0
votes
1answer
118 views

problem on calculating Big O complexity

i have this function on which i have to calculate the time complexity with the Big O notation: public void print(ArrayList<String> operations, ArrayList<LinkedHashSet<String>> ...
1
vote
2answers
198 views

What is a O(n) algorithm to solve this puzzle?

We are going to hold a meeting where everybody will speak in clockwise direction around a table. There are n people with n spots. Each person has a position preference (e.g. some want to go first, ...
0
votes
4answers
299 views

Binary Search seems superior, why did the committee of C++ still have Find in the algorithm library?

I wish to search for an integer in a vector of integer. I have two candidates for the job: Binary Search Find It seems that Binary Search is the best candidate for the job as although I have to ...
2
votes
4answers
297 views

difference between exponential and logarithmic growth

Why for(k=1;k<=n;k*=2) grows logarathmically = O(logn) but I feel it grows exponentially, as the seq look like 1,2,4,8.... and for fibonacci series people say it grows exponentially. which for me ...
2
votes
4answers
1k views

Complexity in nested loops

Foreword: In this post, I will make the common confusion between O(n) and Theta(n) as complexity notations. I will write pseudo-code to talk about algorithms, using whatever notation I find to my ...
0
votes
0answers
76 views

why the time complexity of Quick sort is better than heap sort and merging sort? [duplicate]

the heap sort\Merging sort\Quick sort all have the same time complexity nlogn. why the quick sort is better than others?
2
votes
1answer
1k views

What is the time complexity of the algorithm to check if a number is prime?

What is the time complexity of the algorithm to check if a number is prime? This is the algorithm : bool isPrime(int number){ if(number < 2) return false; if(number == 2) return true; if(number ...
0
votes
2answers
222 views

Why the bound of a linear function is same as that of a quadratic equation

I am learning algorithms, and I came across something very interesting. The asymptotic bound of the linear equation (a * n)+b is O(n^2), for all a > 0. This is same bound as a * n^2 + b * n + c, ...
8
votes
2answers
2k views

What does it mean by expected running time and average runnnig time of an algorithm?

Let's say we want to analyze running time of algorithms. Sometimes we say that we want to find the running time of an algorithm when the input size is n and for the worst possible case it is denote it ...
3
votes
1answer
2k views

What does it mean when we say that some function is polynomially bigger/smaller than some other function?

I was going over this video lecture on master theorem from Introduction to Algorithm and while explaining case A of the master theorem professor says that some function f(n) is polynomially smaller ...
1
vote
3answers
3k views

Big O(n log n) and Quicksort number of operations

I have an Array with 1,000,000 unsorted elements. I need to calculate expected number of operations that needs to be performed to sort array using Quicksort algorithm in common situations (not the n^2 ...
14
votes
5answers
2k views

What would be the Impact of P=NP? [closed]

I am preparing for a test and I can't find a clear answer on the question: What would be the impact of proving that PTIME=NPTIME. I checked wikipedia and it just mentioned that it would have "profound ...
1
vote
6answers
7k views

Merge sort versus quick sort performance

I have implemented merge sort and quick sort using C (GCC 4.4.3 on Ubuntu 10.04 running on a 4 GB RAM laptop with an Intel DUO CPU at 2GHz) and I wanted to compare the performance of the two ...
11
votes
5answers
11k views

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 ...
3
votes
1answer
3k views

Magic square check for N×N matrix with minimum complexity

Is there any algorithm that works better than O(n²) to verify whether a square matrix is a magic one (e.g. such as sum of all the rows, cols and diagonally are equal to each other)? I did see someone ...
6
votes
4answers
2k views

Smallest lexicographical rotation of a string using suffix arrays in O(n)

I will quote the problem from ACM 2003: Consider a string of length n (1 <= n <= 100000). Determine its minimum lexicographic rotation. For example, the rotations of the string “alabala” ...
2
votes
1answer
750 views

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 ...
1
vote
1answer
146 views

Algorithm analysis refresher help

I haven't touched algorithm complexity stuff in quite a while, so I am trying to do a refresher. I am trying to figure out the number of steps in the following for loop. for(i = 0; i < n; ...
2
votes
6answers
1k views

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 ...
5
votes
4answers
2k views

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 ...
2
votes
4answers
663 views

Difference between complexity and performance guarantee

I'm a bit confused with the performance guarantee and complexity of selection sort. I checked through internet and the complexity of selection sort is O(n^2). This O(n^2) is in terms of time ...
2
votes
6answers
247 views

Complexity vs maintainability in modern hardware

Today with the modern hardware and memory coming cheap, how much sense does it make to spend effort to analyze algoriths or data structure complexity? Wouldn't it be better instead, to focus on clean, ...
2
votes
2answers
2k views

Best resources to really understand run-time complexity

I'm familiar with the basics of run-time analysis such as what makes certain types of code O(n) and O(n^2). But I'm having real trouble learning, understanding, and really remembering how to analyze ...
2
votes
4answers
271 views

Process each row against each other, how much would it cost?

If I have n rows in a database, and I want to compare every row against each other, how many loops (or processes) would I need to do. Is it n2? (so if I have 30,000 rows then it would be 900,000,000) ...
8
votes
1answer
592 views

Subset sum problem is NP-complete?

If I know correctly, subset sum problem is NP-complete. Here you have an array of n integers and you are given a target sum t, you have to return the numbers from the array which can sum up to the ...
2
votes
2answers
418 views

How do we know if a problem is hardest in NP

I read that the definition of NP-complete is : These are the hardest problems in NP. Such a problem is NP-hard and in NP How do we know if a problem is hardest in NP, and no harder problem ...
6
votes
3answers
241 views

NP hard/complete

I have never been very clear on this concept. Please help: At the end of the day, we should want to identify useful problems for which we don't have polynomial solution so far and only have ...
46
votes
16answers
3k views

Is big-O really that relevant when working in industry?

In every interview I have been in, I have been quizzed on mathematical analysis of complexity, including big-O notation. My question is, how relevant is this test to development in industry? How often ...
3
votes
1answer
270 views

Should one write Big Oh complexity in the documentation of algorithms? [closed]

When writing or using an algorithm, should the Big Oh complexity be mentioned?