How Does the findSequence Function Employ Recursion for Brute Force Searching?

Understanding Recursion in FindSequence Function

The provided findSequence function operates on the principle of brute force search with backtracking. Here's a step-by-step explanation of its recursive nature:

At each recursive call, the function attempts two possible transformations:

1. Addition: It adds 5 to the current number and stores the equation along with the new number.
2. Multiplication: It multiplies the current number by 3 and updates the equation accordingly.

The recursive calls continue, starting from 1 and exploring these additions and multiplications until one of the following conditions is met:

1. Goal Reached: If the transformed number matches the given goal, the function returns the corresponding equation describing how to reach that goal.
2. Number Exceeded: If the transformed number becomes greater than the goal, the function returns null, indicating a failure to find a valid sequence.

Example: Reaching the Goal of 14

To illustrate the working of the recursion, let's trace the steps taken to find a sequence for the target 14:

1. Starting number 1, the function attempts both addition and multiplication.
2. Adding 5 yields 6, which is not the goal. Multiplying by 3 gives 3, which is also not the goal.
3. The function backtracks to the 6 and attempts multiplication, leading to 18. This exceeds the goal, so the function returns null.
4. Backtracking again, it tries multiplication on 3, yielding 9.
5. Continuing the recursive calls, the function attempts both transformations on 9. Multiplication by 3 yields the desired goal, so it returns the corresponding equation: "((13)3) 5".

This detailed explanation provides a clear understanding of the recursion process in the findSequence function, allowing the reader to appreciate its search strategy and the role of backtracking in finding a valid sequence for the given goal.

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