Write a method factorial that accepts an integer parameter n and that uses recursion to compute and return the value of n factorial (also known as n!).
e.g. fact(4) = 4 * 3 * 2 * 1 = 24
Write a method reverse that accepts a string as a parameter and then returns the reverse of the string.
e.g. reverse("hello") = "olleh"
Write a method nested that accepts a string of only parenthesis and then returns if those parenthesis are properly nested.
e.g. nested("((()))") = true e.g. nested("())") = false
Write a method fib that accepts an integer n as a parameter and returns the nth fibonacci number.
e.g. fib(4) = (1 1 2) 3 = 3
Write a method pal that accepts a string s as a parameter and returns a boolean value indicating if that string is a palindrome or not.
e.g. pal("racecar") = true e.g. pal("smile") = false
Write a method power that accepts two numbers, base and exponent, as a parameters and returns the base raised to the exponent.
e.g. power(10,3) = 10 * 10 * 10 = 1000
Write a method binary that accepts an integer n as a parameter and that returns a string of all binary numbers that have n digits in ascending order. All n digits should be shown for all numbers, including leading zeros if necessary. You may assume that n is non-negative. If n is 0, an empty string should be returned. Do not use a loop in your solution; implement it recursively.
Write a method travel that accepts integers x and y as parameters and uses recursive backtracking to return all solutions for traveling in the 2-D plane from (0, 0) to (x, y) by repeatedly using one of three moves:
East (E): move right 1 (increase x) North (N): move up 1 (increase y)
The following shows one such path to the point (5, 3). 0,0 1,0 2,0 3,0 4,0 5,0 5,1 5,2 5,3 ==> EEEEEENNN
You may assume that the x/y values passed are non-negative. If x and y are both 0, return an empty string.