COMP 102 Programming Fundamentals I

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COMP 102Programming Fundamentals I

• Presented by Timture Choi

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Searching

• The process used to find the location of a target
  among a list
• Searching an array finds the index of first
  element in an array containing that value

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Example
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1. Unordered Linear Search

• Search an unordered array of integers for a value
• If the value is found
• Return its index
• Otherwise
• Return -1
• Unordered array

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1. Unordered Linear Search

• Algorithm
• Start with the first array element (index 0)
• while (more elements in array)
• if value found at current index
• return index
• else
• Try next element by incrementing index
• return -1 //if value not found

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1. Unordered Linear Search

• E.g.

// output // if found gt index // otherwise
gt return -1 int search(int datasize, int size,
int value) for (int index0 indexltsize
index) if (dataindex value)
cout ltlt "Value found at index "
ltlt index ltlt endl return index
return -1
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2. Ordered Linear Search

• Ordered array
• Algorithm
• Start with the first array element (index 0)
• while (more elements in the array)
• if value at current index is greater than value
• value not found
• return 1
• if value found at current index
• return index
• Try next element by incrementing index
• return 1 //if value not found
• Advantage
• Linear search can stop immediately
• when it has passed the possible position of the
  search value

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2. Ordered Linear Search

• E.g.

int lsearch(int data, int size, int value)
for(int index0 indexltsize index) if
(dataindex gt value) return -1
else if (dataindex value) return
index return -1
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3. Binary Search

• Start by looking at the middle element of an
  ordered array
• If the value it holds is lower than the search
  element
• Eliminate the first half of the array from
  further consideration
• If the value it holds is higher than the search
  element
• Eliminate the second half of the array from
  further consideration
• Repeat this process
• Until the element is found
• OR until the entire array has been eliminated
• Advantage
• Binary search skips over parts of the array

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3. Binary Search

• Algorithm
• Set first and last boundary of array to be
  searched
• Repeat the following
• Find middle element between first and last
  boundaries
• if (middle element contains the search value)
• return middle element position
• else if (first gt last )
• return 1
• else if (value lt the value of middle element)
• set last to middle element position 1
• else
• set first to middle element position 1

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3. Binary Search
int bsearch(int data, int size, int value)
int first, middle, last // indexes to the array
first 0 last size - 1 while (true)
middle (first last) / 2 if
(datamiddle value) return middle
else if (first gt last) return
-1 else if (value lt datamiddle)
last middle - 1 else
first middle 1

• E.g.

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Recursion

• Typically, a functions can call other functions
  to do part of the work
• But functions can also call themselves
• Recursion
• In some problems
• It may be natural to define the problem in terms
  of the problem itself
• E.g.
• Factorial function
• 6! 6 5 4 3 2 1
• With recursion
• 6! 6 5!

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Recursion

• In general
• if n is larger than 1
• n! n (n-1)! // recursive formula
• if n is equal to 1
• n! 1 // termination condition
• The C equivalent of this definition

int fac(int numb) if (numb lt 1) return
1 else return numb fac(numb-1)
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Recursion

• Advantage
• For certain problems
• E.g. the factorial function
• Leads to short and elegant code
• Disadvantage
• Calling a function consumes more time and memory
  than adjusting a loop counter
• Note
• Must be careful not to create an infinite loop by
  accident
• Contain termination condition

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SUMMARY

• By the end of this lab, you should be able to
• Search an element from an array with
• Unordered linear search
• Ordered linear search
• Binary search
• Write recursive function