(a) A fermite flep binary string is a binary string that is the satne when the otder of the bits is reversed ind then all of the bits are imverted. For example, 010101 (reversed/laackwards order 101010), 0011 (reveravd/backwards order 1100), and 11001100 (reversod/backwards order 00110011) ate fippity ilip binary strings. ( 12 points) 1. How mamy fippity flip binary strings ure there of lergth 2n ? ii. How many bits would the most efficient encoding of such strings use? (in terms of n.) iii. Develop your own encoding/decoding algorithm where the code uses this number of bits. (Please give a brief description of how it warks on an arbitrary input.) iv. Use your encoding to encode the following flippity tlip binary stringss - 0011010011 - 0110101001 - 010101 v. Use your decoding to decode the following strings: (put "not decodable" if you can't decode the string.) - 110 - 101 - 000 (b) A valley permutation of length n is an arrangement of the numbers 1 through n in such a way that the numbers deerease down to a podnt and increase after that and each number is used exactly once. For example: (6,4,1,2,3,5) is a villey permutation of length 6.(5,4,2,1,3,6,7) is a valley permutation of length. 7. Note that this includes permutations that are strictly decreasing. litse (5,4,3,2,1), and permutations that are strictly increasing, Hike (1,2,3,4,5,6). (12 points) i. How many n-length valley permutations are there? ii. How many bits would the most efficient encoding of such permutations use? (in terms of n.) iil. Develop your own encoding/decoding algorithn where the code uses this number of bits.. (Please give a brief description of how it works on an arbitrary input.) iv. Use your encoding to encode the following villoy permutations: - (8,6,4,2,1,3,5,7) - (3,2,1) - (1,2,3,4,5,6,7) v. Ube your decoding to decode the following strings- (put "not decodable" if you can't decode the string.) - 001001 - 10111 - 00100