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30
votes
5answers
5k views

Divide and Conquer algorithms – Why not split in more parts than two?

In divide and conquer algorithms such as quicksort and mergesort, the input is usually (at least in introductory texts) split in two, and the two smaller data sets are then dealt with recursively. It ...
19
votes
4answers
3k views

When speaking, how can I say that the time complexity order of an algorithm is O(N log N)?

What term can I use to describe something with O(N log N) complexity? For example: O(1): Constant O(log N): Logarithmic O(N): Linear O(N log N): ?????? O(N2): Quadratic O(N3): Cubic
17
votes
5answers
9k views

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

I have the follow algorithm which finds duplicates and removes them: public static int numDuplicatesB(int[] arr) { Sort.mergesort(arr); int numDups = 0; for (int i = 1; i < arr.length; ...
13
votes
2answers
605 views

Trying to understand the 2N lnN compares for quicksort

I was going through the analysis of quicksort in Sedgewick's Algorithms book. He creates the following recurrence relation for number of compares in quicksort while sorting an array of N distinct ...
12
votes
7answers
13k views

Why is binary search,which needs sorted data, considered better than linear search?

I have always heard that linear search is a naive approach and binary search is better than it in performance due to better asymptotic complexity. But I never understood why is it better than linear ...
11
votes
7answers
5k views

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 ...
11
votes
2answers
345 views

Time complexity of 2^sqrt(n)

I am solving an algorithm question and my analysis is that it would run on O(2^sqrt(n)). How big is that? Does it equate to O(2^n)? Is it still non-polynomial time?
9
votes
3answers
6k views

Why Big Data Needs To Be Functional?

I started working on a new project lately related to Big Data for my internship. My managers recommended to start learning functional programming (They highly recommended Scala). I had a humbled ...
8
votes
1answer
1k views

Possible Damerau-Levenshtein improvement?

I recently implemented the Damerau-Levenshtein distance algorithm from the pseudocode on Wikipedia. I couldn't find any explanation of exactly how it works and the pseudocode uses completely ...
6
votes
5answers
737 views

Why interviewers want Optimal Algorithms

In an interview with a software company they asked me some algorithm design questions. Being strong in mathematics I was able to solve it mathematically, but each time when I propose my algorithm ...
6
votes
2answers
1k views

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 ...
5
votes
8answers
2k views

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 ...
5
votes
3answers
861 views

Loop runtime question

I had an exam today and I feel that I did pretty well, except I could not for the life of me figure out what appears to be an unbelievably simple question. We were asked to give theta notation run ...
5
votes
3answers
809 views

Is O(log n) + O(log n) = O(n)? [duplicate]

We know that binary search takes O(log n) in Big O notation but if we need to run twice an algorithm of O(log n), would it be the same as O(n) in time complexity? For example, if I have a method to ...
5
votes
4answers
903 views

Find the peak of each islands in sparse matrix

I have a sparse matrix that contains several islands of unknown size. I would like to find the highest peak of each islands. Consider this matrix as an example: 0 0 1 0 0 0 0 0 0 1 2 1 0 0 0 0 0 3 2 ...
5
votes
1answer
1k views

Compute Adjacent Pair

I was given the following problem: Integer V lies strictly between integers U and W if U < V < W or if U > V > W. A non-empty zero-indexed array A consisting of N integers is given. A ...
5
votes
2answers
2k views

difference between accounting and potential methods in Amortized Analysis

I was going through the Introduction to Algorithms by Cormen et al.In the chapter titled Amortized Analysis,the difference between accounting and potential methods is given like this The ...
5
votes
2answers
308 views

Bin sorting problem - Please help categorize

I have a problem I am developing a solution for and currently I solve it with a brute force solution that checks all possibilities. It works for small numbers of bins but I'd like to work with a ...
4
votes
3answers
171 views

Algorithm Analysis: In practice, do coefficients of higher order terms matter?

