparisons are made
  to sort a list of size n
• We therefore say that these sorts are of order n2
• Other sorts are more efficient order n log2 n

Slide from Lewis Loftus Java Software
Solutions
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• Sorting - Bubble Sort

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Bubble Sort

• The approach of Bubble Sort
• Walk through the list
• If the value at the given spot is in incorrect
  order with the next element, swap positions
• repeat as the list gets sorted from either
  smallest to biggest or vice versa

Slide from Lewis Loftus Java Software
Solutions
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Bubble Sort

• An example (backwards)
• original 3 9 6 1 2
• round 1 3 6 1 2 9
• round 2 3 1 2 6 9
• round 3 1 2 3 6 9
• round 4 1 2 3 6 9
• (The 4th round is necessary for last 2 elements)

Slide from Lewis Loftus Java Software
Solutions
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Bubble Sort

• An example (forwards)
• original 3 9 6 1 2
• round 1 1 3 9 6 2
• round 2 1 2 3 9 6
• round 3 1 2 3 6 9
• round 4 1 2 3 6 9
• (The 4th round is necessary for last 2 elements)

Slide from Lewis Loftus Java Software
Solutions
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Bubble Sort

• Code Example backwards

define SIZE 7 int arrSIZE 1, 99, 25, 68,
92, 38, 74 for( int i1 iltSIZE i )
for( int j0 jltSIZE-i j ) if ( arrj gt
arrj1 ) swap( arr, j, j1 )
Do outer loop size-1 times