# Questions tagged [algorithm-analysis]

Analyzing an algorithm to determine its time and space performance.

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### fastest way to find number of smaller elements to the right of an array

In Daily Coding Problem, Miller&Wu have the following problem : Given an array of integers, return a new array where each element in the new array is number of smaller elements to the right of ...
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### What is the most suitable data structure for IPv4 addresses with intersecting ranges?

Mostly in all routers and operating systems the Longest Prefix Match algorithm is used for searching the trie of IPv4 addresses. Packet filters like Iptables don't need some special data structure for ...
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### Could H correctly decide that P never halts?

Because a halt decider must compute the mapping from its inputs to an accept or reject state on the basis of the actual behavior of its actual inputs, when H is a simulating halt decider H(P,P) would ...
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### Counting primitive operations on recursive functions

I'm reading Algorithm Design and Applications, by Michael T. Goodrich and Roberto Tamassia, published by Wiley. They teach the concept of primitive operations and how to count then in a given ...
268 views

### 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") } }...
393 views

### Processing a 2D matrix - need to speed up my O(n^4) algorithm

I have an n x n matrix which I need to convert into a list sorted by value. Starting with the maximum value cell at (row x1, col y1), I must immediately exclude all cells where (x >= x1, y <= y1)...
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1 vote
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### Does a microcontroller provide better accuracy for comparing algorithms' run-times?

I have a set of algorithms to choose from based on their execution speed. I know that it is very hard to get an accurate measurement due to the process scheduling, the time that is actually consumed ...
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### 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 ...
4k views

### Using a different algorithm depending on the size of the input

I recently finished a course on advanced algorithms, and another on complexity & computability theory, and in the past few days my mind has been somewhat preoccupied by this question. Why don't we ...
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### How can I know when a paper is too hard for me to be able to implement their code and/or understand their math - within a given deadline?

I've been assigned to explore implementing (along with modifications, so understanding it is a must) this algorithm for the 'Redistricting Problem': https://dl.acm.org/doi/pdf/10.1145/3274895.3274979 ....
1 vote
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### Rectangle packing / Bin packing with multiple frames

I have multiple rectangular frames, with different fixed heights. The width should be minimized and there is a maximum width. Then there are many different smaller rectangles. These should be packed ...
213 views

### Time complexity for a small code

I'm trying to find the time complexity for the following code. N= number of elements in array D= a constant: D>1 V= a constant: V>1000 counter=1; //the maximum value of the counter is N/D. ...
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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 ...
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### Time complexity of a Nested While loop in a for loop

I'm trying to derive the simplified asymptotic running time in Theta() notation for the two nested loops below. For i <-- 1 to n do j <-- 1 while j*j <= i j = j+1 For i <...
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### Do I have do use HashTables/Maps/Hashmaps in this algorithm?

I am doing the Ransom Note algorithm in Hackerrank. The thing is I am not using maps and all the tests pass except for three which execution time takes a lot more. (Kotlin language) I have two ...
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### Do we include output space in space complexity?

For example. I have a function which generates an array with random numbers. int[] generateNum(int n) { int[] result = new int[n]; /* Logic to generate random number */ ............... ...
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### static, dynamic analysis - what mistakes were made in the code?

A software company develops software packages for commercial animal farming. A special function in C calculates the daily amount of feed for different kind of animals dependent on their bodyweight....
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### Logfile correlation finder (for j4Log)

I'm currently analyzing a problem in a old "distributed" system, that only occurs sporadically - as the system does not support other means of debugging help I have to rely on the logs (I did not ...
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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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### Is it better to write an efficient algorithm or code that is easier to understand?

So I was recently given a coding assignment from a large financial firm, and I thought of two ways to solve the problem. One of the ways involved 1 outer for loop and 1 inner for loop. In this case, ...
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### Battery level prediction model

I have the idea of develop a model that predicts the battery charge level of my system for now until the following 5 days. The battery is charged using a solar panel. I am writing my code in Python 2....
1 vote
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### How to reason about complexity of Merging k sorted linked lists?

I am trying to understand Big O notation better to be able to reason about it in a much clearer way and therefore, need some feedback on my analysis given below for problem: Merge k-sorted linked ...
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### Algorithm: Binary Search / Tree / Partitioning on unsortable data?

