This function uses a curious mix of iteration and recursion: function F(n) if n < 1 t<- O return 1 for i <- 0 to n for j <- i to n t<- t + j return t + F(n-1) The number of basic operations (additions and subtractions) performed is: ○ Ⓒ (n) ℗ (n²) Ⓒ (n² log n) Ⓒ (n³) Ꮎ Ⓒ (n4)
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- The following function f uses recursion:def f(n):if n <= 1return nelsereturn f(n-1) + f(n-2)5Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n):a <- 0b <- 1if n = 0return aelsif n = 1return belsefor i in 1..nc <- a + ba <- bb <- creturn b b) def f(n):a <- 0i <- nwhile i > 0a <- a + i + (i-1)return a c) def f(n):arr[0] <- 0arr[1] <- 1if n <= 1return arr[n]elsefor i in 2..narr[i] <- arr[i-1] + arr[i-2]return arr[n] d) def f(n):arr[0..n] <- [0, ..., n]if n <= 1return arr[n]elsea <- 0for i in 0..na <- a + arr[i]return aThe following function f uses recursion:def f(n):if n <= 1return nelse return f(n-1) + f(n-2)Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion?a) def f(n):a <- 0b <- 1 if n = 0return aelsif n = 1 return belsefor i in 1..nc <- a + b a <- b b <- c return bb) def f(n):a <- 0i <- n while i > 0 a <- a + i + (i-1) return ac) def f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1return arr[n]elsefor i in 2..n arr[i] <- arr[i-1] + arr[i-2]return arr[n]d) def f(n): arr[0..n] <- [0, ..., n] if n <= 1return arr[n]elsea <- 0 for i in 0..n a <- a + arr[i]return aUsing C Write a recursive function find_sum that calculates the sum of successive integers starting at 1 andending at n (i.e., find_sum(n) = (1 + 2 +. . . + ( n − 1) +n ).You have to use recursive function to solve this problem.
- For funX |C Solved xb Answer x+ CodeW X https://codeworko... 田) CodeWorkout X267: Recursion Programming Exercise: Cumulative Sum For function sumtok, write the missing recursive call. This function returns the sum of the values from1 to k. Examples: sumtok(5) -> 15 Your Answer: 1 public int sumtok(int k) { 2. } (0 => ) return 0; 3. } else { return > 6. { Check my answer! Reset Next exercise 1:09 AMWrite a recursive function to compute the following series:What does the following recursive function do? int f(int n)X if (n==1) return 1; else return n+f(n-1); } Sum of numbers from 1 to n Factorial of number n Square of numbers from 1 to n Print the numbers from 1 to n
- Write a recursive function that returns the nth Fibonacci number from the Fibonacciseries.int fib(int n);The following function f uses recursion: def f(n): if n <= 1 return n else return f(n-1) + f(n-2) 5 Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n): a <- 0 b <- 1 if n = 0 return a elsif n = 1 return b else for i in 1..n c <- a + b a <- b b <- c return b f(n): a <- 0 i <- n while i > 0 a <- a + i + (i-1) return a f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1 return arr[n] else for i in 2..n arr[i] <- arr[i-1] + arr[i-2] return arr[n] f(n): arr[0..n] <- [0, ..., n] if n <= 1 return arr[n] else a <- 0 for i in 0..n a <- a + arr[i] return aAckermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s function. Use the following logic in your function: If m = 0 then return n + 1 If n = 0 then return A(m-1, 1) Otherwise, return A(m-1, A(m, n-1)) Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
- Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive. >>> sum(1) 1 >>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"8. Ackerman's Function Ackermann's Function is a recursive mathematical algorithm that can be used to test how well a system optimizes its performance of recursion. Design a function ackermann(m, n), which solves Ackermann's function. Use the following logic in your function: If m = 0 then return n + 1 If n = 0 then return ackermann(m-1,1) Otherwise, return ackermann(m-1,ackermann(m,n-1)) Once you've designed yyour function, test it by calling it with small values for m and n. Use Python.Recursive ConversionConvert the following function to one that uses recursion.void sign(int n){while (n > 0)cout << "No Parking\n";n−−;}Demonstrate the function with a driver program.