Q4. Write the Recursive algorithm for Binary search. Consruct the recurrence relation for recursive algorithm of Binary search and solve using backward subsitution method.

Give an account of the stopping condition for the recursive binary search, and elaborate on why such a condition is required of all recursive algorithms.

Q5. Write the Recursive algorithm for Merge Sort.Consruct the recurrence relation for recursive algorithm and solve using bachward Subtution.

The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.

Please show and explain so I can nderstand.

Give an account of the stopping condition for the recursive binary search, and elaborate on why such a condition is required of all recursive algorithms.

Use recursive functions only Python only** onlyAU - Given an RNA sequence, returns a new sequence consisting of only the 'A' and 'U' bases from the original sequence with the 'C' and 'G' bases removed. Define onlyAU with 1 parameter Use def to define onlyAU with 1 parameter Do not use any kind of loop Within the definition of onlyAU with 1 parameter, do not use any kind of loop. Use a return statement Within the definition of onlyAU with 1 parameter, use return _ in at least one place. Call onlyAU Within the definition of onlyAU with 1 parameter, call onlyAU in at least one place.