Largest integer from concatenation
If I have a list of integers, I can concatenate their base-10 strings to get one large integer. However, if I reorder them, then concatenate them, I could get a larger integer. The task here is to find the largest integer you can create by concatenating a given set of integers.
Here are some test cases:
(maxcat [1 2 3 4 5 6 7 8 9]) ;=> 987654321
(maxcat [12 34 56 199]) ;=> 563419912
Conway's Game of Life
Conway's Game of Life is a famous cellular automaton. The rules are simple:
Cells are arranged in a square grid. A cell is either alive (black) or dead (white). Cells have eight neighbors that surround it. A dead cell comes to life if it has exactly three live neighbors. A live cell dies if it has four or more neighbors. A live cell dies if it has one or zero neighbors.
Langton's ant (from Rosetta Code)
Langton's ant is a cellular automaton that models an ant sitting on a plane of cells, all of which are white initially, the ant facing in one of four directions.
Each cell can either be black or white.
The ant moves according to the color of the cell it is currently sitting in, with the following rules:
range consolidation (from Rosetta Code)
We can represent a range of numbers as a tuple, like this [1 4]. That means all real numbers between 1 and 4, including 1 and 4. The task is to write a function that takes a collection of ranges and consolidates them so that there are no overlapping ranges.
For example, [1 4] and [3 5] overlap, so they would be consolidated to [1 5]. [10.2 15] does not overlap, so it doesn't change.
(consolidate [[1 4] [3 5] [10.2 15]]) ;=> [[1 5] [10.2 15]]
coin sums
(This one is from Project Euler).
In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:
1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
It is possible to make £2 in the following way:
binary divisible by 3
Write a function that takes a string of binary numbers, separated by commas. It will look like this:
"1100,101,111,1111"Take that string, parse out the numbers, and return a string, in the same format, that only includes numbers divisible by 3.
remove the nth element from a list
Clojure's two main sequences, lists and vectors, do not easily let you remove an item from the collection when that item is in the middle of the sequence. Sometimes we need to do that. Write a function remove-at that removes the element at position n from a sequence.
(remove-at 3 [1 2 3 4 5 6])
; => (1 2 3 5 6)Make this robust. You'll have to make some hard design decisions like how to handle the empty sequence, how to handle out-of-bounds n, and more.
list of digits
Write a function that takes a number and returns a sequence of digits. Here's an example:
(digits 3452)
;=> [3 4 5 2]For extra credit, let digit take another parameter, which is the base of the number in which to represent digits. The default will be 10, but it should work for any number >= 2.
generate combinations
If I have 4 flowers to choose from (#{:rose :lily :daisy :tulip}), I can generate 4 different combinations of 3 flowers.
(#{:rose :lily :daisy}, #{:rose :lily :tulip}, #{:rose :daisy :tulip}, #{:lily
:daisy :tulip})Write a function combinations that takes a collection of values and a number of items to choose and generates all combinations of that size.
Run-length encode a sequence
Run-length encoding is a way to represent a sequence in a more compact form. Instead of saying :p :p :p, you say “3 :ps”. Write a function that takes a sequence and returns that sequence with run-length encoding.
For example:
(rle [:a :a :a :b :c :d :d :d :d])
;=> ([3 :a] [1 :b] [1 :c] [4 :d])