Wie funktioniert die Rekursion in der Funktion „FindSequence'?

Delving into the Recursion of "FindSequence"

Eloquent Javascript introduces a challenging problem: writing a function that generates a sequence of additions and multiplications to reach a given goal number. The provided code employs recursion, which raises questions about its operation.

Within the findSequence function resides a nested function find. This function recursively explores two possible transformations from a current number: adding 5 or multiplying by 3. Each transformation produces a new number, and the process continues until either the goal is met or the current number exceeds the goal.

At each step, a textual representation of the expression is passed along. For instance, starting with the number 1, the initial expression is "1". If adding 5 is chosen, the expression becomes "(1 + 5)". By recording these expressions, the function tracks the steps taken to reach each number.

If the goal is reached, the expression from the final step represents a valid sequence. Otherwise, the function returns null, indicating failure. Multiple recursive calls are made, each exploring a different path until a valid sequence is found or all paths have been exhausted.

To illustrate the recursion, let's consider finding a sequence for the goal number 14.

(1, "1")
(5, "1 + 5")
(10, "(1 + 5) + 5")
(15, "((1 + 5) + 5) + 5")  // Discard, exceeds goal
(30, "((1 + 5) + 5) * 3")  // Discard, exceeds goal
(15, "(1 + 5) * 3")  // Discard, exceeds goal
(3, "1 * 3")
(8, "(1 * 3) + 5")
(13, "((1 * 3) + 5) + 5")
(18, "(((1 * 3) + 5) + 5) + 5")  // Discard, exceeds goal
(39, "(((1 * 3) + 5) + 5) * 3")  // Discard, exceeds goal
(24, "((1 * 3) + 5) * 3")  // Discard, exceeds goal
(9, "(1 * 3) * 3")
(14, "((1 * 3) * 3) + 5")  // Success!

Through this stepwise process of recursion, the function eventually finds the sequence: "((1 3) 3) + 5", which represents the addition of 5 to the product of 1 and 3 cubed.

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