# Questions tagged [big-o]

The Big-O notation is used to represent asymptotic upper bounds. It describes relevant time or space complexity of algorithms. Big-O analysis provides a coarse and simplified estimate of a problem difficulty.

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### Change of the complexity class through compiler optimization?

I am looking for an example where an algorithm is apparently changing its complexity class due to compiler and/or processor optimization strategies.
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### Notation for the average time complexity of an algorithm

What notation do you use for the average time complexity of an algorithm? It occurs to me that the proper way would be to use big-theta to refer to a set of results (even when a specific try may ...
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### How meaningful is the Big-O time complexity of an algorithm?

Programmers often talk about the time complexity of an algorithm, e.g. O(log n) or O(n^2). Time complexity classifications are made as the input size goes to infinity, but ironically infinite input ...
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### Is this a Proper “Rule” for Identifying the “Big O” Notation of an Algorithm?

I've been learning more about Big O Notation and how to calculate it based on how an algorithm is written. I came across an interesting set of "rules" for calculating an algorithms Big O notation and ...
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### Constants and Big O [duplicate]

Are constants always irrelevant even if they are large? For example is O(10^9 * N) == O(N) ?
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### Problems Calculating Big-O Complexity

I'm a complete beginner to Java, only in my second quarter of classes. I'm having trouble understanding our current chapter about calculating big-O for methods. So I thought I was right in saying that ...
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### Finding the time complexity of the following program that uses recursion

I need to find the time complexity in terms of Big Oh notation for the following program which computes the factorial of a given number: The program goes like this: public int fact(int n){ if (n &...
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### Help with algorithmic complexity in custom merge sort implementation

I've got an implementation of the merge sort in C++ using a custom doubly linked list. I'm coming up with a big O complexity of n^2, based on the merge_sort() > slice operation. But, from what I've ...
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### Big Oh notation does not mention constant value

I am a programmer and have just started reading Algorithms. I am not completely convinced with the notations namely Bog Oh, Big Omega and Big Theta. The reason is by definition of Big Oh, it states ...
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### Programmaticaly finding the Landau notation (Big O or Theta notation) of an algorithm?

I'm used to search for the Landau (Big O, Theta...) notation of my algorithms by hand to make sure they are as optimized as they can be, but when the functions are getting really big and complex, it's ...
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### Please explain the statement that the function an+b belongs to O(n^2) and Θ(n)?

Let's say I have a linear function f(n)= an+b, what is the best way to prove that this function belongs to O(n2) and Θ(n)? I do not need mathematical rigor here. I need a programmers answer. Some ...
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### questions on a particular algorithm

Upon searching for a fast primr algorithm, I stumbled upon this: public static boolean isP(long n) { if (n==2 || n==3) return true; if ((n&0x1)==0 || n%3==0 || n<2) return false; ...
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### Determining if an Algorithm is O (log n)

I'm refreshing my CS Theory, and I want to know how to identify that an algorithm O (log n) complexity. Specifically, is there an easy way to identify it? I know with O(n), you usually have a single ...
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### What is O(…) and how do I calculate it?

Help! I have a question where I need to analyze the Big-O of an algorithm or some code. I am unsure exactly what Big-O is or how it relates to Big-Theta or other means of analyzing an algorithm's ...
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### Best Upper Bound & Best Lower Bound of an Algorithm

I am studying for a final exam and I came past a question I had on an earlier test. The questions asks us to find the minimum value in an unsorted array of integers. We must provide the best upper ...
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### Get 100 highest numbers from an infinite list

One of my friend was asked this interview question - "There is a constant flow of numbers coming in from some infinite list of numbers out of which you need to maintain a datastructure as to ...
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### Do real-world algorithms that greatly outperform in the class below exist? [closed]

Last night I was discussing with another programmer that even though something may be O(1), an operation which is O(n) may outperform it if there are is a large constant in the O(1) algorithm. He ...
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### Why is the formal definition of Big O notation formulated as such?

Consider the formal definition: f(n) = O(g(n)) Why is it not: f(n) = O(f(n)) or f(n) = O(c*f(n)) since for the Big O analysis, f(n)=2n and g(n)=n are identical? I am confused by ...
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### Big-O for nested loop

I am reading this post on Big-O It says that the following code is O(n^2): bool ContainsDuplicates(String[] strings) { for(int i = 0; i < strings.Length; i++) { for(int j = 0; j &...
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### What is O in Big O?

What is Big and O in Big O notation? I've read the definitions and it doesn't tell what is O pronounced as 'oh'. For example - I understand that O(n) is complexity of a linear algorithm where n could ...
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### Space complexity of Iterative Deepening DFS

We read on Wikipedia > Iterative deepening depth-first search that The space complexity of IDDFS is O(bd), where b is the branching factor and d is the depth of shallowest goal. Wikipedia also ...
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### Why is Big O taught instead of Big Theta?

Big O notation provides an upper bound to a function whereas Big Theta provides a tight bound. However I find that Big O notation is typically (and informally) taught and used when they really mean ...
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### How do I determine the runtime of a double recursive function?

Given any arbitrarily double-recursive function, how would one calculate its run time? For Example (in pseudocode): int a(int x){ if (x < = 0) return 1010; else return b(x-1) + a(x-1);...