Questions tagged [comparison]

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20
votes
7answers
4k views

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 ...
20
votes
12answers
12k 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 ...
7
votes
2answers
2k views

More efficient algorithm for determining if one list is a sublist of another list

I'm trying to build an algorithm which takes two lists of natural numbers and finds if every element of the first list is displayed at least once in the second list. What if the list is sorted? An ...
5
votes
3answers
9k 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 ...
4
votes
2answers
335 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'(...
4
votes
1answer
685 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) ...
3
votes
3answers
224 views

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

We get two arrays: ordering = ["one", "two", "three"] and ...
3
votes
1answer
107 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. ...
3
votes
2answers
73 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 ...
3
votes
1answer
1k views

Cost of partitioning in quicksort

I'm reading "Algorithms Fourth Edition" by Sedgewick & Wayne and am wondering if I have spotted an error in the book or if I just can't wrap my head around something so simple. When talking about ...
3
votes
1answer
36 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 ...
3
votes
1answer
610 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?
3
votes
1answer
135 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 ...
3
votes
1answer
316 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 ...
3
votes
0answers
866 views

How to determine the fewest number of comparisons for Heapsort?

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 $...
2
votes
3answers
94 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 ...
2
votes
2answers
78 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 ...
2
votes
2answers
2k 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 ...
2
votes
2answers
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 ...
2
votes
2answers
133 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 ...
2
votes
2answers
44 views

What is a sorting algorithm that is robust to a faulty comparison?

I want to sort a list of n items with a comparison sort. However, one of the comparisons made by the algorithm will be flipped from what it's supposed to be. ...
2
votes
2answers
77 views

Constraint satisfaction problem: solve system, then evaluate whether many additional constraints are satisfied one at a time

I have a system that consists of binary inequality constraints between variables, plus some indicator variables that can assume only two values: ...
2
votes
1answer
83 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 ...
2
votes
0answers
85 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 ...
1
vote
2answers
231 views

Sorting an array with x sorted subarrays

I have been given two True/False questions regarding sorting an array. The questions are as following - Question A Given an array A with 3n keys that contains three equal parts A[1,n], A[n+1,2n] and ...
1
vote
1answer
590 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 ...
1
vote
2answers
103 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: ...
1
vote
1answer
914 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 ...
1
vote
1answer
379 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 ...
1
vote
1answer
75 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 ...
1
vote
3answers
733 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 ...
1
vote
1answer
366 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 ...
1
vote
1answer
76 views

Finding maximum of $n$ many $m$-bit integers

Suppose you want to determine the largest number in an $n$-element set $X = (x_1, x_2, \dots , x_{n})$, where each element $x_i$ is an integer between $1$ and $2^m − 1$. Describe an algorithm that ...
1
vote
1answer
384 views

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 ...
1
vote
0answers
14 views

How to find the number of common edges in two sequences?

Lets say I have two sequences such as these: Sequence 1: A B C E D F Sequence 2: A B D F C E Both sequences contain the same set of elements and each element is unique. I want to find the number of ...
1
vote
0answers
93 views

What is the best way to compare two images for similarity if the brightness of the second image was changed?

I calculate similarity percent between two images. Another image is the same with changed brightness. I've already tried comparing by pixel (euclidean distance for grayscale and 0/1 values), comparing ...
1
vote
0answers
41 views

QuickSort when the range of data is known

In QuickSort Algorithm, the pivot is chosen as the first element or a randomised element. However, if the range of data to be sorted is known, For example, from 1 to 100, and they are mostly equally ...
1
vote
0answers
31 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 ...
1
vote
0answers
42 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 ...
1
vote
0answers
534 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 ...
0
votes
1answer
55 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 ...
0
votes
2answers
5k 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 $5 \cdot {4\choose 2} = 30$ ...
0
votes
1answer
132 views

Algorithm to compare two data sets

I have two data sets of a particular structure: ...
0
votes
1answer
27 views

Longest palindrome substring in logarithmic runtime complexity

In a palindrome of size N, the amount of candidates for the longest palindrome is N^2. Therefore, the information theoretic lower bound (IBT) should be lg(N^2), which is equivalent to a runtime ...
0
votes
1answer
2k 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, ...
0
votes
1answer
252 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 ...
0
votes
1answer
207 views

Compare vs Radix

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 ...
0
votes
1answer
149 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 ...
0
votes
2answers
202 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 ...
0
votes
0answers
25 views

Counting the number of comparisons in red black tree

I have an array with $N$ elements and I run an algorithm that find how many distinct elements are in the array by using a red black tree as follows: for each element if element not in tree insert ...