A game is played by moving a che number of different ways a Cn =Cn-2 + Cn-3, C1=0, Write a recursive algorithm to
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- A game is played by moving a marker ahead either 2 or 3 steps on a linear path. Let ca be the number of different ways a path of length n can be covered. Given, Cn =Cn-2 + Cn-3, C1=0, c2=1, c3=1 Write a recursive algorithm to compute Cn.Please do not give solution in image format thanku Implement the following recursively using sudo code: Suppose an elevator which is on a floor on n. For this elevator to go from the nth floor to the base(ground) floor, it should go to every floor under the nth floor. Let's consider an elevator on the 4th floor. This elevator 1st comes on the third(3rd) floor. 4th-> 3rd then 3rd-> 2nd then 2->1 and next 1->0(ground floor) The recursive equation defined is F(n)=1+F(n-1)A recursive sequence is defined by - d k = 6 d k − 1 + 3 , for all integers k ≥ 2 and d1 = 2 Use iteration to guess an explicit formula for the above sequence.
- 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…Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…
- 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.8. Give a recursive definition of the sequence {an}, n =1, 2, 3, ... ifa) an = 4n − 2. b) an = 1 + (−1)n.c) an = n(n + 1). d) an = n2.Ackermann’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)
- Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1One-friend recursion vs iteration.1. Your task is to accept a tuple a1, a2, ... , an and return the reversed tuplean, an−1, ... , a1. Being lazy, you will only strip off an element from one end oradd an element back onto one end. But you have recursive friends to help you.Provide both a paragraph containing the friend’s explanation of the algorithm,and the recursive code.2. Now suppose that you have a stack, but no friends. (See Chapter 3). Quickly sketchan iterative program that solves this same problem. Be sure to include loop invariants and other the key steps required for describing an iterative algorithm.3. Trace each of these two programs. Step by step, compare and contrast their computations on a computer.Show that f(x, y) = x +y is primitive recursive.