First, this question is not really about binary search as I neither have sorted data, nor any sortable data at all. :-) W.r.t the "unsortable" claim see below; but I think the title term "unsortable"...
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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 ...
1 vote
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### Reverse engineering a checksum or CRC

I am trying to reverse engineer a checksum or CRC wherein an 8 bit number* gets converted to a 5 bit number for error checking. I have an incomplete list of data values and checksums, and need to ...
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### Effecient algorithm for data deduplication in procedural code

I have written a data cleansing application which, for the most part, works well. It is not designed to handle large volumes of data: nothing more than about half a million rows. So early on in the ...
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### Why is the optimal choice for a pivot in quicksort algorithm the median element?

Lately i have been taking an course at brilliant.org, i was exploring a lesson on QuickSort algorithm, found a question. Which of the following would provide the optimal pivot selection at each step ...
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### Sorting method for music avoiding title and artist repetition

I'm looking for pseudocode suggestions for sorting my mp3 files in a way that avoids title and artist repetition. I listen to crooners - Frank Sinatra, Tony Bennett, Ella Fitzgerald etc. singing old ...
215 views

### Why in Tournament Sorting do we neglect the number of comparisons to find the Minimum?

Here the professor said that, Tournament sort needs (n-1) + 2(n-1)logn comparisons. {Where (n-1) for calculating Maximum or say creating Tournament structure and 2(n-1)logn for other elements to sort}...
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### What is wrong with this algorithmic solution of mine that checks whether a given function returns a sorted array when an array is given as input?

An interviewer asked me this question: Given a function f(ar[]) where ar[] is an array of integers, this functions claims to sort ar[] and returns it's sorted version ars[]. Determine if this ...
1 vote
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### Loop invariant of Selection Sort

Selection Sort(A[1,2..n]:array of integers) 1.for i=1 to n-1 2.for j=i+1 to n 3.if A[j]<A[i] 4 swap(A[i],A[j]) I am trying to prove the correctness of this algorithm,I read from my book ...
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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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### Algorithm to find Minimum bounding rectangle of fixed area [closed]

I have set of spatial points defined by coordinates (x,y) . I want to find the bounding rectangle of given area that maximizes the number of point inside the rectangle. The obtained rectangle should ...
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### How bad would be this algorithm that converts a string to a multiple precision number?

I've been developing a C++ library for multiple precision computations (integers/fixed point), assume positive numbers. The class is something like: class Integer { public: //constructor //...
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### Is the Time complexity of this function o(n) ? Can it be optimized any further?

This is a very simple function to find if a string is composed of unique characters. I believe that this is a O(n) time complexity as it loops once and has a single if condition. Am I correct? Is ...
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### What is the time complexity of permutations?

I want to just say that it's time O(n) and space complexity is O(n!), but I am not certain. Can anyone confirm this or tell me what it is? https://docs.python.org/2/library/itertools.html#itertools....
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### Algorithms comparison and complexity

I want to sole this problem: Write a method to return all valid combinations of n-pairs of parentheses. The method should return an ArrayList of strings, in which each string represents a ...
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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,...
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### How does the dividing Step in Merge Sort have Constant Time Complexity?

I am highly confuse while calculating time complexity of Merge Sort Algorithm. Specifically on the Dividing Step. In the dividing step we have to calculate the mid point of "n" i.e. "q = n/2". How ...
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### Loop Invariant in Recursive function

When I was reading Introduction to Algorithms (3rd edition, P188), there is an algorithm called Tail-Recursive-QuickSort and we have to prove the correctness of this algorithm. TAIL-RECURSIVE-...
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### Time complexity of an algorithm [closed]

What is the complexity of the following loop? for(i=1;i<n;i=2^i) sum+=i;
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### String Pattern Matching from Lookup Table - Non-Exponential Solution?

Given the problem... Given a String comprising of non-alhpabetical symbols, and a Lookup Table where a subset of those symbols may equate to a single alphabetical character, output all possible ...
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### 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 ...
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### 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 are ...
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### Unable to Solve Dynamic Programming

I had an assignment on dynamic programming due last night, but I had to turn it in unfinished because i could not understand how to solve the last problem: The state wants to monitor traffic on a ...
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### How to find complexity of T(n) = 8T(n/2)+n^2.93(log n)^93?

I believe we have to use a variant of master theorem...can someone suggest me how to find complexity of such equation which doesn't directly fit into Masters theorem.
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### 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?
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