Data Structures & Algorithms in Java ---- Arrays

1、Summary
• Arrays in Java are objects, created with the new  operator. 
 
• Unordered arrays offer fast insertion but slow searching and deletion. 
   • Wrapping an array in a class protects the array from being inadvertently altered.       • A class interface comprises the methods (and occasionally fields)  that the class user can access.      • A class interface can be designed to make things simple for the class user.      • A binary search can be applied to an ordered array.       • The logarithm to the base B of a number A is (roughly) the number of times you can divide A by B before the result is less than 1.       • Linear searches require time proportional to the number of items in an array.       • Binary searches require time proportional to the logarithm of the number of items.       • Big O notation provides a convenient way to compare the speed of algorithms.       • An algorithm that runs in O(1) time is the best, O(log N) is good, O(N) is fair, and O(N2)  is pretty bad.  
2、Big O notation
Automobiles are divided by size into several categories: subcompacts, compacts, midsize, and so on. These categories provide a quick idea what size car you're talking about, without needing to mention actual dimensions. Similarly, it's useful to have a shorthand way to say how efficient a computer  algorithm is. In computer science, this rough measure is called Big O notation. 
3、Binary Search with the find() Method  

	public int find(double searchKey)
	{
		int lowerBound = 0;

		int upperBound = nElems - 1;

		int curIn;

		while (true)
		{
			curIn = (lowerBound + upperBound) / 2;

			if (a[curIn] == searchKey)
			{
				return curIn; // found it
			}
			else if (lowerBound > upperBound)
			{
				return nElems; // can't find it
			}
			else // divide range
			{
				if (a[curIn] < searchKey)
				{
					lowerBound = curIn + 1; // it's in upper half
				}
				else
				{
					upperBound = curIn - 1; // it's in lower half
				}

			} // end else divide range

		} // end while

	} // end find()