Question

Problem 2: - Write a recursive function that takes an array and a callback function and returns True if any value of that array returns True from that callback function otherwise returns False. As a callback function for this problem, assume that the callback function is used to check if a given input is an even number. - Analyze the running time of your algorithm.

Answer 1

A recursive function will traverse an array and use a callback to check for an even element, stopping and returning True when found or False if not. The function's recursive nature leads to a running time of O(n), where n is the array's length.

Step-by-step explanation:

The student is asking how to write a recursive function that evaluates an array with a callback function, returning True if any value in the array makes the callback function return True, otherwise False. Since recursion involves calling the function within itself, we will be looking for a base case where the function stops recursing. This base case will be when the array is empty (all elements have been checked), returning False, or when the callback function returns True for an element.

Here is a simplified representation of the recursive function in pseudocode:

function recursiveCheck(array, callback) {
if array is empty
return False
if callback(array[0]) == True
return True
else
return recursiveCheck(array[1:], callback)
}

The associated callback function for checking if a number is even could be:

function isEven(number) {
return number % 2 == 0
}

To analyze the running time of this algorithm, we assume that the callback function has a constant running time, i.e., O(1). The running time of the recursiveCheck function is therefore dependent on the size of the array, since it will call itself once for each element until it hits the base case. This gives us a running time of O(n) where n is the number of elements in the array.