problems.txt

Solve all problems in order. Do not copy and paste, but do refer to previously solved problems. Show me each problem as it's solved if I'm available. 

The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.

Given positive integer n, return a list of the of the Collatz sequence from n to 1. Recursive and iterative.
3 -> [3, 10, 5, 16, 8, 4, 2, 1]

Given positive integer n, return the number of steps required to go from n to 1. Recursive and iterative.
3 -> 7

Given positive integer n, return a list of length n where each 1-index is the number of steps required for that number to reach 1. Recursive and iterative
4 -> [0, 1, 7, 4]

The Fibonacci numbers form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1.

Return a list of the first n numbers of the Fibonacci sequence. Recursive and iterative.
0 -> []
1 -> [0]
4 -> [0, 1, 1, 2]

Return the nth (0 index) number of the Fibonacci sequence. Recursive and iterative.
0 -> 0
9 -> 21

Return the greatest Fibonacci number less than or equal to n. Recursive and iterative.
12 -> 8
13 -> 13

Given a whole number, return if that number is a Fibonacci number. Recursive and iterative.
1 -> True
4 -> False

Given a whole number n, return a list of n+1 booleans where each item in the list represents if its 0-index is a Fibonacci number.
6 -> [True, True, True, True, False, True, False]

Given a string, return a new string keeping only the first occurrence of each character in order.
'caardc' -> 'card'

Given a string, return a new string keeping only the first two occurrences of each character in order.
'abacbabbcd' -> 'abacbcd'

Given a string, return a new string keeping only the last occurrence of each character in order.
'caardc' -> 'card'

Given a dictionary, reverse the keys and value in place. Keys and values are disjoint sets.
{'a': 0, 'b': 1} -> {0: 'a', 1: 'b'}