# 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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### What is the Big O notation of modifying an existing element in a heap data structure?

Wikipedia says "increase key" is O(log n) for a binary heap, but it is referring to an internal function. I'm not asking about that: Imagine the data structure had an external/public ...
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### Why is big O notation an asymptotic notation/analysis?

An asymptote in mathematics represents a value (line) to which the observed function constantly approaches. In other words, as the value of X increases towards infinity, i.e. decreases towards minus ...
295 views

### Algorithms: How do I sum O(n) and O(mlog(n)) together?

I'm doing a running time analysis using the aggregate method and I'm a bit confused about what would be the result in this case. I have some intuition in inferring that it would be O(mlog(n)) but I'm ...
1 vote
262 views

### How do we define a "step" when calculating big O notation in an algorithm?

I'm learning about Big O notation and how it relates to computer science and I understand the sentiment behind Big O, however I'm struggling at understanding how we define a "step". In the ...
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### What is the big O of this algorithm? [duplicate]

I think it's O(m*n) but someone said it's O(n). If you think it's O(n) could you provide an explanation? def convert(self, s: str, numRows: int) -> str: if numRows == 1: return ...
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### Why isn't a counter used to avoid nested for loops for index based operations?

Let's assume we have a method that we want to run as fast as possible and it needs to loop on a 2D array, naturally we would do a nested for loop as such: int[][] arr = new int; for(int ...
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### O(nlogn) + O(logn) =? [duplicate]

So I came upon this time complexity result and I was confused about it, it said that : O(nlogn) + O(logn) =O(log(n+1)) Why is that the case? Shouldn't the result be O(nlogn)?
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### Calculating time complexity of a code snippet

I am trying to calculate the time complexity of the below code snippet def func() { for(i=1; i<=n; i++) { for(j=1; j<=n; j=j+i) { print("hello") } }...
180 views

### Big O notation of a program that takes 10x time for 3n input

I have a program that calculates N digits of Pi. I have measured that it takes 10x time to calculate 3n numbers, compared with the time for calculating n numbers. The source code also gives an ...
316 views

### Why the names Omega and Theta in Big Omega and Big Theta?

There was a question asking what the "O" stands for in "Big O", the answer to which seems to be "Ordnung von"/"order of". I wonder what's the origin of the ...
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### Running time for simple for loops - Big O notation

I am currently doing some exercises with algorithms and I find myself in a huge problem. It seems that everybody understands this type of problem but I have a really hard time figuring it out. For ...
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### Is looping an array to compare to itself considered O(n^2)? [duplicate]

Often when I'm doing an operation comparing an array to itself, I write code along these lines: function operation (array) { for (let i = 0; i < array.length; i++) { for (let j = i + 1; j <...
378 views

### What is the worst case Time Complexity for only the Divide Portion of the Merge Sort Algorithm?

Please, consider the below merge sort algorithm. Here we start with a divide portion which splits the array into halves and we do recursive operation on each half separately. I have ignored the merge ...
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### Are there any programs or IDEs that calculate Big-O notation on functions? Is this something that is possible to program into an IDE?

Is there anything that can calculate the Big-O notation of a function? While learning about Big-O, it is implied that it is pretty trivial to do in your head once you know the basic rules, however if ...
10k views

### Why is the worst case for this function O(n^2)?

I'm trying to teach myself how to calculate BigO notation for an arbitrary function. I found this function in a textbook. The book asserts that the function is O(n2). It gives an explanation as to why ...
266 views

### Big-O Notation and Calculus [closed]

I was wondering if there are any calculus relationships implicit in Big-O notation. For example, an algorithm linear according to Big-O notation reduces the size of the problem by a constant amount ...
162 views

### What is the O of this operation?

Say for a given positive integer number n, you have to find a level k so that 1 + 2 + 3 + ... + k = S is below or equals n but S + k + 1 is above n. For example in python: def find_level(n): ...
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### Is the complexity of this code quasilinear time?

Algorithm explanation: based on an unsorted list I want to find the indexes of the values in another sorted list. Note that all values are unique and the two lists have the same values, only in ...
266 views

### How should I document a method's computational complexity in the code?

I am currently working on a project that has very little documentation overall. The team is working to change that. I am doing my part, by adding xml comments to the methods I make and the ones I edit,...
1 vote
222 views

### Big O Complexity when iterating in 3 dimensions

What time complexity would you classify the following as having? int n = 100; for(int x = 0; x < n; x++) for(int y = 0; y < n; y++) for(int z = 0; z < n; z++) DoWork(...
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### Questions around calculation of time complexity of an algorithm [duplicate]

I am a newbie to algorithms. One thing that i always get confused is about calculation of algorithm runtimes. For example: The following piece of code in Python for i in range(n): #O(?) i*=k ...
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### What is the complexity of find and checking prime numbers?

I'm trying to figure out the complexities of these two functions that I've written but could not understand.def First, I thought it is supposed be O(N). But it is not clear how many times the loop ...
452 views

### Generating O(N^2) without loops [closed]

I understand you can generate an O(N^2) algorithm by using loops: eg: for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { //do something N^2 times. } } Is it ...
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### Is my reasoning to determine this algorithm's Big-O correct?

Take the following algorithm with two separate sections, and the sections do not influence each other whatsoever (the function is not recursive, as well). void algorithm(int x) { // This section ...
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### What is meant with finding real and integer constants in Big Oh notation?

