cs2381 Notes: 12 Array List

Midterm

The midterm exam will be in Lecture next Monday, October 2nd.

Arrays vs Cons Lists

ArrayList

We’ve seen arrays and the idea of a wrapper object.

Let’s add one more method:

    void append(T vv) {
        int ii = length();
        resize(ii + 1);
        set(ii, vv);
    }

Now we can fill an Array with items like this:

    var xs = new ArrayWrap<Integer>();
    for (int ii = 0; ii < 10; ++ii) {
       xs.append(vv); 
    }

Problem: What is the asymptotic complexity of that loop?

• What’s the complexity of xs.append?
• And we do that n times.

Counting inserts:

• 1 for first item.
• 1 for second, plus copy 1 = 2
• 1 + copy 2
• 1 + copy 3
• …
• 1 + copy (n-1)
• ~ O(n^2)

We can do better than that. Let’s write an ArrayList.

Trick:

• Add a length field, allowing the length of the ArrayList to be shorter than the length of the backing array.
• Grow by doubling the length of the backing array.

Now let’s try counting inserts.

• 1 for first item (cap = 1)

• 1 + 1 for second (cap = 2)

• 1 + 2 for third (but now cap = 4)

• just one for 4th

• = 7

• 1 + 4 for fifth (cap = 8)

• just 3 for next 3

• = 15 for 8th

• 1 + 8 for 9th (cap = 16)

• just 7 for next 7

• = 31 for 16th

• = 63 for 32

• = 127 for 64

• = 2*n-1 for n

• ~ O(n) to insert n

Let’s build (or at least describe) some more methods for ConsList and ArrayList:

• Insert after index
• Delete item
• Concatenate
• Split into two
• What if we don’t want to destroy the old one?