Can someone explain how the output of this recusrsive function is 5? I find recursion difficult to understand def R(n):
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Can someone explain how the output of this recusrsive function is 5? I find recursion difficult to understand
def R(n):
if n<=0:
return 20
return R(n-1)-n
print(R(5))
Step by step
Solved in 2 steps with 1 images
- Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…Question 4: The function T(n) is recursively defined as follows: 1 if n = 1, 고 +. T(n -1) if n> 2. Prove that T(n) = 0(n log n).Using R, I need to create a code that checks whether a number x is a prime number or not using RECURSION ONLY (while, for, and any iterative operators are not allowed. I made one but it seems that my code has a problem when I run it : is_prime <- function (x) { divisor <- 2 divisor_check <- function (x, divisor) { if (x <= 2) { if (x == 2){ return(TRUE) } else { return(FALSE) } } else if (x %% divisor == 0) { return(FALSE) } else if (divisor * divisor > x) { return(TRUE) } else if (x == 0 || x != floor(x)){ return(NULL) } else { return(FALSE) } } divisor_check(x, divisor+1)} above is the code and when I run it, the results are as follows: > is_prime(1) [1] FALSE > is_prime(2) [1] TRUE > is_prime(3) [1] FALSE > is_prime(4) [1] TRUE > is_prime(5) [1] TRUE
- The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…r Examples: Find the tight bound of the following recursive functions, T(n). T(n)=9T(n/3) +n T(n)= T(2n/3) +1 ● T(n)=3T(n/4)+nlogn ● T(n) = 2T (n/2)+nlogn T(n)=2T(n/2) + O(n) • T(n)=8T(n/2) +0(n²) ● T(n) = 7T(n/2) + O(n²)In programming, a recursive function calls itself. The classical example is factorial(n), which can be defined recursively as n*factorial(n-1). Nonethessless, it is important to take note that a recursive function should have a terminating condition (or base case), in the case of factorial, factorial(0)=1. Hence, the full definition is: factorial(n) = 1, for n = 0 factorial(n) = n * factorial(n-1), for all n > 1 For example, suppose n = 5: // Recursive call factorial(5) = 5 * factorial(4) factorial(4) = 4 * factorial(3) factorial(3) = 3 * factorial(2) factorial(2) = 2 * factorial(1) factorial(1) = 1 * factorial(0) factorial(0) = 1 // Base case // Unwinding factorial(1) = 1 * 1 = 1 factorial(2) = 2 * 1 = 2 factorial(3) = 3 * 2 = 6 factorial(4) = 4 * 6 = 24 factorial(5) = 5 * 24 = 120 (DONE) Exercise (Factorial) (Recursive): Write a recursive method called factorial() to compute the factorial of the given integer. public static int factorial(int n) The recursive algorithm is:…
- Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is: **** *** ** * ** *** ****For function addOdd(n) write the missing recursive call. This function should return the sum of all postive odd numbers less than or equal to n. Examples: addOdd(1) -> 1addOdd(2) -> 1addOdd(3) -> 4addOdd(7) -> 16 public int addOdd(int n) { if (n <= 0) { return 0; } if (n % 2 != 0) { // Odd value return <<Missing a Recursive call>> } else { // Even value return addOdd(n - 1); }}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 AM
- Question: Let t(x) be the number of primes that areIn 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 int binomialR(int n, int k) that computes the binomial coefficient given by the following for any 2 integers n and k satisfying n2k20: ) = (";") + C-), with () = () = 1SEE MORE QUESTIONS