Searching Algorithms

• Searching problem: given an array of items, and key, determine if the key is present in the array.
  • The key is of the same type as the items in the array.
  • The key may or may not be present in the array.
• There are two basic searching algorithms:
  • Sequential search, for when the data is not ordered.
  • Binary search for when the data is ordered.
• Ordered means that there is some order applied to the data.
  • Usually that the items are ranked such that A[i] ≤ A[i+1] for all i between 0 and size-2.
• Sequential Search
  • Given an array A, a size s, and an item key, determine if key is present in A.

  • set position to 0
    set found to false
    while position < size and not found
       if  A[position] = key
          found = true
       else
           position = position + 1
    
    return found  (alternative, return position)
           

• Consider:

  • Index	Data
    0	dog
    1	fox
    2	ant
    3	cat
    4	rat

  • Size = 5
  • Search for dog
  • Search for rat
  • Search for ant
  • Search for cow.
• Binary Search
  • Again, this assumes that the items are ordered

  • Index	Data
    0	ant
    1	cat
    2	dog
    3	fox
    4	rat

  • Size = 5
  • Given an ordered array A, a size s, and an item key, determine if key is present in A.

  • set first to 0
    set last to size-1
    set found to false
    while first ≤ last and not found
        mid = (first + last) /2
        if A[mid] == key
           found = true
        else if A[mid]  < key
           first = mid+1
        else
           last = mid-1
           

• Trace this and look for
  • ant, cat, dog, fox, rat
  • aaa, zzz, egg, cow
• Can you describe, in English, how this search works?
• Discuss performance.