Recall that the set {0,1}* is the set of finite length bit strings defined recursively by the following rules: Foundation rule: The empty string λ = {0,1}*. Constructor rule: For s = {0,1}*, s1 = {0,1}* and sO E {0,1}*. Consider the recursive function flip which takes a bit strings for input and gives a bit strings as output, defined by the following: a. Foundation rule: flip(X) = A. Constructor rule: For s = {0,1}*, flip(s0) = flip( s )1 and flip(s 0) = flip(s)1. What is the output when flip is applied to the following strings? For full- credit, you must show the step-by-step application of the flip function. i. 010 ii. 1101 iii. 0010 5 10 13*
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- Recursive Palindrome! Recall that a palindrome is a string that reads the same forward and backward. Write a recursive function is_palindrome (s:str) -> bool to check whether a string s is a palindrome. Here's a hint: think about how you can use is_palindrome(t), where t is a substring of s, to help you decide whether s is a palindrome. Your Answer: 1 # Put your answer here 2 SubmitWrite a recursive function that, given a sequence of comparable values, returns the count of elements where the current element is less than the following ( next ) element in the given sequence. See the examples given below. def count_ordered ( seq ) : """ Input : A sequence of comparable elements Output : The number of elements that are less than the following element in the sequence Example : >>> count_ordered ( [ 1 , 2 , 3 , 4 , 5 , 6 ] ) 5 >>> count_ordered ( ( 1 , 12, 7.3 , -2,4 ) ) 2 >>> count_ordered ( 'Python' ) 2 >>> count_ordered ( [ 6 ] ) 0 >>> count_ordered ( [ ] ) 0 """ In the first example above , count_ordered ( [ 1,2,3,4,5,6 ] )the returned answer is 5 because for all the first 5 numbers the current number is less than the next number. In the second example above, count_ordered ( ( 1,12,7.3 , -2,4 ) )the…Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.
- For function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}Write a recursive Racket function "update-if" that takes two functions, f and g, and a list xs as parameters and evaluates to a list. f will be a function that takes one parameter and evaluates true or false. g will be a function that takes one parameter and evaluates to some output. The result of update-if should be a list of items such that if x is in xs and (f x) is true, then (g x) is in the list. The output list's elements should keep the input list's items in the same relative order. For example (update-if even? add1 '(1 2 3 4)) should evaluate to '(3 5) because 2 and 4 make even? true and add1 turns 2 and 4 into 3 and 5.Python Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: def printAll(seq): if seq: print(seq[0]) printAll(seq[1:]) Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it? how ???
- Python Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: def printAll(seq): if seq: print(seq[0]) printAll(seq[1:]) Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it? its supposed to print something like thisWrite a recursive function that lists al of the two-element subsets of a given set of letters in the folowing format. For example, when twoElementSubsets takes "ACEG"as parameter, wil print twoelement-subsets in the folowing format (A, C) (A, E) (A, G) (C, E} (C, G) E. G) Write a C program to test your function. Read the string (a set of letters) from he user. The number of parameters that twoElementSubsets function may take depends on your recursive function de sign. Sample Inputi ACEG Sample Outputi: (A C) (A. E) (A G) (C. E) (C. G) (E. G)Write a recursive function that lists al of the two-element subsets of a given set of letters in the folowing format. For example, when twoElementSubsets takes "ACEG" as parameter, it wil print twoelement-subsets in the folowing format (A. C) (A, E) (A, G) (C. E) (c, G) E. G) Write a C program to test your function. Read the string (a set of letters) from he user. The number of parameters that twoElementSubsets function may take depends on your reaunsive function de sign. Sample Ingutt ACEG Sample Outputi (A C) (A E) (A G) (C, E) (C. G) (E. G) Sample Input EDCBA Sample Output2: (E. D) (E. C) (E, B) (E. A) (D. C) (D. B) (D. A) (C, B) (C. A) (B. A) For additional samples, please look at the input/output fles.
- Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: def printAll(seq): if seq: print(seq[0]) printAll(seq[1:]) Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it?Lee has discovered what he thinks is a clever recursive strategy for printing the elements in a sequence (string, tuple, or list). He reasons that he can get at the first element in a sequence using the 0 index, and he can obtain a sequence of the rest of the elements by slicing from index 1. This strategy is realized in a function that expects just the sequence as an argument. If the sequence is not empty, the first element in the sequence is printed and then a recursive call is executed. On each recursive call, the sequence argument is sliced using the range 1:. Here is Lee’s function definition: Write a program that tests this function and add code to trace the argument on each call. Does this function work as expected? If so, are there any hidden costs in running it?python code Write a recursive function such that, given a list of intergers (say v) and an integer value (say x), the function returns resulting subset if there is a subset of intergers in v that sum up to x. Otherwise the function returns an empty list; Also write a sample code that runs this function using an example list and value x, and state the expected result