# Questions tagged [comparison]

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### Why do we use the number of compares to measure the time complexity when compare is quite cheap?

I think one reason a compare is regarded as quite costly is due to the historical research as remarked by Knuth, that it came from tennis match trying to find the second or third best tennis player ...
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### Difference between GA and ABC for inference

If I have an agent-based model and I want to infer the parameters, I would normally used ABC (approximate bayesian computation), but I was recently working with someone who was using GA (genetic ...
148 views

### Sorting array of strings (with repetitions) according to a given ordering

We get two arrays: ordering = ["one", "two", "three"] and ...
17 views

### Comparison tree to get a minimum number of comparisons for merging sorted lists

Suppose A is a sorted list of length n and B is a sorted list of length 2. I am asked to ...
86 views

### Recurrence Relation of Ternary search and the number of comparisons with binary search

i was reading the binary search and ternary search algorithms. But i had a doubt with recurrence relation of ternary search as somewhere it is T(n/3)+c and T(2*n/3)+c. I want to know which one is ...
181 views

### Minimum number of comparision to find the third largest element in an array of distinct integers?

For the second largest element, I know that the formula is $n+ \lceil\log n \rceil -2$ Is there any formula for the third largest element? and if so, what is the derivation?
29 views

### Algorithm for comparing object dates and types

I'm looking for a good / efficient algorithm to compare classes of driver licences (or any type of similar objects) and their dates, so that they do not overlap and come in certain order. eg. We have ...
52 views

### Goemans' Extended Formulation of the Permutahedron And Comparator Networks that are not Sorting Networks

I am interested in using Michel Goemans' extended formulation first developed for the permutahedron to study comparator networks that are not sorting networks. In his paper "Smallest Compact ...
30 views

### How to justify using available code (in different language) for comparing algorithms [closed]

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm in the literature. Our algorithm is in MATLAB, and ...
235 views

### Turing machine - compare two words

I have a simple turing machine with single tape. I need to compare two words <w1>$<w2>$ and write output. Language is all letters and numbers. I did ...
83 views

### Why is finding minimum number of comparisons to sort $n$ elements so difficult?

In The Art of Computer Programming 2nd Ed, Vol 3, Section 5.3.1 then discuss a function $S(n)$ which is define as: $S(n)$ : The minimum number of comparisons that suffice to sort $n$ elements. ...
34 views

### Finding maximum takes at least $\lceil n/2 \rceil$ comparisons

We are given an array $A$ with $n$ elements, $n \in \mathbb{N}$ and all elements are in the set $\{1,2,3, \cdots, n \}$. I want to prove that finding the maximum in $A$ (that is, outputting the index ...
51 views

### Are comparison sort algos appropriate for SUBJECTIVE sorting?

I've been tasked with creating an online feature that ranks 50 fantasy characters from a variety of domains based on combat acumen and polls users one which one is the most powerful based on their ...
52 views

### An algorithm to drop low-priority items from a heap-based priority queue

I am looking for an efficient algorithm to drop from a complete binary min heap all items whose weight exceeds a given value. (Or, equivalently, to drop from a priority queue realised by such a heap ...
411 views

### Sorting lower bounds for almost sorted array

Can't find a good way to tackle the problem. Would appreciate any help. $A$ is an $n$ items array from an ordered set, in which every item is at most $\log n$ indices away from its position in the ...
190 views

### d-ary heap implementation vs Fibonacci heap implementation Dijkstra performance comparions

Let's say that Dijkstra’s algorithm with the priority queue using a d-ary heap. if adjusting d, we can try to achieve the best runtimes for the algorithm with d being $\sim |E|/|V|$. Then for a ...
62 views

### Optimize sorting matrix entries by row and column

I am writing a routine to store an $M$-by-$N$ sparse matrix in a balanced binary tree. The insertion routine calls a comparison function to determine where a new matrix entry $(i,j)$ should be ...
790 views

### How to compare an element with other elements within an array efficiently for a condition

I need to compare each index with one another and associated array value as well. For example, ...
57 views

### sort n numbers in the range [0,1] without multiplying or dividing

Given an array with n real numbers, each in the range [0,1], I need to sort them. Moreover, the only operations that are allowed are comparisons or copying. It means I cannot multiply or divide the ...
39 views

### Merge unstructured with structured data

We have a database with well-formated and structured data. From time to time we get Excel - files from our clients. This Excel Files have to be imported to the database. It it very important that we ...
9k views

### Data structure or algorithm for quickly finding differences between strings

I have an array of 100,000 strings, all of length $k$. I want to compare each string to every other string to see if any two strings differ by 1 character. Right now, as I add each string to the ...
91 views

### What is the name for the comparison used in C's memcmp?

The C memcmp function (and strcmp) does a comparison similar to the function below for comparing integers: ...
41 views

