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()