Consider an^2 + bn + c. I understand that for large n, bn and c become insignificant. I also understand that for large n, the differences between 2n^2 and n^2 are pretty insignificant compared to the ...
4
votes
4answers
2k views

How to discriminate from two nodes with identical frequencies in a Huffman's tree?

Still on my quest to compress/decompress files with a Java implementation of Huffman's coding (http://en.wikipedia.org/wiki/Huffman_coding) for a school assignment. From the Wikipedia page, I quote: ...
4
votes
1answer
740 views

How this Fibonacci exponentiation by squaring algorithm works?

This is one of the best algorithms to calculate the nth Fibonacci sequence. it needs O(log(n)) time to do its job, so it's so efficient. I found it somewhere but don't know how it works! Can anyone ...
3
votes
1answer
2k views

A* Algorithm Completeness Proof

The A* Algorithm is the optimal (provided the heuristic function is underestimated), complete & admissible (provided some conditions). I know the proofs of admissibility & optimality. But how ...
3
votes
1answer
279 views

Sentence Tree vs. Words List

I was recently tasked with building a Name Entity Recognizer as part of a project. The objective was to parse a given sentence and come up with all the possible combinations of the entities. One ...
3
votes
2answers
221 views

Big O Nested For Loop Breakdown

I understand how to get a general picture of the big O of a nested loop, but what would be the operations for each loop in a nested for loop? If we have: for(int i=0; i<n; i++) { for(int j=i+...
3
votes
1answer
198 views

How much times command executed? Looking for mistake

I have following piece of code: int sum = 0; for (int i = 1; i <= N; i++) for (int j = 1; j <= N; j++) for (int k = 1; k <= N; k = k*2) for (int h = 1; h <= k; h++)...
3
votes
1answer
96 views

Are these graph coloring algorithms equivalent?

Suppose you want to color the vertices of a graph in a greedy fashion, given a predetermined order of these vertices. The goal is to avoid giving two adjacent (linked by an edge) vertices the same ...
2
votes
4answers
506 views

What is Big-O notation for purely functional languages?

Is it still relevant? Instead of var result = new List<int>(); for (var i = 0; i < prev.Count; ++i) { result.Add(prev[i] * 2); } where the result.Add, prev[i], and * 2 instructions ...
2
votes
4answers
409 views

Approach to simplifying an algorithm

For completely random reasons*, I wrote some code that calculates and displays the following expression: P=1*(2+2)(3+3+3)(4+4+4+4)..(n+n...… Which is equivalent to (n!)^2 The version I wrote (...
2
votes
3answers
255 views

Close to knapsack problem?

I think that I am trying to solve a problem somewhat similar to a knapsack problem. I am not sure though. Please see the input given below and my solution. There are three types of items and 4 ...
2
votes
2answers
462 views

Estimating run time of algorithm

For instance if i have an algorithm that is O(n2) and it will run for 10 seconds for a problem size of 1000. Now if i were to double the problem size to 2000 i want to know the approximate run time in ...
2
votes
1answer
414 views

Asymptotic running time of for-loops

I have this question which I need answered: What is the asymptotic running time for the following piece of code? if (N < 1000) for (int i = 0; i < N; i++) for (int j = 0; j < N; j++...
2
votes
3answers
98 views

recalculation model for GUIs

I often come across this problem. Say to have a form with some controls: A B C = A + B D E = C * 2 ONLY IF D==TRUE F G = A - F The user fills A, then B. The system calculates C. The user fills D (...
2
votes
1answer
632 views

Sublinear Extra Space MergeSort

I am reviewing basic algorithms from a book called Algorithms by Robert Sedgewick, and I came across a problem in MergeSort that I am, sad to say, having difficulty solving. The problem is below: ...
2
votes
1answer
360 views

Why create a Huffman tree per character instead of a Node?

