Rhyming scheme equivalence
Roses are red A
Violets are blue B
Sugar is sweet C
And so are you B
English teachers like to represent the rhyming pattern of poems with letters. Each line rhymes with lines with the same letter. In this case, B lines rhyme together, but the A and C lines don't rhyme. We will call that a "ABCB" rhyming scheme. However, the choice of letters is arbitrary. We could have called it "IBPB" or "XALA".
Autocomplete
I always liked flexible autocomplete where you can type a few letters, even skipping some letters, and it can find the file or word for you.
Your task is to write a function that determines if you can complete a sequence of characters to a given string.
Examples
(completes? "a" "autocomplete") ;=> true
Backspace jam
Let's say we have users typing keys on the keyboard. We capture the characters they represent in strings. However, sometimes the user hits the backspace key, which removes the previous character. We will represent a backspace key press with a # character. Write a function that applies the behavior of backspace to the string.
Examples
(apply-bs "abc#") ;=> "ab"
(apply-bs "abc###") ;=> ""
(apply-bs "###abc") ;=> "abc"
Consecutive numbers
Write a function that determines whether a sequence of integers can be rearranged into a sequence of consecutive numbers without duplicates. The function should return the sequence of consecutive numbers or nil if it is not possible.
Examples
(consec []) ;=> () ;; trivially true
(consec [1]) ;=> (1) ;; ditto
(consec [3 1 2]) ;=> (1 2 3)
Ulam sequence
The Ulam sequence is an interesting mathematical sequence of integers. It starts with [1 2]. At each step, the next element is:
Let's walk through an example.
Phrase maximization
Imagine we have the following sentence.
she sells sea shells by the sea shore
We want phrases that are as big as possible, yet no bigger than 10 characters long. A phrase must contain entire words and a space between them. And an instance of a word should only exist in the first phrase that matches.
We start at the beginning. "she sells" is <= 10 characters. We can't add the following "sea" because "she sells sea" is 13 characters. That means "she sells" is a maxmizing phrase. We now start at "sea" and continue.
Reverse-Polish calculator
Reverse-Polish notation is a way to write mathematical expressions where the operator appears after the operands. For example:
1 2 + => 1 + 2 = 3
In traditional parenthetical notation, that is equivalent to (1 + 2) and in Lisp (+ 1 2). If we assume there are four binary arithmetic operators (+, -, *, and /), we can write arbitrarily complex expressions with no need for parentheses.
Product of digits of sum
Write a function that takes one or more numbers as arguments. It should sum them, then multiply the digits. If the answer is one digit long, it's done. If it's more than one digit, repeat and multiply the digits again.
Examples
(sum-prod 4) ;=> 4
(sum-prod 10) ;=> 0 (since the sum is two digits, then 1 * 0)
(sum-prod 11 12) ;=> 6
Longest Alternating Substring
Write a function that takes a string of digits and returns the longest substring that contains only alternating odd/even digits. If two substrings have the same length, return the one that appears first.
Examples
(longest-alt-subs "") ;=> ""
(longest-alt-subs "1") ;=> "1"
(longest-alt-subs "123") ;=> "123"
Dueling Knights
A chess board has nothing but knights ♞ and empty spaces. In this setup, the color of the knights doesn't matter. Each knight could potentially capture any other. Your job is to write a function to figure out which knights can capture each other, if any.
A board is represented as a vector of vectors, each 8 elements long. A 0 represents an empty square. A 1 represents a knight. Your function should return a collection of pairs. The pairs represent the positions of the two knights that can capture each other.
For reference, see this site for understanding how knights move and capture.
Examples