Combinatorics is the branch of computer science and math that focuses on the enumerable arrangements of a finite set. This includes permutations, combinations, and partitions.
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The maximum number of induced cycle in a simple directed graph
Given a simple directed graph G=(V,E) an induced cycle is a cycle where no two vertices of the cycle have an edge that is not in the cycle.
(Chordless cycles are induced cycles with at lease 4 ...
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Algorithm to create all unique sets of the alphabet using arbitrary group sizes
I'm looking for an algorithm to help me out with a combination of combinations problem.
I have generated two lists of combinations of letters: (26 choose 6) & (26 choose 5)
My goal is to be able ...
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Mapping match-up combinations into an integer
First of all, I want to say I wasn't sure if I should post this here or in math.stackexchange but I think the question is too programming-related to belong to the latter community. Definetly not a SO ...
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Restricted randomization of a binary vector
Suppose I have a binary vector of sample size N with each of the two possible values (e.g., 0 and 1 occurring equally often).
For example, if N=10, the binary vector is: 0 0 0 0 0 1 1 1 1 1
Suppose ...
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What algorithm to use to count realization of high combinatorics setup?
I'll use the MobA games to illustrate what I'm asking since it's easier to explain even tho I want to apply that algorithm to time series.
In a MobA game you have more than 100 characters and every ...
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Approaches to combinatorial optimization problem
Problem
I have the following combinatorial optimization problem:
A set of applications need to be distributed among a set of nodes.
Each node has a capacity and each application has a required ...
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355 views
Fast indexing of k-combinations
I'm revisiting an old problem that I was working on some time ago.
A typical scenario is "3 bits are set within an 8 bit integer", i.e. 00000111.
All unique combinations with 3 set bits can easily ...
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Algorithm to compute k-permutation without repeating and no duplicates
I have a set of integers, for example 1..20 and I want to get all possible combinations of that set drawing 5 numbers.
So each combination has 5 numbers from that set of integers. But I don't want ...
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Given an array of n bits, how to generate every permutation with i 1's and n-i 0's?
It's simple enough to brute force a collection of strings and then filter for every occurrence with the required count of 1's.
As n increases the number of possible permutations becomes very large, ...
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Domain analysis for discrete values - ON and OFF points in these cases
Following my previous question (with great answer from Bart van Ingen Schenau), I noticed a discrepancy I could not wrap my head around:
Bart mentioned that:
The point ON the boundary is by
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Domain analysis - why OFF points are inside of the domain when the border is open
I have asked on a few other sites, no response but it must be something silly as many authors mention in their books.
Here is the best text I found:
My ultimate question is:
Why the OFF point lies ...
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Number of strings containing a specific substring
I've seen numerous questions (and answers) concerning the number of binary strings (e.g "10010" containing some binary substring (e.g "00"). I'd like to know if there is a way to generalize this:
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Number of sequences when no adjacent items can be the same
I came across this one problem,
There is a particular sequence only uses the numbers 1, 2, 3, 4 and no two adjacent numbers are the same.
Write a program that given n1 1s, n2 2s, n3 3s, n4 4s ...
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How do I create every permutation [closed]
I have a list of letters, this is just an example list:
['a','b','c','d','e']
How do I compute every combination of the list? The letters cannot repeat, for example.
a,b,c,d,e
a,c,b,d,e
a,c,d,b,e
...
