Searching

• Searching is possible in arrays.
• A search takes an array and a key
  • And returns the position of the key in the array
  • Or some pre-arranged value indicating the key is not in the array
    • -1 is good
    • Or the size of the array.
  • Sometimes the function only returns a bool indicating if the value is in the array or not.
• There are really two searching strategies
  • Linear or sequential search.
  • Binary search, but this requires the array to be ordered, so we will not discuss it yet.
• Sequential search
  • Assumes nothing about the array.
  • Input: array, array size, key
  • Output: location of the key in the array or the size.
• Algorithm

• Search(A, size, key) 
  
   found = false;
   pos = 0
   while pos < size and not found
       if A[pos] == key
          found = true
       else 
          ++pos
   return pos;
  
      

• Implement this.
• Find the number of unique words in a file. Assume less than 1000 unique words.
• Performance
  • When we evaluate the speed of algorithms, we generally look at
    • The worst case.
    • In terms of the size of the input.
  • For this algorithm, the size of the input is the size of the array.
  • And the worst case is we do not find it.
  • In general, we try to find a polynomial to represent the number of operation.
    • $T(n) = 6n + 3$
    • But we throw away all but the highest term of the polynomial.
    • For this case $O(n) = n$
• Sequential search is $O(n)$.