遍历数组列表的时间复杂度

Question

I have an array list which I iterate through. In each iteration I call get() to get one element, and if that item passes some condition, it is added to a new array list using add()

List<Item> items = new ArrayList<Item>();
List<Item> lessItems = new ArrayList<Item>();
for(int index = 0; index < items.size(); index++){
    Item toCheck = items.get(i);
    if(toCheck meets some condition){
        lessItems.add(toCheck);
    }
}

I am not sure what the time complexity is here. I am calling get() on all items so that is O(n). Then I am also calling add() on potentially all the items so there's another O(n). Not too sure on this one.

Answer 1

1. Your first loop for iterating items list: complexity is O(n)
2. Insert each item to end of list lessItems : in normal array it will be O(n) as others said. But Java implements for ArrayList using amortized array . This means when inserting at the end of array, algorithm only costs Amortized O(1) . Or you can say O(1)

So complexity of your code is: O(n) * amortized O(1) . In short is O(n)

Another reference:

dynamic array

Additional note 1:

If complexity of inserting at the end of array is O(N) , so the total complexity is O(N^2) , not O(2*N) as other answers said. Because the total complexity for inserting would be: 1 + 2 + 3 + ...+ n = n*(n+1)/2

Addtional Note 2:

as official document states:

The size, isEmpty, get, set, iterator, and listIterator operations run in constant time. The add operation runs in amortized constant time , that is, adding n elements requires O(n) time. All of the other operations run in linear time (roughly speaking). The constant factor is low compared to that for the LinkedList implementation.

Additional note 3:

Here is the logic of grow method that I have taken from official java source code:

private void ensureExplicitCapacity(int minCapacity) {
        modCount++;

        // overflow-conscious code
        if (minCapacity - elementData.length > 0)
            grow(minCapacity);
    }

private void grow(int minCapacity) {
        // overflow-conscious code
        int oldCapacity = elementData.length;
        int newCapacity = oldCapacity + (oldCapacity >> 1);
        if (newCapacity - minCapacity < 0)
            newCapacity = minCapacity;
        if (newCapacity - MAX_ARRAY_SIZE > 0)
            newCapacity = hugeCapacity(minCapacity);
        // minCapacity is usually close to size, so this is a win:
        elementData = Arrays.copyOf(elementData, newCapacity);
    }

As the source code has said, when program add element that make size of array larger than current capacity, Array will be grown. new size of grown array will be:

int newCapacity = oldCapacity + (oldCapacity >> 1);

This is a trick that make inserting is amortized O(1)

Answer 2

You are doing an iteration, and that's of O(n).

You're also adding items to an ArrayList, which is of O(1) ( Amortized )

Getting an index is also O(1).

So your doing O(n) times, operations of O(1), which is going to be of O(n) .

Answer 3

Big-O and similar notations are asymptotic bounds on time complexity. They discard the numeric coefficient and are used to estimate run-time as a function of size of input.

So, 2*n , 3*n ,etc. are represented as O(n) , and 2*nlog(n) , 3*nlog(n) ,etc. are represented as O(nlog(n)) .

Since the add() operation inserts only one element in this case, its runtime is approximately, (some small constant)k*1 , giving the total runtime as (some constant)j*(n+some constant(k)) , in other words j*n , or O(n) .

In this case and all such similar cases, any constant k multiplied by n would be represented as O(n) meaning the runtime varies linearly with size of the input ArrayList.

Answer 4

For iterating through the array list, the time complexity will be O(n). n will be the size of the list.

for getting the value using get(), it will be O(1), random access is possible in array list using index.

And for adding the values using add(), the value is getting added at the last, so it will be O(1).

The time complexity of this operation will be O(n).