Questions about methods for estimating the increase in runtime of an algorithm as the input size increases.

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2answers
75 views

Where does the lg(lg(N)) factor come from in Schönhage–Strassen's run time?

According to page 53 of Modern Computer Arithmetic (pdf), all of the steps in the Schönhage–Strassen Algorithm cost $O(N \cdot lg(N))$ except for the recursion step which ends up costing $O(N\cdot ...
1
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1answer
27 views

Runtime analysis of sorting an array with known number of inversions

I'm having difficulties with analyzing the worst-case runtime of this following case: I'm given an array that has $n$ natural numbers. Out of all $\binom{n}{2} = \frac{n(n-1)}{2}$ possible pairs ...
4
votes
1answer
143 views

Complexity of Hopcroft-Karp

I have a rather basic question about the number of operations taken by the Hopcroft-Karp algorithm for finding a maximum matching in a bipartite graph. It is commonly reported as $O(m \sqrt{n})$ where ...
2
votes
1answer
52 views

What is the complexity of depth first traversal that don't label nodes as discovered?

I've found an algorithm that acts like a depth first traversal that don't recognizes nodes that have been visited before. A / \ B C \ / D | E If run ...
1
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2answers
59 views

How fast can we identifiy almost-duplicates in a list of strings?

I'm having trouble figuring out the upper bound running time for this scenario: Input: $N$ number of strings $M$ upper bound of string length $T$ threshold for edit distance (2 strings with a ...
2
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2answers
70 views

Why do we compute time complexity for algorithms? [closed]

I read about Big-O notation with modular arithmetic. So, Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation ...
0
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0answers
22 views

Using arithmetic progression sum to show an algorithm is both $\Theta(n^2)$ and $O(n^2)$ [duplicate]

Exercise 4 in http://discrete.gr/complexity/ askes to give an arithmetic progression sum to show that the following algorithm is both $O(n^2)$ and $\Theta(n^2)$. ...
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2answers
54 views

Time cost of thread creation

While creating an algorithm, the following question came up: In uniform cost, what is the time cost of a process that creates a thread? Is there a difference between creating a thread in a ...
4
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5answers
2k views

Optimal Algorithm for checking if a number is a multiple of three

I'm just starting a course on Computational Number Theory and have very little Computer Science background but definitely know enough about the big-O notation. I currently have an assignment to work ...
0
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0answers
29 views

What is the time complexity of Matlab's Hierarchical Clustering?

I'm using mat lab's implementation of hierarchical clustering algorithm, with pdist, linkage , cophenet, dendrogram, and cluster. But I'm not exactly sure where or how to find the time complexity It ...
1
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1answer
50 views

Number of iterations of the Euclidean algorithm

I have a doubt about the runtime of the Euclidean algorithm; the slide of my Professor says: The calculation of $\mathrm{GCD} (a, b)$ stops at the most after $2\log_2 a$ iterations. Since ...
1
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1answer
92 views

Big O running time for this algorithm?

Here's the code for the algorithm: Foo(n) lcm = 1 for i = 2 to n lcm = lcm*i/Euclid(lcm,i) return lcm The running time of ...
1
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1answer
32 views

Lower bound on number of comparisons needed to search for a number in a sorted 3-d array

Suppose we have an $N \times N \times N$ 3-d sorted array meaning that every row,column, and file is in sorted order. Searching for an element in this structure can be done using $O(N^2)$ comparisons. ...
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3answers
49 views

Confusion with the Running Time of an algorithm that finds duplicate character

I have the following simple algorithm to find duplicate characters in a string: ...
1
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1answer
36 views

Time Complexity of Halley's Method

What is the time complexity of Halley's Method? I am thinking ${\cal O}(\log(n)F(n))$, or something very similar to Newton-Raphson, but I feel as though there should be some change to the complexity ...
2
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0answers
28 views

Lower-bounds of running-time for output sensitive Algorithms

Let me ask my general question using a specific example, namely range searching: Given a set of points in the plane and an axis parallel rectangle, report all points lying in the rectangle. If the ...
4
votes
2answers
186 views

Performance impact due to time required for shuffling in Quicksort

As a programmer with non CS background, I am learning algorithms. When explaining the performance of quicksort in an Algorithm book and also elsewhere on the web, I do not see any reference to the ...
0
votes
2answers
55 views

Why don't we calculate swaps and other steps except comparison for finding time complexity of a sorting algorithm? [duplicate]

I was learning some basic sorting techniques with their complexity. However I cannot understand why only the number of comparisons are taken into account while calculating time complexity and ...
0
votes
0answers
16 views

Time complexity of complex nested for loops [duplicate]

What are the time complexities of the following code? I posted this on the general stackexchange website, but it was suggested that I post it here. ...
4
votes
2answers
202 views

Expected number of updates of minimum

I came across the following problem in a exam. We choose a permutation of n elements $[1,n]$ uniformly at random. Now a variable MIN holds the minimum value seen so far at it is defined to $\infty$ ...
1
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0answers
25 views

Complexity of a nested for loop [duplicate]

I'm trying to work through various exercises in Skiena's "Algorithm Design Manual." One problem that I am stuck on is as follows: What value is returned by the following function? Express your ...
2
votes
1answer
41 views

Analysis of Algorithms: Applying Concepts [duplicate]

I believe I understand the concepts of algorithm analysis. However, I'm not fully confident in applying those concepts. I'd appreciate help in bridging the gap between concept and application. I ...
0
votes
1answer
115 views

Why is there a 2n+1 comparison for a linear search algorithm?

