Lecture 09 Ticket Solution

Complete before the beginning of class on Wednesday, 09/21

  1. Suppose \(a\) is an array of binary values of size \(n\). That is, for every index \(i\), we \(a[i] = 0\) or \(1\). Give pseudocode for a procedure that sorts \(a\) in \(O(n)\) time.

  2. Each row below represents a 12-bit binary integer (where the right most bit is the 1s bit, etc). Sort the list of numbers in ascending order.

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  110110100110
  100110001001
  001000101000
  101100111001
  000010001010
  111100011100
  101111001100
  010100010010
  011011100010

Solution

  1. Consider the following code:
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  BinarySort(a):
    i <- 1
	j <- size(a)
	while i < j do:
	  if a[i] = 1 and a[j] = 0 then
	    swap(a, i j)
		i <- i+1
		j <- j-1
	  else
	    if a[i] = 0 then i <- i+1
		if a[j] = 1 then j <- j-1
	  endif
	endwhile
  1. Here’s a sorted list:
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  111100011100
  110110100110
  101111001100
  101100111001
  100110001001
  011011100010
  010100010010
  001000101000
  000010001010