What does "access time O (1)" mean?

Question

I saw that the term "access time O (1)" means "fast", but I do not understand what it means. Another term that I see with him in the same context is "access time O (n)". Can someone explain a simple way what these terms mean?

see also

• What is a Big O Note? Do you use it?
• Big-O for eight year olds?

Answer 1

You want to read the Order of Difficulty.

http://en.wikipedia.org/wiki/Big_O_notation

In short, O (1) means that it takes a constant time, such as 14 nanoseconds, or three minutes, regardless of the amount of data in the set.

O (n) means that it takes a certain amount of time, linear with the size of the set, so the set is two times the size of two. You probably don't want to put a million objects in one of them.

Answer 2

In essence, this means that finding the value in your collection takes as much time as you have a small number of items in your collection or a lot (within the limits of your equipment)

O (n) means that the time required to search for an element is proportional to the number of elements in the collection.

Typical examples of this are arrays that can be accessed directly, regardless of their size and related lists, which must be traversed in order from the beginning to access this element.

Another operation commonly discussed is insertion. The collection may be O (1) for access, but O (n) for insertion. Actually, the array has exactly this behavior, because to insert an element in the middle you will need to move each element to the right by copying it to the next slot.

Answer 3

Each answer that answers this question tells you that O(1) means constant time (no matter what happens with the measurement, there may be a runtime, the number of operations, etc.). This is not true.

To say that the runtime is O(1) means that there is a constant c , so that the runtime is limited above c , regardless 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 also O(1) :

 int identity(int i) { if(i == 0) { sleep(60 * 60 * 24 * 365); } return i; } 

The lead time here is limited to 1 year, but in most cases, the lead time is of the order of nanoseconds.

To say that the runtime is O(n) means that there is a constant c , so the runtime is limited above c * n , where n measures the size of the input. For example, searching for the number of occurrences of a certain integer in an unsorted array of integers n using the following algorithm: O(n) :

 int count(int *a, int n, int item) { int c = 0; for(int i = 0; i < n; i++) { if(a[i] == item) c++; } return c; } 

This is because we have to go through the array, checking each element one at a time.

Answer 4

O (1) does not necessarily mean fast. This means that the time it takes is constant and not based on the size of the input function. A constant can be fast or slow. O (n) means that the time the function takes will vary in direct proportion to the size of the function input, denoted by n. Again, this may be fast or slow, but it will slow down as size n increases.

Answer 5

O (1) means that the access time to something does not depend on the number of elements in the collection.

O (N) means that the access time to an item is proportional to the number (N) of items in the collection.

Answer 6

He called the Big O notation and describes the search time for various algorithms.

O (1) means that the execution time of the worst case is constant. For most situations, this means that you do not need to look for a collection, you can quickly find what you are looking for.

Answer 7

Big Notation is a way to express the speed of algorithms. n is the amount of data the algorithm works with. O(1) means that no matter how much data it will run for a constant time. O(n) means that it is proportional to the amount of data.

Answer 8

Basically, O (1) means that its calculation time is constant, and O (n) means that it will depend on the size of the input, i.e. a loop through an array has O (n) - just a loop - because it depends on the number of elements, and when calculating the maximum between ordinary numbers, it has O (1).

Wikipedia can also help: http://en.wikipedia.org/wiki/Computational_complexity_theory

Answer 9

O(1) always executed at the same time regardless of the data set n. An example of O (1) would be an ArrayList receiving its element with an index.

O(n) , also known as linear ordering, productivity will grow linearly and in direct proportion to the size of the input data. An example of O (n) would be inserting and deleting an ArrayList at a random position. Since each subsequent insertion / deletion in a random position will cause the elements in the ArrayList to move left and right from the internal array to preserve their linear structure, not to mention creating new arrays and copying elements from the old to a new array, which requires costly processing time and reduces productivity.

Answer 10

This means that access time is constant. If you access 100 or 100,000 records, the search time will be the same.

In contrast, access time O (n) indicates that the search time is directly proportional to the number of records you are accessing.

Answer 11

This means that access takes a constant time, that is, it does not depend on the size of the data set. O (n) means that access will depend on the size of the data set linearly.

O is also known as Big-O.

Answer 12

The easiest way to distinguish between O (1) and O (n) is to compare the array and list.

For an array, if you have the correct index value, you can instantly access the data. (If you do not know the index and must pass through the array, then it will no longer be O (1))

For a list, you always need to scroll through it whether you know the index or not.

Answer 13

Introduction to Algorithms: Second Edition of Cormen, Leiserson, Rivest, and 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 last designation is a minor abuse, however, since it is unclear which variable tends to infinity. We often use the notation Theta (1) means either a constant or constant function with respect to some variable .... We denote by O (g (n)) ... the set of the function f (n) such that there exist positive constants c and n0 such that 0 <= f (n) <= c * g (n) for all n> = n0 .... Note that f (n) = Theta (g (n)) means f (n) = O (g (n)), since Theta notation is stronger than the notation O.

If the algorithm runs O (1) times, this means that it is asymptotically independent of any variable, which means that there is at least one positive constant, which, when multiplied by one, is greater than the asymptotic complexity (~ runtime ) functions for values ​​of n above a certain value. Technically, this time is O (n ^ 0).

Answer 14

O (1) means random access. In any random access memory, the time taken to access any item anywhere is the same. Here, the time can be any integer, but the only thing to remember is the time taken to extract the element in (n-1) th or n-th place will be the same (i.e. constant).

While O (n) depends on the size of n.

Answer 15

According to my perspective

O (1) means that the time to complete one operation or command at a time is one, when analyzing the time complexity of the algorithm for the best case.