Recursive algorithms play a major role in shaping a desired recursive function to execute a specific task. You can solve different problems in programming and the logical world with the help of a recursive function. In Recursion, a function keeps on calling itself again and again until a base condition is reached.
The recursive function is used for problems which can be broken down into simpler steps. It solves a task by adopting the “divide and rule” method. In this article, let us get more familiar with how these recursive functions work and derive an algorithm for some of the popular programming problems.
Recursive Algorithm Meaning
An algorithm is something which can help us define a desired structure for solving a given set of problems. In a recursive algorithm we solve a problem by making a function call itself again and again until it reaches a base condition. A recursive algorithm is used to solve a problem which can be broken down into similar smaller executable problems.
Key Components of Recursive Algorithm
There are two major components of a recursive algorithm which is given to you below.
- Base Case: The base case defines the stopping condition for a recursive function call and ensures that functions do not go into infinite recursion.
- Recursive Case: The recursive logic is used to execute the desired statement and solution to a specific problem in programming. It majorly divides the problem into similar smaller problems.
For example, let us suppose we want to print a factorial of a number using the recursive function. Then we need to go from the starting number to the last number to get to the result of the factorial. Let us check how we walk through for finding a factorial of 5.
5! = 5 x 4 x 3 x 2 x 1 = 120 which is equivalent to f(5) = f(5-1) x f(4-1) x f(3-1) x f(2-1) recursive function call.
Breakdown of a Recursive Algorithm
Let us visualize how we can represent a recursive function in two parts. Let us suppose we take a factorial recursive problem.
Structure of a Recursive Algorithm
The structure of a recursive algorithm is simple and easier to interpret. Let us learn how we can frame a better and optimised structure of a recursive function.
| def recursive_function(parameters):
if base_condition: return result return some_operation(recursive_function(modified_parameters)) |
- The base case in the function makes sure that your function stops at the desired place to avoid infinite recursion.
- The recursive case calls the function with a smaller and simpler subproblem to execute the task.
Fibonacci Sequence using Recursion
Let us solve a fibonacci sequence using Python Recursion and understand how the base case and recursive call works in the function. The two major elements in this function are listed below.
- F(n) = F(n-1) + F(n-2) (Recursive Function Call)
- F(0) = 0 and F(1) = 1 (Base Case)
| def fibonacci(n):
if n == 0: return 0 if n == 1: return 1 return fibonacci(n – 1) + fibonacci(n – 2) print(fibonacci(6)) |
Points To Take Care While Creating a Recursive Algorithm
Let us learn the steps to build a recursive algorithm and execute a specific set of solutions for a problem.
- Make sure you define a correct base condition for the recursive function to prevent infinite recursion and make the function stop at the desired place.
- Ensure that the recursive function progresses towards the base case i,e. Problem size is reduced as the steps move forward.
- Avoid redundant computations for a problem if possible, you can use the memoization approach to optimise the performance of your recursive algorithm.
- You might be familiar with the overhead and space complexity repeated function calls do to the stack hence for deep recursion problems you can switch to iterative or tail recursion methods.
- You can use tail recursion to allow better optimisation of your recursive algorithm.
Recursive Call Stack of a Recursive Algorithm
Let us analyse how the function call takes place in a recursive function with a simple Fibonacci Sequence example below.
The recursive function call keeps on taking place until the function reaches the base condition i,e. zero . As the function reaches the base condition it starts returning the base condition one by one until it reaches the beginning state.
Applications of Recursive Algorithm
Let us define a recursive algorithm for some of the popular problems below.
Recursive Algorithm for Binary Search
The given algorithm can help you perform the binary search with the help of a recursive function.
| def binary_search(arr, low, high, target):
if low > high: return -1 mid = (low + high) // 2 if arr[mid] == target: return mid if target < arr[mid]: return binary_search(arr, low, mid – 1, target) return binary_search(arr, mid + 1, high, target) |
Recursive Algorithm for Tower of Hanoi
We can easily solve the Tower of Hanoi problem with the help of Recursive function method.
| def tower_of_hanoi(n, source, auxiliary, destination):
if n == 1: print(f”Move disk 1 from {source} to {destination}”) return tower_of_hanoi(n – 1, source, destination, auxiliary) print(f”Move disk {n} from {source} to {destination}”) tower_of_hanoi(n – 1, auxiliary, source, destination) |
Advantages of Using Recursive Algorithm
Some of the biggest benefits of using Recursive algorithms are mentioned below.
- Recursive functions are very much effective in solving complex problems by breaking down into smaller subproblems.
- It reduces the code size and makes it more readable with fewer lines of code in the function program.
- With a recursive function we break down the problem into smaller components and execute the task.
- Recursive function prevents us from writing the same piece of code again and promotes reusability.
- It is one of the best solutions for problems such as backtracking, tree traversals, sorting solutions, tower of hanoi and more.
- Recursive algorithms are cleaner and more optimised and can be completed in two steps i,e. Base case and recursive logic.
Disadvantages of Using Recursive Algorithm
While being beneficial for most of the problems, recursive algorithms suffer through major challenges. Let us check some of the major disadvantages below.
- Recursive function calls lead to higher memory usage which leads to overhead and more memory usage.
- Most of the time recursive functions are slower as compared to a normal iterative function.
- If the base condition is not defined properly it might lead to infinite recursion calls and wastage of the memory stack space.
- Recursive algorithms can be very difficult to debug for complex problems mainly.
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Recursive Algorithm FAQs
Q1. What is a Recursive Algorithm?
Ans: Recursive algorithms play a major role in shaping a desired recursive function to execute a specific task. You can solve different problems in programming and the logical world with the help of a recursive function.
Q2. What are two major components of a Recursive algorithm?
Ans: The two major components of a recursive algorithm are base condition and repeated function call logic. It is important to use both in your function to execute the specific task successfully.
Q3. What is the biggest advantage of a recursive algorithm?
Ans: Recursive functions are very much effective in solving complex problems by breaking down into smaller subproblems. It reduces the code size and makes it more readable with fewer lines of code in the function program.
Q4. What is the biggest challenge of a Recursive function?
Ans: Recursive function calls lead to higher memory usage which leads to overhead and more memory usage.