### Compare two atan2

I tried to implement points location algorithm using Fortune's algorithm to get Voronoi diagram and another sweepline algorithm to locate many points in $O(n\cdot\log(n))$. If there are multiple ...
543 views

### finding best n players in minimum number of comparisons

I am trying to find out if there is any generic way to find out first to nth best player in a tournament if n is less than the square root of input size i.e. 5 best players in the sample size of 25 ...
707 views

I'm currently doing an exercise that asks to prove that Standard-Heapsort requires at fewest $\frac{1}{8} n \log(n) - O(n)$ comparisons, in its best case. In its average case, Heapsort only requires $... 2answers 1k views ### Proving at least$n-1$comparisons are needed to test if an array is sorted so I need to prove the following: Prove that$n-1$comparisons are sometimes necessary to test whether an array with$n$distinct elements is sorted in increasing order, for any$n \geq 1$. The ... 1answer 375 views ### Identify similar functions I was wondering if there is any technique in order to recognize similar functions behaviour. In particular, suppose that I implement two functions$f$and$g$in a certain programming language$P$and ... 1answer 552 views ### Median-of-medians in O(log n) memory Is there a way to use median-of-medians to find a median in, simultaneously, ​ ​O(log n) ​ ​memory and O(n) comparisons? The user orlp on this site seems to claim that there is. Getting ​ ​O(log n) ... 2answers 268 views ### Is there a metric for the similarity of two image filters? Definitions An image filter is a matrix$m \in \mathbb{R}^{k_1 \times k_2 \times k_3}$which gets applied to an image$I \in \mathbb{R}^{l_1 \times l_2 \times l_3}$as a discrete convolution$$I'(... 1answer 135 views ### Comparing 2 video files [closed] I have a bunch of wmv files (~300), named the following way: video1.wmv -> videox.wmv. Some of these video files, are exact ... 1answer 98 views ### Sorting algorithm which sorts half the possible inputs in linear time Prove that there isn't any comparison sort algorithm which for an input of size$n$can sort at least half of the permutations of the input in linear time. (For the other half the algorithm can ... 1answer 134 views ### How to compare two objects for percentage of equivalence I'm trying to create a nodeJS application. It allows users to rate a bunch of songs and it stores them in their user profiles. I use this information to compare them to other users, and try to find ... 2answers 200 views ### How to determine(with some confidence) if two extremely long lists of numbers (terabytes) are similar? I have two very large files with numbers seperated by commas. What is most efficient/fastest way to say with some confidence that these two files have same numbers. The main rule if if two ... 3answers 6k views ### How do I find the max and min value of an array in 3n/2−2 comparisons? So I'm using this method to find the min and max value of an array simultaneously where I split the array into n/2 and n/2 parts. I then keep splitting each part until I have either a pair of numbers ... 0answers 530 views ### Text data comparison Okay lets say i have two data structures . two phone data for example containing their Name and spec ( cpu , ram , display etc ) . I want to check if these two phones are the same or not . Their names ... 3answers 83 views ### Fast comparison with a tolerance I am trying to find a way to compare two real numbers (actually floating-point) with a tolerance, i.e. test$|r-s|\le\epsilon$. Without loss of generality,$\epsilon=1$. I want to do this by ... 1answer 50 views ### prove sufficient number of comparisons for the merge problem It is given two subsequences. Their length are following:$2$and$5$. I can show that lower bound of comparisons is$5$. My problem is that I can't show that$5$is sufficient number of comparisons ... 2answers 3k views ### prove that minimal number of comparisons to find median among five elements is 5 [closed] I would like to prove that we need at least five comparisons to find median amoung five numbers. And my proposition: Let's consider tree of comparisons. There are at least$5 \cdot {4\choose 2} = 30\$ ...
190 views

Is it better to use comparison or radix sort to sort a long sequences of java int array? I know that I should probably use mergesort (NlogN) for comparison sort, since it is one of the fastest and ...
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### comparison in speed between the processor and the hard disk

I'm reading through William Stalling's operating system intrnals and design principles book. Talking about interrupts, it gives the following examples when comparing the speed of a processor and a ...
1k views

### Pseudocode for checking if two arrays contain the same elements?

I'm not so much confused as to write the actual code as I am to write the pseudocode. To determine if two arrays of the same size contain the same elements, I know you would need two for loops, then ...
2k views

### Application of cosine similarity to detect plagiarism

Can anyone tell me how using cosine similarity to see the correlation between two documents actually shows you if someone is plagiarising the other? I understand how cosine similarity works but don't ...
111 views

### Why comparison is dominant time consumption for comparison-based sorting algorithms? [duplicate]

Comparison-based sorting algorithms does a number of different operations to accomplish the sorting, why comparisons are the dominant time consumption? While I understand the standard analyses of ...