<p>Given a string <code>s</code> and a dictionary of strings <code>wordDict</code>, add spaces in <code>s</code> to construct a sentence where each word is a valid dictionary word. Return all such possible sentences in <strong>any order</strong>.</p>

<p><strong>Note</strong> that the same word in the dictionary may be reused multiple times in the segmentation.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;catsanddog&quot;, wordDict = [&quot;cat&quot;,&quot;cats&quot;,&quot;and&quot;,&quot;sand&quot;,&quot;dog&quot;]
<strong>Output:</strong> [&quot;cats and dog&quot;,&quot;cat sand dog&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;pineapplepenapple&quot;, wordDict = [&quot;apple&quot;,&quot;pen&quot;,&quot;applepen&quot;,&quot;pine&quot;,&quot;pineapple&quot;]
<strong>Output:</strong> [&quot;pine apple pen apple&quot;,&quot;pineapple pen apple&quot;,&quot;pine applepen apple&quot;]
<strong>Explanation:</strong> Note that you are allowed to reuse a dictionary word.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;catsandog&quot;, wordDict = [&quot;cats&quot;,&quot;dog&quot;,&quot;sand&quot;,&quot;and&quot;,&quot;cat&quot;]
<strong>Output:</strong> []
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 20</code></li>
	<li><code>1 &lt;= wordDict.length &lt;= 1000</code></li>
	<li><code>1 &lt;= wordDict[i].length &lt;= 10</code></li>
	<li><code>s</code> and <code>wordDict[i]</code> consist of only lowercase English letters.</li>
	<li>All the strings of <code>wordDict</code> are <strong>unique</strong>.</li>
	<li>Input is generated in a way that the length of the answer doesn&#39;t exceed&nbsp;10<sup>5</sup>.</li>
</ul>

class Solution {
public:
    vector<string> wordBreak(string s, vector<string>& wordDict) {
        // Map to store results of subproblems
        unordered_map<int, vector<string>> dp;

        // Iterate from the end of the string to the beginning
        for (int startIdx = s.size(); startIdx >= 0; startIdx--) {
            // List to store valid sentences starting from startIdx
            vector<string> validSentences;

            // Iterate from startIdx to the end of the string
            for (int endIdx = startIdx; endIdx < s.size(); endIdx++) {
                // Extract substring from startIdx to endIdx
                string currentWord = s.substr(startIdx, endIdx - startIdx + 1);

                // Check if the current substring is a valid word
                if (isWordInDict(currentWord, wordDict)) {
                    // If it's the last word, add it as a valid sentence
                    if (endIdx == s.size() - 1) {
                        validSentences.push_back(currentWord);
                    } else {
                        // If it's not the last word, append it to each sentence
                        // formed by the remaining substring
                        vector<string> sentencesFromNextIndex = dp[endIdx + 1];
                        for (const auto& sentence : sentencesFromNextIndex) {
                            validSentences.push_back(currentWord + " " +
                                                     sentence);
                        }
                    }
                }
            }
            // Store the valid sentences in dp
            dp[startIdx] = validSentences;
        }
        // Return the sentences formed from the entire string
        return dp[0];
    }

private:
    // Helper function to check if a word is in the word dictionary
    bool isWordInDict(const string& word, const vector<string>& wordDict) {
        for (const auto& dictWord : wordDict) {
            if (dictWord == word) {
                return true;
            }
        }
        return false;
    }
};
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