Sorting and Searching

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Sorting and Searching

• Dr. Ying Xie

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• Selection Sort

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Recap Bank-ATM problem

• We want to design some efficiently search
  algorithm for Banks member function
  VerifyAccounts().
• An efficient search algorithm is build on a
  sorted list.

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Selection Sorting Algorithm
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void selectionSort(int arr, int n) //for
loop for (int startP 0 startP lt n-2
startP) //1. find the smallest number
in the sublist //2. swap the smallest
number and the first number of this sublist
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pass 1
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pass 2
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pass 3
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pass 4
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stop
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Find the smallest number is a sublist

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startP
startP1
startP2
startP3
indexForSmallest
startP
startP1
startP1
startP3
int indexForSmallest startP For (int
jstartP1 jltn-1 j) if (arrj lt
arrindexForSmallest)
indexForSmallest j
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• swap the smallest number and the first number in
  the sublist (swap arrstartP and
  arrsubscriptForSmallest)
• int temp arrstartP
• arrstarP arrsubscriptForSmallest
• arrsubscriptForSmallest temp

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• void selectionSort(int arr, int n)
• for (int startP 0 startP lt n-2 startP)
• //1. find the smallest number in the
  sublist
• int subscriptForSmallest startP
• For (int jstartP jltn-1 j)
• if (arrj lt arrsubscriptForSmalles
  t)
• subscriptForSmallest j
• //2. swap the smallest number and the
  first number of this sublist
• int temp arrstartP
• arrstarP arrsubscriptForSmallest
• arrsubscriptForSmallest temp

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• Binary Search

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Binary Search (Only works on a sorted array)
Target midValue
first
Last-1
mid
Last
mid (first last)/2 MidValue arr mid
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• Case 1 target midValue, search is done

Target midValue
first
Last-1
mid
Last
if (midValue target) // found match
return mid
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• Case 2 target lt midValue, continue the search in
  the lower sublist first, mid)

first
mid-1
last-1
last
New last mid
// search the lower sublist If (target lt
midValue) ltreposition last to midgt ltsearch
sublist arr firstarr mid-1
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Case 3 target gt midValue, continue the search in
the upper sublist mid 1, last)
last-1
last
first
New first mid 1
If (target gt midValue) first mid
1 Continue the search in first, last)
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• Terminate Condition
• a match is found (return the index of
  that match)
• the sublist finally become empty (return
  -1)
• first gt last

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int binSearch (const int arr , int first, int
last, int target) // while the sublist is
not empty // find the midValue of
sublist and // compare the midValue with
the target // if they are equal
// return mid // else if
target lt midValue // reposition
last to mid, generate the lower sublist
// else // repostion first to
mid 1, generate the upper sublist //
return -1
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int binSearch (const int arr , int first, int
last, int target) int mid, midValue //
while the sublist is not empty while (first
lt last) // find the midValue of sublist
and mid (firstlast)/2
midValue arrmid // compare the
midValue with the target // if they are
equal, return mid if (target
midValue) return mid //
else if target lt midValue //
reposition last to mid, generate the lower
sublist else if (target lt midValue)
last mid // else
// repostion first to mid 1, generate
the upper sublist else
first mid1 // return -1