Why is array considered a data structure ? How is array a data structure in tetms of efficiency? Please explain by giving some examples
It's a data structure because it's collection of data and the tools to work it.
Primary features:
Extremely fast lookup by index.
Extremely fast index-order traversal.
Minimal memory footprint (not so with the optional modifications I mentioned).
Insertion is normally O(N) because you may need to copy the array when you reallocate the array to make space for new elements. However, you can bring the cost of appending down to amortized O(1) by over-allocating (i.e. by doubling the size of the array every time you reallocate).[1]
Deletion is O(N) because you will need to shift N/2 elements on average. You could keep track the number of unused elements at the start and end of the array to make removals from the ends O(1).[1]
Lookup by index is O(1). It's a simple pointer addition.
Lookup by value is O(N). If the data is ordered, one can use a binary search to reduce this to O(log N).
Keeping track of the first used element and the last used element would technically qualify as a different data structure because the functions to access the data structure are different, but it would still be called an array.
Can anyone explain the time complexity of (deletion at ending in dynamic array)?
I think the answer is O(1)
But in book its mentioned O(n).
Since we are talking about dynamic arrays, that is, arrays with the ability to add/remove elements to/from them, there are two possible solutions to implement a dynamic array:
You allocate enough memory to hold all the current and future elements. Also, you need to know the last possible index. Using this setup, the complexity of removing the last element is O(1), since you just decrement the last index. However, removing a non-last element has a linear complexity, since you need to copy all the later elements to the previous before you decrement the last index. Also, you might have difficulty in identifying the maximum possible size at allocation time, possibly leading to overflow issues or memory waste.
You can implement it using a list. This way you will not know what the address of the last element is, so you will need to iterate your list till the penultimate item and then free the memory of the last item and set the next of the penultimate item to point to nil. Since the book mentioned a complexity of O(n) to remove the last element, we can safely assume that by dynamic array, the book meant this second option.
In C, which is more efficient in terms of memory management, a linked list or an array?
For my program, I could use one or both of them. I would like to take this point into consideration before starting.
Both link list and array have good and bad sides.
Array
Accessing at a particular position take O(1) time, because memory initialized is consecutive for array. So if address of first position is A, then address of 5th element if A+4.
If you want to insert a number at some position it will take O(n) time. Because you have to shift every single numbers after that particular position and also increase size of array.
About searching an element. Considering the array is sorted. you can do a binary search and accessing each position is O(1). So you do the search in order of binary search. In case the array is not sorted you have to traverse the entire array so O(n) time.
Deletion its the exact opposite of insertion. You have to left shift all the numbers starting from the place where you deleted it. You might also need to recrete the array for memory efficiency. So O(n)
Memory must be contiguous, which can be a problem on old x86 machines
with 64k segments.
Freeing is a single operation.
LinkList
Accessing at a particular position take O(n) time, because you have to traverse the entire list to get to a particular position.
If you want to insert a number at some position and you have a pointer at that position already, it will take O(1) time to insert the new value.
About searching an element. No matter how the numbers are arranged you have to traverse the numbers from front to back one by one to find your particular number. So its always O(n)
about deletion its the exact opposite of insertion. If you know the position already by some pointer suppose the list was like this . p->q->r you want to delete q all you need is set next of p to r. and nothing else. So O(1) [Given you know pointer to p]
Memory is dispersed. With a naive implementation, that can be bad of cache coherency, and overall take can be high because the memory allocation system has overhead for each node. However careful programming can get round this problem.
Deletion requires a separate call for each node, however again careful programming can get round this problem.
So depending on what kind of problem you are solving you have to choose one of the two.
Linked list uses more memory, from both the linked list itself and inside the memory manager due to the fact you are allocating many individual blocks of memory.
That does not mean it is less efficient at all, depending on what you are doing.
While a linked list uses more memory, adding or removing elements from it is very efficient, as it doesn't require moving data around at all, while resizing a dynamic array means you have to allocate a whole new area in memory to fit the new and modified array with items added/removed. You can also sort a linked list without moving it's data.
On the other hand, arrays can be substantially faster to iterate due to caching, path prediction etc, as the data is placed sequentially in memory.
Which one is better for you will really depend on the application.
In the worst case while appending an element(inserting at end) array can be full. So a new array is created and n elements are copied from this array to the new array.
I read in literature that worst case time complexity of this operation is O(1), why so? shouldn't it be O(n)?
I did read this question. But did not make any sense to me!
The operation itself is O(n).
If you get the average operations per element, you get O(1), this is the amortized cost.
