UNCTIONS AND RECURSIVE FUNCTIONS Use #include Implement the picture sho
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MULTIPLE FUNCTIONS AND RECURSIVE FUNCTIONS
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- For function log, write the missing base case condition and the recursive call. This function computes the log of n to the base b. As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 and log(10, 100) -> 2 public int log(int b, int n ) { if <<Missing base case condition>> { return 0; } else { return <<Missing a Recursive case action>> }}The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written recursively.In C programming Mathematically, given a function f, we recursively define fk(n) as follows: if k = 1, f1(n) = f(n). Otherwise, for k > 1, fk(n) = f(fk-1(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns fk(n). int f(int n);int fcomp(int n, int k){
- Write a recursive function in f#, named specialSum, that has the followeing signature: int * int -> int, where sum(m,n) = m + (m +1) + (m+2) + ... + (m + (n-1)) + (m+n) for m >= 0 and n >= 0: (Hint use two clauses with (m,0) and (m,n) A PATTERNS.) start code with let rec specialSum (m,n) match m,n with | m,0 -> | m,n - >Write a recursive fibonacci (n) function with an expression body. The function should return an Int; it will be too slow to deal with inputs whose fibonacci numbers are too large anyway. You do *not* need to use memoization. Note that: fibonacci(0) = 0 fibonacci(1) = 1 fibonacci(n, where n is greater than 1) = fibonacci(n-2) + fibonacci(n - 1)Write a recursive function using python for the problem: A palindrome is a sequence of characters which is the same when the sequence is reversed. Given an array A indexed from p to q containing characters, determine if the sequence of characters in A[p..q] forms a palindrome. Return True is a palindrome is formed and return False if it does not.
- Write 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…a) Write a non-recursive function in C++/ to multiply all even numbers from 2 to n, where n is an input to the function, and n>=2. (reminder: An even number is divisible by 2 and generates a remainder of 0. for example 2,4,6,... are even numbers). b) Analyze your algorithm in part (a) in the worst-case. Show all your work. Then express the time as Big-O().(a) Give a recursive definition of F(n) where F(n) =1+2+3+....+n. (b) Find the value of a4 if a1 = 1, a2 = 2, and an =an−1 + an−2 +· · ·+a1
- Write a recursive function named decrypt, which takes a string s and a dictionary d where each key in the dictionary is a string word associated with a secret code as its key. This function should return the list of all possible ways (order it returns it in doesn’t matter) in which the string s can be decoded by splitting it into secret codes and separating the corresponding words of the decoded word with spaces. For instance, calling decrypt('turing', {'turing': 'A', 'tur': 'B', 'ing': 'C', 'tu': 'D', 'ring': 'E', 'ri': 'F', 'ng': 'G'}) returns ['A', 'D E', 'D F G', 'B C']. def decrypt(s: str, d: {str: str}) -> [str]:Write a recursive function for Euclid's algorithm to find the greatest common divisor (gcd) of two positive integers. gcd is the largest integer that divides evenly into both of them. For example, the gcd(102, 68) = 34. You may recall learning about the greatest common divisor when you learned to reduce fractions. For example, we can simplify 68/102 to 2/3 by dividing both numerator and denominator by 34, their gcd. Finding the gcd of huge numbers is an important problem that arises in many commercial applications. We can efficiently compute the gcd using the following property, which holds for positive integers p and q: If p > q, the gcd of p and q is the same as the gcd of q and p % q.Define a recursive function (rem r b) that, given a regular expression r and a bool b, returns a new regular expression r′ that matches exactly the set of all strings s such that string bs is matched by r. We will call r′ the remainder of r after division by b. For example, if r matches {T,FF T,TFF} and b = T, then r′ can be any regular expression that matches exactly the set {ε,FF} (because T and TFF are the only strings matched by r that begin with b = T, and their remainders are ε and FF, respectively). Here are some examples of what your function could output (but these are not the only answers!): • rem (false(false+true)∗) false = (false+true)∗ • rem (false(false+true)∗) true = ∅• rem (false∗ + true∗) true = true∗• rem ((false∗)(true∗)) true = true∗ Your implementation need not output these exact regular expressions as long as it always outputs an equivalent regular expression (i.e., one that matches the same set of strings as the given answer). These are also not the only test…