You are given a string, s, and an array of strings, word_dict, representing a dictionary. Your task is to add spaces to s to break it up into a sequence of valid words from word_dict. We are required to return an array of all possible sequences of words (sentences). The order in which the sentences are listed is not significant.

Note: The same dictionary word may be reused multiple times in the segmentation.

Constraints:

• $1 \leq$ s.length $\leq 20$

• $1 \leq$ word_dict.length $\leq 1000$

• $1 \leq$ word_dict[i].length $\leq 10$

• s and word_dict[i] consist of only lowercase English letters.

• All the strings of word_dict are unique.

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

The naive approach to solve this problem is to use a traditional recursive strategy in which we take each prefix of the input string, s, and compare it to each word in the dictionary. If it matches, we take the string’s suffix and repeat the process.

Here is how the algorithm works:

• Base case: If the string is empty, there are no characters in the string that are left to process, so there’ll be no sentences that can be formed. Hence, we return an empty array.

• Otherwise, the string will not be empty, so we’ll ...