From my book "Data Structures & Algorithms in Java: Sixth Edition" the definition of Big Oh is the following: Let f(n) and g(n) be functions mapping positive integers to positive real numbers....
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### Am I allowed to simplify terms while calculating Big O?

I want to calculate the runtime of the following function T(n) = (1+2+3+4+5+...+n)/n At first this doesnt seemed hard to me because it can be solved easily by transforming the formula T(n) = (n(n-1)...
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### What do you call it when you change the Big O execution time of a function [closed]

Let's say I have a function which sorts a database in O(n^2) time. I want to go about refactoring it so it runs in O(n log(n)) time, and in doing so I will change the fundamental way the operation ...
170 views

### Big-O when worst case numerical value is known

If I have an algorithm and part of it has a known worst case numerical value, which is reasonably small compared to the rest of the problem, is it ok to argue that part as O(1)? E.g. If part of the ...
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### randomly filling in empty spaces in a matrix - O(N) amortized time?

Here are two ways to answer the following question. I'm trying to confirm what I believe their time complexity to be: If I had a snake game with a x,y matrix of spaces, some of which were occupied ...
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### What's the needed math for building algorithms? [closed]

What's the needed math for building algorithms? Because I was reading a book and I can't understand much. It says I need simple math from high school. I don't want to learn all the math that exist ...
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### Can "sub-linear" still be a straight line?

I'm working on a problem that requires a "sub-linear" solution. A quick search for sub-linear will return a lot of this... ... where the sub-linear line is modelled as logarithmic/asymptotic. But I ...
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### Calculating Complexity

I am having trouble calculating the complexity of this problem: REVERSE3(A): // Reverse the order of elements in an array // P is an array; assume generating next permutation takes 1 step. for ...
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### Does the workload problem belong to a class of computer science problem?

I went for an interview, and got a workload problem: Problem: write a function to tell whether a series of workloads will exceed the maximum workload or not Input: MaxWorkLoad: example 10 ...
1 vote
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### What does time complexity of n log n signify? [duplicate]

Is it the number of iterations or recursive calls made? Or is it the number of times the conditional check has been applied? Ex: if there are 10 elements in an array in descending order. The time ...
105 views

### Help with Big-O notation complexity [duplicate]

How do I find the O - notation complexity for the following? int sum = 0; for (int i = 1; i <= n*2; i++ ) sum++; I read the guide on Big - O and other posts on Big -O complexity, but I'm ...
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### What programming environments can be used to illustrate and benchmark the unoptimized space complexity of an algorithm?

What programming language along with implementation and compiler can I use to study the pure, unoptimized space complexity of an arbitrary algorithm? And what methods can I use to do so? For example,...
2k views

### Big-Oh notation of a stackarray

I am studying data structures and I have hit a bit of a road block. The top is Big oh notation and it is simply confusing. While I can find the upper bound for the simplest of loops, when it comes to ...
1 vote
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### omega why K + N better than N

I was reviewing the big O cheatsheet at http://bigocheatsheet.com/ and ran into some listings under sort that I do not understand. Runtimes are color coded, green being better than yellow. There are ...
502 views

### Time complexity of an algorithm [closed]

What is the complexity of the following loop? for(i=1;i<n;i=2^i) sum+=i;
1 vote
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### Big-O notation and halting problems

I'm trying to understand why it's impossible to create a tool that calculates Big-O notation automatically. I have read about Halting problems, but not related on Big-O notation and I was wondering, ...
60 views

### Time complexity Computation

What will be the result of the time complexity of this piece of code i.e. int sum(int A[], int n) { int sum = 0, i; for(i = 0; i < n; i++) { sum = sum + A[i]; } ...
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### Efficient way to calculate how many items to destroy if each has a 70% chance to be destroyed

We start with a variable that holds an integer for the "number of items" that we have somewhere, somehow. Then, the algorithm is applied: each one of those items have a 70% chance to be destroyed. ...
1 vote
660 views

### Should I use this very short Python Quicksort implementation?

def quicksort(N): if len(N) < 2: return N else: less = quicksort([number for number in N[1:] if number < N]) more = quicksort([number for number in N[1:] if ... 19k views

### Finding longest subsequence with sum less than or equal to a fixed number

I was trying to solve Problem 279-B. Given an natural number, t, and an array, a,...,a[n-1], of natural numbers, find the maximum length of a continuous subarray, a[i],...,a[j] in a where a[i]+.....
1 vote
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### Understanding θ(f(n)) as defined in the Structure and Interpretation of Computer Programs

I'm having trouble understanding a small passage in The Structure and Interpretation of Computer Programs, and I'm hoping someone can help me interpret it. In the book's introduction to Orders of ...
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### O(n^2 * 2^(log n)) == O(n^2)

Is O(n^2 * 2^(log n)) == O(n^2) ? Why I think that this could be the case: In big O, you only take the parts of the term that are most relevant, right? O(n^2 + 3n + 9) == O(n^2). The n^2 has a lot ...
1 vote
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### Does algorithm time complexity O(5) considered as O(1)? [duplicate]

I have someone homework to make and in the instructions it says that we need to implement a function in O(1). Now, does it mean that I can make my function in O(5) or O(2) or whatever?
1 vote
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### Binary Search O(log(n)) or O(n)

I see where most readings online derive that the Big-Oh notation of a Binary Search is O(log(n)), but doesn't this assume a balanced tree? What if the tree is completely unbalanced (i.e. similar to a ...