2. Code a top-down recursive solution for the classic Fibonacci Sequence (starting from 0) using dynamic programming with heap memory for storage. 3. Code a bottom-up iterative solution for the classic Fibonacci Sequence (starting from 0) using dynamic programming with heap memory for storage.
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- Why does dynamic programming provide faster solutions that recursive algorithms solving the same problem? 1.avoids resolving overlapping subproblems 2.dynamic programming uses dynamic memory that is more efficient than stack memory 3.loops are always faster than recursion 4.dynamic uses arrays that are faster than function callsRecursion 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…Suppose you are given two integer values x and y. Construct a recursive algo-rithm that uses any combination of the following operations: addition, subtraction, comparison. Calculate the remainder of x divided by y. Specify a set ofexample values for x and y which will result in at least 3 or more recursive calls,and draw the recursion trace diagram for your example.
- 3. Implement a recursive function for an in Python.Dynamic Programming is mostly just a matter of taking a recursive algorithm and finding the overlapping subproblems. Do some research on dynamic programming, and then explain the following two question: We have discussed how to apply recursion to finding the Fibonacci Sequence. The following code shows how to do it using dynamic programming. Explain why this code works.Write a recursive function to generate nth fibonacci term in C programming. How to generate nth fibonacci term in C programming using recursion. Logic to find nth Fibonacci term using recursion in C programming. Fibonacci series is a series of numbers where the current number is the sum of previous two terms. For Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, ... , (n-1th + n-2th) Example: Input: Input any number: 10 Output 10th Fibonacci term: 55 please use C language
- Define the term recursion.Define the term " recursion general case " .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.
- Ackermann's function (A) is defined as:A(m,n):Ackermann's function (A) is defined as:A(m,n):n+1, if m=0A(m-1,1), if m>0 and n=0A(m-1,A(m,n-1)), if m>0 and n> 0Write a recursive Python function to implement Ackermann's function. How many recursive calls willbe required to evaluate A(2,3)?n+1, if m=0A(m-1,1), if m>0 and n=0A(m-1,A(m,n-1)), if m>0 and n> 0Write a recursive Python function to implement Ackermann's function. How many recursive calls willbe required to evaluate A(2,3)?A technique for the mathematical optimization of a complicated issue known as "dynamic programming" includes partitioning the issue into a number of more manageable subproblems and finding solutions to each one in a recursive fashion?There are two important parts to every simple recursive function: the base case, and the recursive call that makes progress towards the base case. Something that can go wrong with recursion when it is used incorrectly is a stack overflow. Explain two different ways that a recursive function could be written incorrectly that could lead to stack overflow. Hint: one has something to do with the base case, and the other with the recursive call. 1. Enter your answer here 2. Enter your answer here