See more at http://en.wikipedia.org/wiki/Amortized_analysis
I see it the same way that you do.
If it was a List, then it was O(1) to add an element at the end.
But in the case of an array, if it´s full you need to create a new one, copy all the elements in the old array, and then add the new element.
For me it´s O(n) too.
In case of static list/array the time complexity must be O(n), but in case of dynamic array/list, the time complexity comes O(1) because in dynamic array there is a facility to allocate extra memory for the append operation .
I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list. I was hoping someone could give me some examples of when the linked list is notably better.
Linked lists are preferable over arrays when:
you need constant-time insertions/deletions from the list (such as in real-time computing where time predictability is absolutely critical)
you don't know how many items will be in the list. With arrays, you may need to re-declare and copy memory if the array grows too big
you don't need random access to any elements
you want to be able to insert items in the middle of the list (such as a priority queue)
Arrays are preferable when:
you need indexed/random access to elements
you know the number of elements in the array ahead of time so that you can allocate the correct amount of memory for the array
you need speed when iterating through all the elements in sequence. You can use pointer math on the array to access each element, whereas you need to lookup the node based on the pointer for each element in linked list, which may result in page faults which may result in performance hits.
memory is a concern. Filled arrays take up less memory than linked lists. Each element in the array is just the data. Each linked list node requires the data as well as one (or more) pointers to the other elements in the linked list.
Array Lists (like those in .Net) give you the benefits of arrays, but dynamically allocate resources for you so that you don't need to worry too much about list size and you can delete items at any index without any effort or re-shuffling elements around. Performance-wise, arraylists are slower than raw arrays.
Arrays have O(1) random access, but are really expensive to add stuff onto or remove stuff from.
Linked lists are really cheap to add or remove items anywhere and to iterate, but random access is O(n).
Algorithm ArrayList LinkedList
seek front O(1) O(1)
seek back O(1) O(1)
seek to index O(1) O(N)
insert at front O(N) O(1)
insert at back O(1) O(1)
insert after an item O(N) O(1)
ArrayLists are good for write-once-read-many or appenders, but bad at add/remove from the front or middle.
To add to the other answers, most array list implementations reserve extra capacity at the end of the list so that new elements can be added to the end of the list in O(1) time. When the capacity of an array list is exceeded, a new, larger array is allocated internally, and all the old elements are copied over. Usually, the new array is double the size of the old one. This means that on average, adding new elements to the end of an array list is an O(1) operation in these implementations. So even if you don't know the number of elements in advance, an array list may still be faster than a linked list for adding elements, as long as you are adding them at the end. Obviously, inserting new elements at arbitrary locations in an array list is still an O(n) operation.
Accessing elements in an array list is also faster than a linked list, even if the accesses are sequential. This is because array elements are stored in contiguous memory and can be cached easily. Linked list nodes can potentially be scattered over many different pages.
I would recommend only using a linked list if you know that you're going to be inserting or deleting items at arbitrary locations. Array lists will be faster for pretty much everything else.
The advantage of lists appears if you need to insert items in the middle and don't want to start resizing the array and shifting things around.
You're correct in that this is typically not the case. I've had a few very specific cases like that, but not too many.
It all depends what type of operation you are doing while iterating , all data structures have trade off between time and memory and depending on our needs we should choose the right DS. So there are some cases where LinkedList are faster then array and vice versa . Consider the three basic operation on data structures.
Searching
Since array is index based data structure searching array.get(index) will take O(1) time while linkedlist is not index DS so you will need to traverse up to index , where index <=n , n is size of linked list , so array is faster the linked list when have random access of elements.
Q.So what's the beauty behind this ?
As Arrays are contiguous memory blocks, large chunks of them will be loaded into the cache upon first access this makes it comparatively quick to access remaining elements of the array,as much as we access the elements in array locality of reference also increases thus less catch misses, Cache locality refers to the operations being in the cache and thus execute much faster as compared to in memory,basically In array we maximize the chances of sequential element access being in the cache. While Linked lists aren't necessarily in contiguous blocks of memory, there's no guarantee that items which appear sequentially in the list are actually arranged near each-other in memory, this means fewer cache hits e.g. more cache misses because we need to read from memory for every access of linked list element which increases the time it takes to access them and degraded performance so if we are doing more random access operation aka searching , array will be fast as explained below.
Insertion
This is easy and fast in LinkedList as insertion is O(1) operation in LinkedList (in Java) as compared to array, consider the case when array is full, we need to copy contents to new array if array gets full which makes inserting an element into ArrayList of O(n) in worst case, while ArrayList also needs to update its index if you insert something anywhere except at the end of array , in case of linked list we needn't to be resize it, you just need to update pointers.
