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.
Related
I got this interview question I think is impossible.
If you have an array and you must in place remove all unique elements from it in place while keeping the order and with no extra memory.
E.g.
input = [1,1,2,3,4,3,4]
output = [1,1,3,4,3,4]
I tried, sorting, but you have to keep the items in place.
Two pointers, which are O(n^2) and counters which use extra memory but those weren't efficient enough.
Maybe something with bit flips?
as we know, the time complexity of deleting an array element is o(n), so what is the time complexity of deleting the entire array?
i think is o(1), because the array address space is continuous. is my guess correct?
Deleting the array itself would be O(1) because it would simply release the memory to the pool while deleting every item in the array would be O(n) because each item needs to be removed individually.
There are exceptions, some implementations may for example use an algorithm that clears memory in chunks larger than the size of each item in the array (which would be O(n/c) where c is how many times bigger a chunk is compared to an item in the array), and some languages might simply release the original array and have pointers point to a new empty array which would be O(1). The above answer however is assuming a naive implementation.
I am learning about arrays, single linked list and double linked list now a days and this question came that
" What is the best option between these three data structures when it comes to fast searching, less memory, easily insertion and updating of things "
As far I know array cannot be the answer because it has fixed size. If we want to insert a new thing. it wouldn't always be possible. Double linked list can do the task but there will be two pointers needed for each node so there will be memory problem, so I think single linked list will fulfill all given requirements. Am I right? Please correct me if I am missing any point. There is also one more question that instead of choosing one of them, can I make combination of one or more data structures given here to meet all the requirements?
"What is the best option between these three data structures when it comes to fast searching, less memory, easily insertion and updating of things".
As far as I can tell Arrays serve the purpose.
Fast search: You could do binary search if array is sorted. You dont get that option in linkedlist
Less memory: Arrays will take least memory (but contiguous memory )
Insertion: Inserting in array is a matter of a[i] = "value". If array size is exceeded then simply export data into a new array. That is exactly how HashMaps / ArrayLists work under covers.
Updating things: Only Arrays provide you with Random access. a[i] ="new value".. updated in O(1) time if you know the index.
Each of those has its own benefits and downsides.
For search speed, I'd say arrays are better suitable due to the quick lookup times.
Since an array is a sequence of same-size elements, retrieving the value at an index is just memoryLocation + index * elementSize. For a linked list, the whole list needs traversing.
Arrays also win in the "less memory" category, since there's no need to store extra pointers.
For insertions, arrays are slow. You'll need to traverse the array, copy contents to a new array, assign the new array, delete the old one...
Insertions go much quicker in linked- or double lists, because it's just a matter of changing one or two pointers.
In the end, it all just depends on the use case. Are you inserting a lot? Then you probably want to consider a non-array structure.
Do you need many quick lookups? Consider those arrays again. Etc..
See also this question.
A linked list is usually the best choice when we don’t know in advance the number of elements we will have to store or the number can change dynamically.
Arrays have slow insertion and deletion times. To insert an element to the front or middle of the array, the first step is to ensure that there is space in the array for the new element, otherwise, the array needs to be RESIZED. This is an expensive operation. The next step is to open space for the new element by shifting every element after the desired index. Likewise, for deletion, shifting is required after removing an element. This implies that insertion time for arrays is Big O of n (O(n)) as n elements must be shifted.
Using static arrays, we can save some extra memory in
comparison to linked lists because we do not need to store pointers to the next node
a doubly-linked list support fast insertion/removal at their ends. This is used in LRU cache, where you need to enter new item to front and remove the oldest item from the end.
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.
I would like to write a piece of code for inserting a number into a sorted array at the appropriate position (i.e. the array should still remain sorted after insertion)
My data structure doesn't allow duplicates.
I am planning to do something like this:
Find the right index where I should be putting this element using binary search
Create space for this element, by moving all the elements from that index down.
Put this element there.
Is there any other better way?
If you really have an array and not a better data structure, that's optimal. If you're flexible on the implementation, take a look at AA Trees - They're rather fast and easy to implement. Obviously, takes more space than array, and it's not worth it if the number of elements is not big enough to notice the slowness of the blit as compared to pointer magic.
Does the data have to be sorted completely all the time?
If it is not, if it is only necessary to access the smallest or highest element quickly, Binary Heap gives constant access time and logn addition and deletion time.
More over it can satisfy your condition that the memory should be consecutive, since you can implement a BinaryHeap on top of an array (I.e; array[2n+1] left child, array[2n+2] right child).
A heap based implementation of a tree would be more efficient if you are inserting a lot of elements - log n for both locating/removing and inserting operations.