Questions tagged [rational-numbers]
This challenge involves the manipulation of rational numbers, i.e. those which can be represented as a fraction of integers. Do not use this tag if rational numbers are just one of several admissible input/output formats, but rather if the use of exact rational arithmetic is required.
101
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NaN is not equal to NaN
In many programming languages, the floating-point value NaN, or "not a number", in some programming languages generated by the expression ...
- 1,391
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10
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Egyptian fraction representations of 1 without prime denominators
Background
As noted in this question, for all positive integers \$n>2\$ there exists at least one Egyptian fraction representation (EFR) of \$n\$ distinct positive integers \$a_{1} < a_{2} < \...
- 211
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Longest sequence of Egyptian fractions with n as denominator
Background
From Wikipedia: An Egyptian fraction is the sum of distinct unit fractions. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, ...
- 203
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Find the smallest integer multiple of a Decimal
The Challenge
Given a rational number, determine the smallest number which is a positive integer multiple of it. Eg.
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Decimalize a Fraction
Preamble
A common pain-point when working with rational numbers and decimals is how infrequently one can represent their rational number as a clean, non-repeating decimal. Let's solve this by writing ...
- 10.9k
21
votes
13
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Minkowski's ?(x) for rational x
Here is Minkowski's question mark function:
It is a strictly increasing and continuous function from the reals to themselves that, among other unusual properties, maps rational numbers to dyadic ...
- 3,845
16
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15
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Find Index of Rational Number in Calkin-Wilf Sequence
Related
From Wikipedia:
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number \$1\$, and any ...
- 7,131
11
votes
5
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Whole Number Groups
Given a list of fractions, group them so that each group sums to a whole number. This should be done in such a way to maximize the number of non-empty groups.
You may assume a solution exists. Order ...
- 12.7k
19
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10
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Enumerate the rationals
The cardinality of the set \$\mathbb Q\$ of rational numbers is known to be exactly the same as that of the set \$\mathbb Z\$ of integers. This means that it is possible to construct a bijection ...
- 20.9k
0
votes
8
answers
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Print ascending proper fractions using integers up to the given input
User inputs an integer. Print out proper fractions using all positive integers up to the user's input, in ascending order.
Rule 1: Eliminate equal fractions.
Rule 2: Fractions should be in their ...
- 175
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20
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Next digit of rational number
Story:
The π was recently computed with accuracy to 100 trillions digits, but it is useless to us. We can't do accurate enough math, because rational numbers are too boring and so we don't know that ...
- 1,885
18
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12
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In between fractions
Given two positive integer fractions \$x\$ and \$y\$ such that \$x < y\$, give the fraction \$z\$ with the smallest positive integer denominator such that it is between \$x\$ and \$y\$.
For example ...
- 99k
1
vote
1
answer
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Best performance on x/(y+z) + y/(x+z) + z/(x+y) = N
Consider the equation $$\frac x {y+z} + \frac y {x+z} + \frac z {x+y} = n$$ for positive integers \$x, y, z\$ and \$n \ge 4\$. Your code will receive \$n\$ as an input, and output three integers \$x, ...
- 1,548
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votes
17
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Infinite Candle Sequence
I have a cake shop that specialises in birthday cakes. The cakes that I sell must have candles placed in a circle. You would probably think I can just divide 360° by the number of candles, but the ...
- 2,327
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votes
7
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Factorials of primes decomposition
You have to decompose a positive integer/fraction as a product of powers of factorials of prime numbers.
For example
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- 5,099