Given a string, s, and a dictionary of strings, word_dict, check if s can be segmented into a space-separated sequence of one or more dictionary words. If yes, return TRUE; else, return FALSE.

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

Constraints:

• $1 \leq$ s.length $\leq 250$

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

• $1 \leq$ word_dict[i].length $\leq 20$

• 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 basic recursive strategy, which considers all possible prefixes of a string and checks if they are present in the dictionary. If a prefix is contained in the dictionary, the rest of the string is checked in the same manner.

Although this approach can get us the desired output, it has a time complexity of $O(2^n)$, where $n$ is the length of the string. This is because at each step, we split the string in two, check the prefix in the dictionary, and repeat the process with the rest of the string. The space complexity of this approach is ...