Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

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1answer
63 views

Decompose a value as a sum of square numbers

My daughter had a question on her maths homework which was to write a value as a sum of 4 or fewer square numbers. For example, x = 73 could be 36 + 36 + 1. I came up with a really brute force ...
3
votes
3answers
66 views

Listing the representations of integer M as a sum of three squares M = x^2 + y^2 + z^2

I am trying a number as the sum of 3 squares. For my particular project I will require a complete list since the next step is to compute nearest neighbors (here). In any case we'd like to find \$ M ...
4
votes
3answers
242 views

Compute (x+yCx)%mod

I want to compute, as quickly as possible, $$ \dfrac{(x+y)!}{x!y!} \mod m $$ with \$x,y \le 10^6\$ and a prime \$m=10^9+7\$ (called mod in my code). My current ...
12
votes
2answers
682 views

TopCoder problem “Lottery” - SRM 144 (Division I Level Two)

The problem statement Summary: The rules of a lottery are defined by two integers (choices and blanks) and two boolean variables (sorted and unique). choices represents the highest valid number ...
12
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3answers
498 views

Random permutation of int[] and ArrayList<Integer>

I wrote a simple program using int[] and ArrayList<Integer> which aims to get a random permutation output between 1 to 10, ...
6
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1answer
203 views

Generate Cartesian product of List in Java

My code, which generates Cartesian product of all lists given as arguments: ...
8
votes
2answers
101 views

Optimizing String combinations in Java

I need to obtain all combinations of a String of length k from the given elements. For example, for ...
5
votes
4answers
231 views

Character permutations - Revisited

Several hours ago I posted this question about Generating character permutations in Python. User rolfl said that my main problem was not using the right tool for the job, as Python is interpreted it ...
3
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2answers
199 views

Generating character permutations

I want to generate a 'dictionary' containing all 8 character permutations of upper-case letters such that the output file looks like: ...
3
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2answers
81 views

A (basic) Knights and Knaves Solver

In case you're not familiar with Knights and Knaves, it's a classic type of logic problem. Here's an example: "A very special island is inhabited only by knights and knaves. Knights always tell ...
2
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1answer
267 views

Nsum problem: find all n elements in an array whose sum equals a given value

I am implementing the algorithm for the following problem with Python. I am pretty new to Python, so I want to listen to any advice that improve my coding style in a "pythonic" way, even about naming ...
14
votes
4answers
733 views

Count number of ways to paint a fence with N posts using K colors

A friend sent me this question, and I'd love somebody to review this and give his opinion. Write an algorithm that counts the number of ways you can paint a fence with N posts using K colors ...
0
votes
1answer
343 views

Generating all possible permutations of the string

This generates all possible permutations of the string. I am also unable to understand the time complexity of this problem. Can someone please explain the complexity to me? ...
3
votes
1answer
47 views

Python small brute-forcer

I have 20+ key set. Keyset is like: Key[0] = { "PossibleKey0", "PossibleKey0Another", "AnotherPossibleKey0" } Key[1] = { .... There is an encryption which needs ...
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3answers
235 views

Advanced and Detailed Minesweeper Probabilities

In an earlier question, I showed my code for calculating the mine probability for each and every field in a Minesweeper board. But it doesn't stop there. In that very same Minesweeper Analyze project, ...
8
votes
2answers
148 views

A Specific Combination

This code is going to be included in my Minesweeper Probabilities project. (so far it only exists on the develop-branch) The purpose is to return a specific combination, let's say for example that ...
2
votes
3answers
123 views

Finding combinations of 3 numbers

What this code tries to do is find possible combinations of three numbers. For example, let's say I have the following numbers: 1, 2, 3, 4, 5, 6, 7 Some ...
5
votes
2answers
105 views

'Countdown' Numbers round - combine numbers arithmetically to reach a target

Countdown is a British gameshow where contestants compete in word and number challenges. During the numbers round, six numbers are chosen semi-randomly and the task is to combine them using addition, ...
1
vote
1answer
390 views

Print all permutations of a given string in Java

I want to print all permutations of a given string in Java. To do this I create one auxiliary array boolean used[] to check if I have used some character or not. ...
5
votes
1answer
1k views

Print all possible combinations of size r, from an array of size n

This is my working solution for the following problem: given an array of integers of size n, print all possible combinations of size r. Before I proceed to the solution, I have the following ...
1
vote
1answer
62 views

Combinations with replacement

I am still new to Scala and wrote a small snippet to find all the combinations with replacement of a sequence (e.g. cwr(ab, 3) should give aaa, aab, abb, bbb). The slow way would be to generate all ...
4
votes
1answer
1k views

Recursive function that generates the permutations of a string

I am looking for a review of my recursive function that generates the permutations of a string. Are there better ways to do this? ...
6
votes
2answers
99 views

How can I optimize this combination method?