For a school assignment we're supposed to make a Java implementation of a compressor/decompresser using Huffman's algorithm. I've been reading a bit about it, specially this C++ tutorial: http://www....
2
votes
1answer
85 views

Optimizing the exponential smoothing of a big array

I have a large set of values (let's say 1M entries) where I need to apply an exponential smoothing algorithm, but only incrementing one value at a time (all others decay to zero). The trivial ...
2
votes
1answer
118 views

Confusion in understanding the theorem on Amortization

I was reading a book on Algorithm Analysis by Micheal T Goodrich. I came across amortization technique and I got struck in understanding the proof of theorem. I am putting the theorem and the proof ...
2
votes
1answer
76 views

Running time of the specified Bubble Sort Algorithm

I have been working on a few algorithm questions the last few days, and one bubble sort problem in particular has been giving me headaches. for (k=1; k <= A.length - 1; k++) { //Line 1 ...
2
votes
1answer
49 views

What is the order analysis of the following (using a list of primes)

I have the following program: Iterate x from 1 to N. Check to see if x is prime. If it is, add it to a list of primes. The way I check to see if it is prime is iterating through the current list ...
2
votes
1answer
236 views

Algorithm in undirected BFS graph

I'm trying to put together an algorithm that will display the node degree for every node in a breadth first tree graph (assume BFS was called). Assume it's an undirected graph. I'm not sure how to ...
2
votes
1answer
323 views

How to compute amoritized cost for a dynamic array?

I am trying to understand how to do the amortized cost for a dynamic table. Suppose we are using the accounting method. Let A of size m be an array of n elements. When n = m, then we create a new ...
1
vote
2answers
342 views

How to approach program design with respect to data strucutres and algorimths - is there an equivelant of the OO design process for d.s.'s + algs? [closed]

My applogies for probably the worst written body of text I have produced in my life and many thanks to those willing to plough through it all. I was (and still am) not able to clearly express what I ...
1
vote
4answers
679 views

How to trace logical errors in algorithms [closed]

I am beginner in algorithms. Last year I participated in Google Code Jam. One of the major issues I faced during the competition was my code was working fine on my test cases, but when I submitted on ...
1
vote
3answers
270 views

What's the big-O complexity of this recursive algorithm?

I am following a course of Algorithms and Data Structures. Today, my professor said the complexity of the following algorithm is 2^n. I waited till the lesson was over, approached him and told him ...
1
vote
1answer
2k views

Calculate Big-O for nested for loops

I found this nested loop to calculate the Big-O notation. for(i=0;i<n;i++) for(j=0;j<i*i;j++) for(k=0;k<j;k++) I got the time complexity for the algorithm with this polynomial ...
1
vote
1answer
186 views

How to calculate the worst-case runtime of this search-algorithm

I've written a special indexOf function for a list of unsorted unique values. I can search for one or multiple (unsorted) values, passed as array/list, and the function will return me an array/list ...
1
vote
3answers
400 views

Big O notation of randomness

I was thinking about inefficient algorithms based on randomness and wondered how to categorise them. For instance. Say you wanted to generate all the numbers from 1 to N in a random order but only ...
1
vote
2answers
147 views

What's the professional name for the software planning diagrams, those with ellipses and rhombuses?

What's the official name for a diagram like this one, used to structure a conditional plan. The shapes of the objects are by convention ellipse for an action, rhombus for a question, rectangle for a ...
1
vote
2answers
826 views

How to measure algorithm accuracy?

I have a few optimization algorithms (for finding function minimum) and I'd like to check how good they are. Suppose I build test cases and compare the actual results to theoretical ones. What ...
1
vote
2answers
686 views

Is the time complexity of a while loop with three pointers different than 3 nested for loops?

This program (written in ruby) finds the largest 3 numbers in an array (without sorting the array). It has a while loop with three pointers. My fist instinct, since there is only one loop is to say ...
1
vote
2answers
2k views

Lower and Upper bound of an algorithm

I am learning about analysis of algorithms. I came across the term "upper bound" and "lower bound" in "worst-case" running time of an algorithm. Are they applicable to only the "worst case" or can ...