How do you create recursive algorithms for solving problems?

1 What is recursion?

Recursion is a technique where a function calls itself repeatedly until a base case is reached. A base case is a condition that stops the recursion and returns a value or a result. A recursive function must have at least one base case and one recursive case. A recursive case is a condition that reduces the problem size and calls the function again with a smaller or simpler input.

2 How to design a recursive algorithm?

Designing a recursive algorithm requires four steps. First, you must identify the problem and the input/output format. Then, you must find the base cases that can be solved without recursion. After that, you must find the recursive cases that can be solved by calling the function with a smaller or simpler input. Finally, you must combine the base cases and the recursive cases into a single function.

3 How to test a recursive algorithm?

To test a recursive algorithm, you need to use a debugger or a trace table. A debugger is a tool that allows you to step through the code and examine the values of the variables and the function calls. A trace table is a table that shows the values of the variables and the function calls for each iteration of the recursion. You can use either method to check if your algorithm works correctly and terminates.

4 What are some examples of recursive algorithms?

Some common examples of recursive algorithms are factorial, Fibonacci, and binary search. Factorial is the product of all integers from 1 to n, with the base case being n = 1, which returns 1, and the recursive case being n > 1, which returns n * factorial(n-1). The Fibonacci sequence is a series of numbers where each number is the sum of the previous two numbers. The base cases are n = 0, which returns 0, and n = 1, which returns 1, and the recursive case is n > 1, which returns fibonacci(n-1) + fibonacci(n-2). Binary search is a method of finding an element in a sorted array by repeatedly dividing the array into two halves and comparing the middle element with the target. The base case is when the array is empty or the middle element is equal to the target, which returns the index or -1. The recursive case is when the middle element is not equal to the target, calling the function with either the left or right half of the array depending on whether the target is smaller or larger than the middle element.

5 What are some challenges and tips for recursive algorithms?

Recursive algorithms present certain challenges and tips that should be taken into account. To avoid infinite recursion, ensure your base case is reachable and your recursive case reduces the problem size. Memoization is a technique of storing the results of previous function calls in a cache or a dictionary, which can improve the performance and efficiency of recursive algorithms with overlapping subproblems. Additionally, iteration can be simpler, faster, or more intuitive than recursion so it should be compared. To do this, try to identify the loop invariant, loop condition, and loop update in your recursive algorithm and convert them into a while or for loop with appropriate variables.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?