Topic 9B Array Sorting and Searching

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Topic 9B Array Sorting and Searching
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Algorithms

• An algorithm is a set of steps that can be
  followed to solve a problem.
• Designed and developing an algorithm is often the
  most difficult part of the problem-solving
  process.
• For each problem, there can be many different
  algorithms that correctly solve the problem.

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Algorithms

• Some algorithms may do so faster than others that
  do the same thing (algorithms that solve the same
  problem may vary in efficiency).
• Some algorithms may be easier to understand and
  may make more sense than others that do the
  same thing (algorithms that solve the same
  problem may vary in complexity).

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Introduction to Sorting

• Many of the algorithms that operate on data
  contained within an array require the data in
  that array to be sorted.
• This means that the data contained in the array
  needs to be in order, from lowest-to-highest, or
  vice versa.
• We will examine a simple technique for putting
  the array in lowest-to-highest order.
• Note that once this problem is solved, the
  reverse, putting the array in highest-to-lowest
  order, is trivial.

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Introduction to Sorting

• There are many approaches to sorting.
• Some sorting algorithms are much better than
  others.
• We will examine one of the simplest sorting
  algorithms, a selection sort.
• This algorithm is intuitive (easy-to-understand),
  although it is not very efficient.

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Selection SortThe Basic Idea

• The basic idea of the selection sort is to
  process the array from left-to-right (index 0,
  index 1, etc)
• At each element, we look to the right and find
  the lowest value. Once we find the lowest value
  (to the right of the current element), we swap
  the two elements.
• Then, we move onto the next element and repeat
  the process.

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Selection SortThe Algorithm

• (1) current_element 0
• (2) Find index_of_min, the index of the smallest
  element in the subarray, arraycurrent_element
  to arraysize 1
• (3) If current_element does not equal
  index_of_min, swap elements at current_element
  and index_of_min
• (4) If current_element size 1 , stop. Else
  current_element goto step (2)

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Selection Sort An Example
24
98
4
3
55
62
3
24
4
98
24
98
98
55
98
62
X1
X2
X3
X4
X5
X0
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Sorting Algorithms

• Keep in mind that a selection sort is simply one
  method of sorting an array.
• It is a very simple-to-understand approach.
• It is also not very efficient.
• Other sorting algorithms that are much more
  efficient, although much harder-to-understand,
  include the bubble sort and the quicksort. We
  will not discuss these algorithms.

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Introduction to Searching

• Searching an array is a closely related problem
  to sorting an array.
• The simplest approach to array searching is the
  linear search.
• This searching method consists of examining the
  array elements from left to right.
• If the target is found, we save the index it was
  found at and stop. If not, and there are still
  more array elements to the right, we move to the
  next element and repeat.

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The Linear Search

• Thus, we simply start at index 0 and see if the
  target is there. If so, we stop.
• If not, we move to index 1 and see if the target
  is there.
• If not, we move to index 2 and see if the target
  is there.
• etc

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Linear Search An Example
We will perform a linear search on the array X in
order to find the target value of 55.
24
98
4
3
55
62
X1
X2
X3
X4
X5
X0
55 is located at index 4!
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Searching Algorithms

• The linear search is not a very efficient
  algorithm.
• Notice that this algorithm does not depend on, or
  require, that the array is sorted, or in any
  order at all.
• If the array is sorted, we can use a much more
  efficient searching algorithm, the binary search.

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The Binary Search

• The binary search is very intuitive.
• (1) Begin with the entire array
• (2) Select the middle element.
• (3) If the target is less than the middle
  element, choose the next subarray to be the half
  of the array to the left (smaller than) the
  middle element. If the target is greater than
  the middle element, choose the next subarray to
  be the half of the array to the right (greater
  than) the middle element.
• (4) Then, repeat on the new subarray.

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Binary Search An Example
We will perform a binary search on the array X in
order to find the target value of 55.
3
4
24
25
55
62
98
X1
X2
X3
X4
X5
X0
X6
55 is located at index 4!
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Summary

• Searching and sorting arrays are common problems
  in computer science.
• Both problems, like almost all problems, have
  multiple solutions.
• Solutions vary on complexity and efficiency.
• We have examined the selection sort, the linear
  search, and the binary search.