ninetynine

P00 - Template for new implementation files.

P01 - find last element of a list.

P02 - find last but one element of a list.

P03 - find Nth element of a list.

P04 - find the number of elements in a list.

P05 - reverse a list.

P06 - find out if a list is a palindrome.

P07 - flatten a nested list structure.

P08 - eliminate consecutive duplicates of list elements.

P09 - pack consecutive duplicates of list elements into sublists.

P10 - run-length encoding of a list.

P11 - modified run-length encoding.

P12 - decode a run-length encoded list.

P13 - run-length encoding of a list (direct solution).

P14 - duplicate the elements of a list.

P15 - duplicate the elements of a list a given number of times.

P16 - drop every nth element from a list.

P17 - split a list into two parts.

P18 - extract a slice from a list.

P19 - rotate a list n places to the left.

P20 - remove the kth element from a list.

P21 - insert an element at a given position into a list.

P22 - create a list containing all integers within a given range.

P23 - extract a given number of randomly selected elements from a list.

P24 - draw n different random numbers from the set 1..m.

P25 - generate a random permutation of the elements of a list.

P26 - generate the combinations of k distinct objects chosen from the n elements of a list.

P27 - group the elements of a set into disjoint subsets.

P28 - sorting a list of lists according to length of sublists.

P31 - determine whether a given integer number is prime.

P32 - determine the greatest common divisor of two positive integer numbers.

P33 - determine whether two positive integer numbers are coprime.

P34 - calculate Euler's totient function phi(m).

P35 - determine the prime factors of a given positive integer.

P36 - determine the prime factors of a given positive integer (2).

P37 - calculate Euler's totient function phi(m) (improved).

Euler's so-called totient function phi(m) is defined as the number of positive integers r (1 <= r < m) that are coprime to m. We let phi(1) = 1.

From the definition of P34, we can see that phi(m) is equal to m * (1 - 1/p1) * (1 - 1/p2) * (1 - 1/p3) * ... where p1, p2, p3, ... are the prime factors of m.

Note that we need to use the primeFactors function from P36.

P38 - Compare the two methods of calculating Euler's totient function.

Use the solutions of problems P34 and P37 to compare the algorithms. Try to calculate phi(10090) as an example.

P39 - a list of prime numbers.

P40 - Goldbach's conjecture.

Goldbach’s conjecture says that every positive even number greater than 2 is the sum of two prime numbers. E.g. 28 = 5 + 23. It is one of the most famous facts in number theory that has not been proved to be correct in the general case. It has been numerically confirmed up to very large numbers (much larger than Scala’s Int can represent).

P41 - a list of Goldbach compositions.

P46 - truth tables for logical expressions.

P47 - Truth tables for logical expressions (2).

Continue problem P46 by redefining and, or, etc as operators. (i.e. make them methods of a new class with an implicit conversion from Boolean.) not will have to be left as a object method.

P49 - Gray code.

P50 - Huffman code.

P55 - Construct completely balanced binary trees.

P56 - Symmetric binary trees.

P57 - Binary search trees (dictionaries).

P58 - Generate-and-test paradigm.

Apply the generate-and-test paradigm to construct all symmetric, completely balanced binary trees with a given number of nodes.

P59 - Construct height-balanced binary trees.