performance of a vector class

• I'm jumping ahead just a bit, section 3.4 of the book.
• What is the basic data behind a vector?
  • An array of objects.
  • A integer representing how many objects are present.

  • private:
       object * objects;
       int size;
           

• So push_back could be

  • Push_Back(E)
    
     Allocate a new array of objects one bigger.
     Copy all objects from the old array to the new one.
     Place E at the last location in the new array
     Delete the old array
    
         

  • What is the performance of this algorithm?
    • You can assume that lines 1 and 4 are constant time.
    • Then Line 2 is O(n) where n is the number of items in the array
  • We can assume the same performance for pop_back()
• What is tricky about an vector class?
  • Make sure push_back is not a O(n) operation.
  • Idea: Each time we need to, double the size of the array.
    • This will require an additional variable

    • private:
         object * objects;
         int size;
         int allocated;
             

    • size stores the number of elements in the array
    • allocated stores the number of spaces in the array.
    • Push_Back becomes

    • Push_Back(E)
      
       If size = allocated
          Allocate a new array of objects size*2.
          Copy all objects from the old array to the new one.
          Delete the old array
          allocated <- size*2
       objects[size] <- E
       size <- size + 1 
      
      

  • Compute the time for this algorithm.
  • Here we will consider the average case.
  • This will be done by amortized analysis.