1. Overview

In this tutorial, we’ll discuss the general idea behind two popular methods in computer algorithms: backtracking and recursion.

Moreover, we’ll present the core differences between them.

2. Introduction to Backtracking

Backtracking is an algorithmic method for finding solutions to a problem by systematically exploring the solution space of the problem. Moreover, the first step of the backtracking method is to generate all candidate solutions to a problem using a brute-force approach. Furthermore, out of all the candidate solutions, we use backtracking to find the solutions that fulfill the requirements of the given problem by making a sequence of decisions.

In particular, we utilize the backtracking method when the solution space is complex and finding the solution is not straightforward.

Furthermore, the backtracking method is well suitable for three types of problems: decision, enumeration, and optimization. In all three types of problems, we must explore the whole solution space to find feasible solutions.

2.1. Properties

Now, let’s discuss some essential properties of the backtracking method.

The backtracking method systematically explores all the possible solutions, ensuring we won’t miss any valid solution. Hence, we can find a complete solution set for a given problem using the backtracking method.

Furthermore, the backtracking method is computationally expensive because it exhaustively explores all possible solutions. Therefore, its applicability depends on the given problem and the availability of resources.

Moreover, the backtracking method uses the recursion technique to find valid solutions. Hence, recursion plays a vital role in deciding the occurrence points of backtracking in the solution space.

2.2. Example

Now, we know the basics of the backtracking method. Let’s enhance our knowledge with a practical problem.

Firstly, we provide a set of numbers as input, and the goal is to generate all possible permutations of the input number set. Moreover, we utilize the backtracking and generate all possible combinations:

generating all permutations using backtracking method

In this example, we start by placing 1 at the first position, followed by 2 and 3. Therefore, we generate our first permutation {1, 2, 3}.

Furthermore, we backtrack to 1 and position 3 at the second spot and 2 at the third. In this way, we generate our second permutation {1, 3, 2}. Similarly, we generate all six permutations using the backtracking method.

3. Introduction to Recursion

Recursion is a popular method in programming and algorithms. In this method, a function calls itself to solve smaller and similar instances of a complex problem. In the recursion method, first, we divide a problem into subproblems. Moreover, the subproblems are solved recursively and merged to form the solution of the original problem.

We use recursion to solve combinatorial, divide and conquer, tree traversal, and hierarchical data structure problems.

3.1. Properties

Let’s explore some unique properties of the recursion method.

In the recursion method, a function calls itself, creating a self-referential structure. Furthermore, the self-referential structure is a unique aspect of the recursion method, which we don’t see in the traditional iterative approaches.

Moreover, solving a problem using recursion can be memory-intensive. Given a problem, we first divide it into smaller subproblems. Furthermore, the subproblems are solved using recursion. Finally, we merge the solutions of the subproblems to find the solution to the main problem.

Moreover, we can use recursion to solve problems with dynamic requirements. Additionally, we can take advantage of the distributed and multi-core computing environment by adding parallelism in recursive algorithms.

3.2. Example

Now, let’s discuss a problem that uses the recursion method to find a solution.

Here, we present the implementation of the Fibonacci series using recursion:

def fibo_imp(n):
    if n <= 1:
        return n
        return fibo_imp(n-1) + fibo_imp(n-2)
n = 6

As we can see, the fibo_imp() function calls itself recursively to calculate the nth number in the Fibonacci series. Hence, it’s a classic example of a recursion algorithm.

4. Differences

Now, let’s take a look at the main differences between the backtracking and recursion methods:

Backtracking Recursion
Recursion is an integral part and is always needed Backtracking isn’t required always
Explore all the candidate solutions and discard the non-optimal solutions at each step A function calls itself, creating a self-referential structure
Complex method and challenging to implement Implementation is comparatively simple
Consumes less memory Consumes more memory than the backtracking method
Find all the possible solutions Find one or all the possible solutions
Suitable enumeration, optimization, and decision problems Suitable combinatorial, divide and conquer, tree traversal, and hierarchical data structure problems

5. Conclusion

In this article, we explored the general idea of backtracking and recursion with examples.

Finally, we highlighted the core differences between them.

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