# 394. Decode String

Leetcode #: 394
Name: Decode String
Difficulty: Medium
Url: https://leetcode.com/problems/decode-string/

# Prompt

Given an encoded string, return its decoded string.

The encoding rule is: `k[encoded_string]`, where the `encoded_string` inside the square brackets is being repeated exactly `k` times. Note that `k` is guaranteed to be a positive integer.

You may assume that the input string is always valid; there are no extra white spaces, square brackets are well-formed, etc. Furthermore, you may assume that the original data does not contain any digits and that digits are only for those repeat numbers, `k`. For example, there will not be input like `3a` or `2`.

The test cases are generated so that the length of the output will never exceed `105`.

Example

`Input: s = "3[a2[c]]"Output: "accaccacc"`

Constraints

• `1 <= s.length <= 30`
• `s` consists of lowercase English letters, digits, and square brackets `'[]'`.
• `s` is guaranteed to be a valid input.
• All the integers in `s` are in the range `[1, 300]`.

# Approach

The scenarios in which there are no nested values are straightforward. We’ll primarily want to focus on the scenarios in which there are nested values and there are 2 — both of which are displayed below:

`1st scenario: "3[a2[c6[d]]]"2nd scenario: "3[a2[b]5[c]]"`

Recursion

These nested brackets represent subproblems, in which you can immediately think of using Recursion as a viable solution. Each level in the Recursion tree would represent how nested a specific subproblem is within their overall subproblem size. As Recursion implements an implicit call stack, this is a good indicator that we can create a Stack to replicate the same behavior and explicitly tell us once we’re done with a subproblem where to pop back up to.

These nested brackets represent subproblems, in which you can immediately think of using Recursion as a viable solution. Each level in the Recursion tree would represent how nested a specific subproblem is within their overall subproblem size. As Recursion implements an implicit call stack, this is a good indicator that we can create a Stack to replicate the same behavior and explicitly tell us once we’re done with a subproblem where to pop back up to.

Explicit Stack

By using an explicit Stack, it’s a LIFO data structure so we know that we should start popping from the Stack once we’ve landed on a closing bracket or ‘]’ We wouldn’t append the closing bracket onto the Stack once we’ve landed on it. We’ll just check every element preceding it as long as the preceding element is not an open bracket or ‘[’. Once we’ve landed on a ‘[’ as we pop from our stack, we have established our substring from ‘[’ and ‘]’ but now we need to calculate what k is for this substring as k determines how many times this substring repeats. We know that k should precede right before the open brackets or ‘[’ so we’ll check each preceding element before the open bracket or ‘[’ and check if it’s a number from 0 to 9. If so, we want to pop that and construct a separate substring that’ll represent k (k can be 2 or even 3 digits, not necessarily 1).

Finally, we can append back to our Stack the substring that we created earlier within our open and closing bracket and repeat it k times as we’ve determined in a separate substring. By repeating this process with all nested brackets or subproblems within our problem size, we’ll eventually have a Stack that is populated with no more open or closing brackets. We can finally join our Stack together into a final concatenated string.

# Code Python | Time: O(n * maxK^countK) | Space: O(sum(n * maxK^countK))