def sum ( lst ):  """ Sums a list of numbers ."""  if len ( lst ) == 0:  return 0  return lst [0] + sum ( lst [1:])    def factorial ( number ):  """ Returns the factorial value of any number """ if (( number == 0) or ( number == 1)):  return 1  else :  return number * factorial ( number - 1) Write down a tail recursive implementation of the function sum in python language. You can use the helper function in your solution. Write down a tail recursive implementation of the function factorial in python language.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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def sum ( lst ):

 """ Sums a list of numbers ."""

 if len ( lst ) == 0:

 return 0

 return lst [0] + sum ( lst [1:])

 

 def factorial ( number ):

 """ Returns the factorial value of any number """

if (( number == 0) or ( number == 1)):

 return 1

 else :

 return number * factorial ( number - 1)

Write down a tail recursive implementation of the function sum in python language. You can use the helper function in your solution. Write down a tail recursive implementation of the function factorial in python language.

Expert Solution
Step 1: Providing Algorithm for Tail-Recursive Sum Function

def sum(lst):
    Tail recursive sum of a list of numbers.
    
    1. Define the `sum` function that takes a list, `lst`, as a parameter.
    
    2. Define a helper function, `tail_recursive_sum`, which takes two parameters:
       - `lst`: The list to sum.
       - `accumulator`: An accumulator for the running total, initialized to 0.

    3. Inside the `tail_recursive_sum` function:
       a. Check if the length of the list `lst` is 0.
       b. If the list is empty, return the `accumulator` as the result.
       c. If the list is not empty:
          - Add the first element of the list `lst[0]` to the `accumulator`.
          - Call the `tail_recursive_sum` function recursively with the tail of the list `lst[1:]` and the updated `accumulator`.

    4. Call the `tail_recursive_sum` function with the input list `lst` and an initial accumulator value of 0.

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