I have this method that is working perfectly fine, but it's very slow, and sometimes I have to wait 15 minutes to get a good result, which is ok. I'm wondering if I can make it faster. Basically I'm ...
4
votes
3answers
130 views

Another permutator

This is a solution to this problem. The problem statement: write a program to display all possible permutations of a given input string--if the string contains duplicate characters, you may have ...
6
votes
1answer
85 views

Generating Cartesian product of strings in R

Sometimes I need to create character vectors like this one: ...
5
votes
2answers
171 views

Binomial coefficient

I wrote a C++ function to calculate the binomial coefficient, trying to avoid overflows as much as possible. ...
5
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2answers
91 views

Possible combinations following a rule

The problem is the following: We have a number of months to buy a number of supplies. The sooner we finish buying them, the better, but we don't know how much we can buy per month and would like to ...
4
votes
1answer
212 views

Seeking improved Objective-C permutation algorithm

This algorithm seeks to find all of the possible permutations of a word: ...
12
votes
3answers
1k views

Generate all possible combinations of letters in a word

This is a JavaScript function that returns ALL the possible combinations of whatever word the user enters. I am looking to clean this code up a bit...any and all suggestions are welcome! ...
4
votes
1answer
242 views

Permutations program in Python

This code asks for letters and a number of letters per word and generates all possible permutations. Then compares those permutations with an English dictionary and creates a list with all the words ...
3
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1answer
98 views

Finding the 'Minimum' AND of all the possible subsets of a set

The subset size should be greater than or equal to 2. How can I speed up this code? ...
8
votes
1answer
118 views

Verifying boardgame mathematics with MATLAB

I recently bought this math-based boardgame for my little cousins, and am now trying to verify its design with some MATLAB code. The relevant parts of the game are: A board with numbers from 1 to ...
23
votes
3answers
611 views

Analyzing Minesweeper Probabilities

Calculating probabilities in Minesweeper might sound like an easy task, but I've seen so many probability calculators that's either incorrect, horribly slow, or with ugly code (or all of them) so I ...
6
votes
5answers
669 views

Improving efficiency of Project Euler 185 (16-place Mastermind)

This a solution for Project Euler Problem 185. It works fine for the example but slow for the problem statement. How can I improve its speed and efficiency? ...
3
votes
2answers
939 views

Calculate all possible combinations of an array of arrays or strings

I'm using code adapted from this Stack Overflow question to calculate all possible combinations from an array, which may contains strings. For example: ...
14
votes
7answers
3k views

Is my solution to return kth row of the Pascal's triangle suitable for a job interview?

Question: Given an index \$k\$, return the \$k\$th row of the Pascal's triangle. For example, given \$k = 3\$, return \$[1,3,3,1]\$. Bonus points for using \$O(k)\$ space. Can it be ...
7
votes
3answers
1k views

Get distinct combinations of numbers

The below code returns all distinct combinations based on the logic that 1,2,3 = 3,2,1 = 2,3,1, so it only returns 1 instance of that set of numbers. ...
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vote
1answer
58 views

Find triangles from line

I have some lines that form triangles. I'd like to challenge the fastest way to find all triangles. In particular the code should take an ArrayList of Line2D object and return an ArrayList of ...
7
votes
2answers
99 views

Simplified Bin Packing using JavaScript

This code determines the maximum number of boxes (one size) that can fit into the back of a truck, checking all possible orientations to ensure maximum Bin Packing excitement. This is (hopefully) the ...
6
votes
1answer
159 views

Given a shape, return all triangles that can be formed

Given a shape, get all triangles that can be possible by connecting the points. Example: given 3 points, only 1 triangle is possible, but given a pentagon, 10 are possible. Also the ...
4
votes
4answers
134 views

Better way to achieve looped output result

I have 4 variables - say A, B, C and D Each variable can have 4 values - say 1, 2, 3 and 4 I need to generate all possible combinations of values Example of Expected Output: ...
3
votes
3answers
85 views

Curious fractions in functional Ruby

Problem 33 in Project Euler asks: The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is ...
7
votes
1answer
142 views

Speeding up subset sum implementation

Important fact: the number of the input is greater than 1. How do I use this fact to speed up this solution? ...
6
votes
3answers
275 views

Optimizing unique partitions of integers

I am working on a project involving the unique partitioning of integers. I.e. I am looking to have all of the partitions of n = x1 + x2 + x3 + ... + xk, where xi = xj implies i = j. For example, if I ...
7
votes
1answer
73 views

Compute stats on two class vectors

Below is a full working code example of code which is used to compute stats on two class vectors (partitions). There are two functions: pairwise_indication and ...
10
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2answers
837 views

Printing permutations of a given string

I want some feedback on the program I developed in C for printing the permutations of a given string. ...
0
votes
1answer
144 views

Finding the number of permutations of an integer array with equaling difference (not in order)

The array size is <= 16. The difference is defined as: diff[i] = array[i+1] - array[i]; I need to find the number of permutations of the original array, which ...
5
votes
0answers
372 views

Nonogram puzzle solution space

I've written some code to brute-force enumerate the solution space of nonogram puzzles up to a certain size. It does a good job up to the first ~4 billion puzzles, but I run out of disk space to store ...
7
votes
2answers
149 views

Generate permutations with symbols

Goal: Create a combination of emails based from inputted first name, last name, middle name, and a domain. Add in common separators. Then I'll check which one is correct with the rapportive API. This ...
4
votes
3answers
675 views

Prints out all ways to multiply smaller integers that equal the original number

Write a program in Java that takes a positive integer and prints out all ways to multiply smaller integers that equal the original number, without repeating sets of factors. In other words, if ...