Deletion
It works like insertions and better in LinkedList than array.
Those are the most common used implementations of Collection.
ArrayList:
insert/delete at the end generally O(1) worst case O(n)
insert/delete in the middle O(n)
retrieve any position O(1)
LinkedList:
insert/delete in any position O(1) (note if you have a reference to the element)
retrieve in the middle O(n)
retrieve first or last element O(1)
Vector: don't use it. It is an old implementation similar to ArrayList but with all methods synchronized. It is not the correct approach for a shared list in a multithreading environment.
HashMap
insert/delete/retrieve by key in O(1)
TreeSet
insert/delete/contains in O(log N)
HashSet
insert/remove/contains/size in O(1)
In reality memory locality has a huge performance influence in real processing.
The increased use of disk streaming in "big data" processing vs random access shows how structuring your application around this can dramatically improve performance on a larger scale.
If there is any way to access an array sequentially that is by far the best performing. Designing with this as a goal should be at least considered if performance is important.
I think that main difference is whether you frequently need to insert or remove stuff from the top of the list.
With an array, if you remove something from the top of list than the complexity is o(n) because all of the indices of the array elements will have to shift.
With a linked list, it is o(1) because you need only create the node, reassign the head and assign the reference to next as the previous head.
When frequently inserting or removing at the end of the list, arrays are preferable because the complexity will be o(1), no reindexing is required, but for a linked list it will be o(n) because you need to go from the head to the last node.
I think that searching in both linked list and arrays will be o(log n) because you will be probably be using a binary search.
Hmm, Arraylist can be used in cases like follows I guess:
you are not sure how many elements will be present
but you need to access all the elements randomly through indexing
For eg, you need to import and access all elements in a contact list (the size of which is unknown to you)
Use linked list for Radix Sort over arrays and for polynomial operations.
1) As explained above the insert and remove operations give good performance (O(1)) in LinkedList compared to ArrayList(O(n)). Hence if there is a requirement of frequent addition and deletion in application then LinkedList is a best choice.
2) Search (get method) operations are fast in Arraylist (O(1)) but not in LinkedList (O(n)) so If there are less add and remove operations and more search operations requirement, ArrayList would be your best bet.
I did some benchmarking, and found that the list class is actually faster than LinkedList for random inserting:
using System;
using System.Collections.Generic;
using System.Diagnostics;
namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
int count = 20000;
Random rand = new Random(12345);
Stopwatch watch = Stopwatch.StartNew();
LinkedList<int> ll = new LinkedList<int>();
ll.AddLast(0);
for (int i = 1; i < count; i++)
{
ll.AddBefore(ll.Find(rand.Next(i)),i);
}
Console.WriteLine("LinkedList/Random Add: {0}ms", watch.ElapsedMilliseconds);
watch = Stopwatch.StartNew();
List<int> list = new List<int>();
list.Add(0);
for (int i = 1; i < count; i++)
{
list.Insert(list.IndexOf(rand.Next(i)), i);
}
Console.WriteLine("List/Random Add: {0}ms", watch.ElapsedMilliseconds);
Console.ReadLine();
}
}
}
It takes 900 ms for the linked list and 100ms for the list class.
It creates lists of subsequent integer numbers. Each new integer is inserted after a random number which is already in the list.
Maybe the List class uses something better than just an array.
Arrays, by far, are the most widely used data structures. However, linked lists prove useful in their own unique way where arrays are clumsy - or expensive, to say the least.
Linked lists are useful to implement stacks and queues in situations where their size is subject to vary. Each node in the linked list can be pushed or popped without disturbing the majority of the nodes. Same goes for insertion/deletion of nodes somewhere in the middle. In arrays, however, all the elements have to be shifted, which is an expensive job in terms of execution time.
Binary trees and binary search trees, hash tables, and tries are some of the data structures wherein - at least in C - you need linked lists as a fundamental ingredient for building them up.
However, linked lists should be avoided in situations where it is expected to be able to call any arbitrary element by its index.
A simple answer to the question can be given using these points:
Arrays are to be used when a collection of similar type data elements is required. Whereas, linked list is a collection of mixed type data linked elements known as nodes.
In array, one can visit any element in O(1) time. Whereas, in linked list we would need to traverse entire linked list from head to the required node taking O(n) time.
For arrays, a specific size needs to be declared initially. But linked lists are dynamic in size.