Sorting

• Given a collection of data
  • Which has an inherent ordering operation.
  • Place that data in order.
• We do this all the time.
  • Arrange people by name, height, ....
  • Arrange grades lowest to highest
• This is an well studied problem
  • There are many algorithms that solve this problem.
  • Work out the difference between problem and solution.
• Selection Sort
  • Repeatedly find the smallest element and move it to the next available position.

  • SelectionSort(A, size)
    
     for current = 0 to size-2
        small = current
        for candidate = current+1 to size-1
           if A[small] > A[candidate] 
               small = candidate
        if small ≠ current
           swap(A[small], A[current])
    

  • Trace this.
  • Do we believe that this works?
  • This algorithm is O($n^2)$.
• A second sort is bubble sort.
  • Starting at position 1, allow the biggest item to bubble to the end.

  • BubbleSort(A, size)
    
     set last to be size-1
     set swapped to be true
     while swapped is true
       set swapped to be false
       for i = 1 to last
           if A[i] < A[i-1]
               set swapped to be true
               swap A[i] and A[i-1]
               set newLast to be i-1
        last = newLast
    

  • Trace this.
  • How does this algorithm work?
    • What does last do?
    • What does swapped do?
    • What happens on a pass when nothing is swapped.
  • Do we believe that this works?
  • This algorithm is O($n^2)$.
  • This should be faster than selection sort
    • It has the possibility to stop early
    • And it seems to move more data closer to the correct spot each time.
  • But it moves data around too much.
• Insertion Sort
  • The idea is to "insert" the newest item into the proper location

  • InsertionSort(A, size)
    
     for position = 1 to size-1
        tmp = A[position]
        candidate = position
        while candidate > 0 and A[candate-1] > tmp
          A[candidate] = A[candidate-1]
          candidate = candidate - 1 
        A[candidate] = tmp