What does O 1 access time mean

Question

I have seen this term  O 1  access time  used to mean  quickly  but I don t understand what it means  The other term that I see with it in the same context is  O n  access time   Could someone please explain in a simple way what these terms mean      See Also         What is Big O notation  Do you use it    Big-O for Eight Year Olds

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According to my perspective   O 1  means time to execute one operation or instruction at a time is one  in time complexity analysis of algorithm for best case

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It means that the access takes constant time i e  does not depend on the size of the dataset  O n  means that the access will depend on the size of the dataset linearly    The O is also known as big-O

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Here is a simple analogy  Imagine you are downloading movies online  with O 1   if it takes 5 minutes to download one movie  it will still take the same time to download 20 movies  So it doesn t matter how many movies you are downloading  they will take the same time 5 minutes  whether it s one or 20  movies  A normal example of this analogy is when you go to a movie library  whether you are taking one movie or 5  you will simply just pick them at once  Hence spending the same time   However  with O n   if it takes 5 minutes to download one movie  it will take about 50 minutes to download 10 movies  So time is not constant or is somehow proportional to the number of movies you are downloading

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Basically  O 1  means its computation time is constant  while O n  means it will depend lineally on the size of input - i e  looping through an array has O n  - just looping -  because it depends on the number of items  while calculating the maximum between to ordinary numbers has O 1    Wikipedia might help as well  http   en wikipedia org wiki Computational complexity theory

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Big O notation  is a way to express the speed of algorithms  n is the amount of data the algorithm is working with  O 1  means that  no matter how much data  it will execute in constant time  O n  means that it is proportional to the amount of data

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Every answer currently responding to this question tells you that the O 1  means constant time  whatever it happens to measuring  could be runtime  number of operations  etc    This is not accurate   To say that runtime is O 1  means that there is a constant c such that the runtime is bounded above by c  independent of the input  For example  returning the first element of an array of n integers is O 1    int firstElement int  a  int n        return a 0       But this function is O 1  too   int identity int i        if i    0            sleep 60   60   24   365             return i      The runtime here is bounded above by 1 year  but most of the time the runtime is on the order of nanoseconds   To say that runtime is O n  means that there is a constant c such that the runtime is bounded above by c   n  where n measures the size of the input  For example  finding the number of occurrences of a particular integer in an unsorted array of n integers by the following algorithm is O n    int count int  a  int n  int item        int c   0      for int i   0  i  lt  n  i              if a i     item  c              return c      This is because we have to iterate through the array inspecting each element one at a time

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O 1  means Random Access  In any Random Access Memory  the time taken to access any element at any location is the same  Here time can be any integer  but the only thing to remember is time taken to retrieve the element at  n-1 th or nth location will be same ie constant    Whereas O n  is dependent on the size of n

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It s called the Big O notation  and describes the search time for various algorithms   O 1  means that the worst case run time is constant  For most situation it means that you dont acctually need to search the collection  you cand find what you are searching for right away

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Introduction to Algorithms  Second Edition by Cormen  Leiserson  Rivest  amp  Stein says on page 44 that      Since any constant is a degree-0   polynomial  we can express any   constant function as Theta n 0   or   Theta 1    This latter notation is a   minor abuse  however  because it is   not clear what variable is tending to   infinity   We shall often use the   notation Theta 1  to mean either a   constant or a constant function with   respect to some variable      We   denote by O g n      the set of   functions f n  such that there exist   positive constants c and n0 such  that   0  lt   f n   lt   c g n  for all n    n0         Note that f n    Theta g n     implies f n    O g n    since Theta   notation is stronger than O notation    If an algorithm runs in O 1  time  it means that asymptotically doesn t depend upon any variable  meaning that there exists at least one positive constant that when multiplied by one is greater than the asymptotic complexity   runtime  of the function for values of n above a certain amount  Technically  it s O n 0  time

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O 1  always execute in the same time regardless of dataset n  An example of O 1  would be an ArrayList accessing its element with index   O n  also known as Linear Order  the performance will grow linearly and in direct proportion to the size of the input data  An example of O n  would be an ArrayList insertion and deletion at random position  As each subsequent insertion deletion at random position will cause the elements in the ArrayList to shift left right of its internal array in order to maintain its linear structure  not to mention about the creation of a new arrays and the copying of elements from the old to new array which takes up expensive processing time hence  detriment the performance

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It means that access time is constant  Whether you re accessing from 100 or 100 000 records  the retrieval time will be the same   In contrast  O n  access time would indicate that the retrieval time is directly proportional to the number of records you re accessing from

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O 1  does not necessarily mean  quickly    It means that the time it takes is constant  and not based on the size of the input to the function   Constant could be fast or slow   O n  means that the time the function takes will change in direct proportion to the size of the input to the function  denoted by n   Again  it could be fast or slow  but it will get slower as the size of n increases

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You re going to want to read up on Order of complexity   http   en wikipedia org wiki Big O notation  In short  O 1  means that it takes a constant time  like 14 nanoseconds  or three minutes no matter the amount of data in the set   O n  means it takes an amount of time linear with the size of the set  so a set twice the size will take twice the time   You probably don t want to put a million objects into one of these

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O 1  means the time to access something is independent of the number of items in the collection   O N  would mean the time to access an item is a proportional to the number  N  of items in the collection

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The easiest way to differentiate O 1  and O n  is comparing array and list   For array  if you have the right index value  you can access the data instantly   If you don t know the index and have to loop through the array  then it won t be O 1  anymore   For list  you always need to loop through it whether you know the index or not

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In essence  It means that it takes the same amount of time to look up a value in your collection whether you have a small number of items in your collection or very very many  within the constraints of your hardware   O n  would mean that the time it takes to look up an item is proportional to the number of items in the collection     Typical examples of these are arrays  which can be accessed directly  regardless of their size  and linked lists  which must be traversed in order from the beginning to access a given item   The other operation usually discussed is insert   A collection can be O 1  for access but O n  for insert   In fact an array has exactly this behavior  because to insert an item in the middle  You would have to move each item to the right by copying it into the following slot

[big-o] What does "O(1) access time" mean?

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