Suppose an algorithm goes through a list of n integers and for every iteration of the loop it is needs to check if the current evaluated element of the list is even. If it is even, return the index of ...
0
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3answers
128 views

Calculating time complexity of two interdependent nested for loops

Consider the following code segment : for (int i = 1; i <= n; i++ ) { for (int j = 1; j <= n; j = j + i ) { printf("Hi"); } } Here, the ...
0
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1answer
108 views

Prim's Minimum Spanning Tree implementation $O(mn)$ or $O(m+n \log n)$?

I am reading Prim's MST for the first time and wanted to implement the fast version of it . $m$ - The number of edges in the graph $n$ - The number of vertices in the graph Here's the algorithm ...
1
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1answer
102 views

Recurrence of T(n) = T(n/3) + T(2n/3) [duplicate]

I've searched online for this but I only seem to find answers for a similar equation: T(n) = T(n/3) + T(2n/3) + cn But the one I'm trying to solve is: ...
-1
votes
1answer
42 views

What's the time complexity of this append method? [closed]

I made a method that appends a sequence to another sequence. So: (append [1,2,3] [4,5,6]) = [1,2,3,4,5,6] CODE In C# ...
0
votes
1answer
27 views

The number of executions of the count statement; how many?

How many times does the statement count in line 5 executes in terms of $n$? ...
4
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3answers
128 views

Are there dynamic programming examples that run in exponential time?

Are there dynamic programming examples that run in exponential time? Every example that I've seen so far constructs the top half of a matrix in a bottom-up fashion ($n^2$) from the base case and ...
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7answers
531 views

Checking if there are 2 elements in an array that sum to X in O(n lg n)

I have thought about the most useful way of checking an array for 2 elements that sum to X. The trivial solution is to check the sum of every element with every element, and the complexity of this ...
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votes
2answers
118 views

How to find the cost of pseudocode with a nested loop and a nested if statement?

How can I find the cost of pseudocode with a nested loop and a nested if statement? On the left hand side is an example from a textbook I am following. On the right hand side is pseudo code that I ...
2
votes
1answer
84 views

Time complexity of proximity search in distance matrix

I am a high school student computationally studying the 3-dimensional structure of chromosomes by 40 kilobase loci. In a nutshell, loci that are close in space tend to express their genes at the same ...
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1answer
66 views
4
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1answer
105 views

Which computational model is used to analyse the runtime of matrix multiplication algorithms?

Although I have already learned something about the asymptotic runtimes of matrix multiplication algorithms (Strassen's algorithm and similar things), I have never found any explicit and satisfactory ...
3
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1answer
61 views

Compare asymptotic WC runtime with measured AC runtime

I have an algorithm and I determined the asymptotic worst-case runtime, represented by Landau notation. Let's say $T(n) = O(n^2)$; this is measured in number of operations. But this is the worst ...
1
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1answer
255 views
1
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1answer
59 views

Runtime analysis of a “find the secret number” algorithm

The algorithm task is to find an integer (range is not known). the function guess(num) returns one of three chars: '>','<' or '='. Find the secret number ...
1
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0answers
95 views

FInd the running time complexity of functions [closed]

For each of the procedures below, let $T(n)$ be the running time. Find the order of $T(n)$ (i.e., find $f(n)$ such that $T(n) ∈ Θ(f(n))$. Do not worry about how rounding errors affect running time. ...
1
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1answer
26 views

Understanding expected time bound for unsuccessful search in R-way tries

As per Tries slides (page 17) from Algorithm 4th edition book by Robert Sedgewick, the asymptotic expected runtime for an unsuccessful search in $R$-way tries miss is $O(\log_R N)$. Can someone please ...
1
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1answer
362 views

Complexity analysis of while loop with two conditions

I am curious how to do a line by line analysis of this piece of code using the "Big O" notation. ...
0
votes
1answer
149 views

How to find the asymptotic runtime of these nested loops? [duplicate]

i=n; while(i>0) { k=1; for(j=1;j<=n:j+=k) k++; i=i/2; } The while loop has the complexity of $\lg(n)$ the j value of inner loop runs ...
5
votes
1answer
128 views

Largest set of vertices that is larger than its set of neighbors

I am reading a unpublished paper describing an algorithm. In one step of the algorithm, there is a bipartite graph $G(X,Y,E)$, where $X=\{1,...,n\}$. For every subset $X' \subseteq X$, they define ...
3
votes
1answer
106 views

Relation between space and time complexity for machines with write once read many (WORM) memory

While thinking about different calculi for predicate logic (like natural deduction and sequent calculus), I noticed that these calculi are (often) presented in a form suitable for "human computers". A ...
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3answers
187 views

Worst run-time for 3 nested loop

Suppose we need to find a tight asymptotic bound on the worst case run time of the following program ...
0
votes
1answer
111 views

What is the complexity of this bubble sort algorithm? [duplicate]

I have been doing a little reading up on bubble sort and have read on wikipedia that it's complexity is measured as $\Theta(n^2)$ This bubble sort however is slightly more efficient. I thought this ...
4
votes
3answers
227 views

When does an algorithm run in $O(1)$ time?

When can an algorithm be said to have $O(1)$ complexity? My doubt is if $n$ is specified to be a large number but constant and we cannot implement it in reality without a loop even then can we call it ...
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1answer
3k views

Best and worse case inputs for heap sort and quick sort?

So given a input of lets say 10 strings, what way can we input these so we get the best or worst case for these two given sorts? ...
-1
votes
2answers
82 views

Recurrence for total number of extraneous key insertions in a hash table

I have a practice exam question that I don't know how to set up a recurrence for. It is dealing with a hash table. The question is as follows: Suppose that a hashing strategy is designed so that ...
1
vote
1answer
214 views

Sum number of times statement is executed in triple nested loop

I have this code fragment: for( i=0; i<n; i++ ) for( j=0; j<i; j++ ) for( k=0; k<j; k++ ) S; I need to find the number of times ...