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Questions tagged [asymptotic-complexity]

Asymptotic complexity is an approximation of the edge case performance of an algorithm used to determine best and worst case scenarios.

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Calculating work done by f x = (x,x)

Let's say I have this function: (Haskell syntax) f x = (x,x) What is the work (amount of calculation) performed by the function? At first I thought it was obviously constant, but what if the type of x is not finite, meaning, x can take an arbitrary…
Guido
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Accessing Elements - Really O(1)?

It is said that an example of a O(1) operation is that of accessing an element in an array. According to one source, O(1) can be defined in the following manner: [Big-O of 1] means that the execution time of the algorithm does not depend on the…
Mr Chasi
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Solve: T(n) = T(n/2) + n/2 + 1

I struggle to define the running time for the following algorithm in O notation. My first guess was O(n), but the gap between the iterations and the number I apply isn't steady. How have I incorrectly defined this? public int function (int n ) { …
sra
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Time complexity of the program using recurrence equation

I want to find out the time complexity of the program using recurrence equations. That is .. int f(int x) { if(x<1) return 1; else return f(x-1)+g(x); } int g(int x) { if(x<2) return 1; else return f(x-1)+g(x/2); } I write its recurrence…
siddstuff
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If f(n)=O(g(n)), then shouldn't f(n)∗log2(f(n)^c)=O(g(n)∗log2(g(n))) depend on the value of C?

If f(n)=O(g(n)), then shouldn't f(n)∗log2(f(n)^c)=O(g(n)∗log2(g(n))) depend on the value of C? Here C is a positive constant. According to me if C is large then the statement would become false and if c is small it'd be true. Hence the outcome is…
Charu
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What is the resizing factor of lists in Python

For example, ArrayLists in Java have a resizing factor of 2. When the array that the ArrayList is wrapped around runs out of space, all the elements of that array are transferred to a new array that is 2 times the size of the original array. Since…
TomLisankie
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Is there any implementation to Remove by Key and get the Value at the same time?

I'm doing a performance critical program (little academic stuff) and I'm looking to optimize wherever possible (not like it proved "this is the" bottleneck). I have a custom dictionary structure (a wrapper around .NET Dictionary<,>) and I would…
nawfal
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Hash Collision Linear Probing Running Time

I am trying to do homework with a friend and one question asks the average running time of search, add, and delete for the linear probing method. I think it's O(n) because it has to check at certain number of nodes until it finds an open one to add.…
Richard
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When do floors and ceilings matter while solving recurrences?

I came across places where floors and ceilings are neglected while solving recurrences. Example from CLRS (chapter 4, pg.83) where floor is neglected: Here (pg.2, exercise 4.1–1) is an example where ceiling is ignored: (EDIT: I gather from public…
Tejas Patil
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Can it be proved that call-by-need has the minimal asymptotic time complexity among all reduction strategies?

When I read the Church Rosser II Theorem here Theorem (Church Rosser II) If there is one terminating reduction, then outermost reduction will terminate, too. I'm wondering: Is there some theorem which strengthens the Church Rosser II Theorem so…
luochen1990
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Is there a programmatic way or eclipse plugin to calculate big O notation for java method

Is there a programmatic way or eclipse plugin to calculate big-O notation for java method ?
Amgad Hanafy
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Find the next greater element in an array

Given an array , for every element I need to find the smallest element to the right of the given element which is greater than the current element. Mathematically, For every index i in array A, I need to find index j such that A[j] > A[i] j > i A[j]…
Sam Radhakrishnan
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Why is SortedDictionary.GetEnumerator O(log n) but SortedSet.GetEnumerator O(1)?

From the SortedSet.GetEnumerator documentation: This method is an O(1) operation From the SortedDictionary.GetEnumerator documentation: This method is an O(log n) operation, where n is count. Can both the statements be true,…
nawfal
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Complexity of the recursion: T(n) = T(n-1) + T(n-2) + C

I want to understand how to arrive at the complexity of the below recurrence relation. T(n) = T(n-1) + T(n-2) + C Given T(1) = C and T(2) = 2C; Generally for equations like T(n) = 2T(n/2) + C (Given T(1) = C), I use the following method. T(n) =…
Gopal
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The time complexity of counting sort

I am taking an algorithms course and there I saw that the time complexity of counting sort is O(n+k) where k is the range of numbers and n is the input size. My question is, when the difference between k and n is too much, such as when k=O(n2)or…
user2110714
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