Synonymous Sentences

One of the intriguing tasks in natural language processing is to produce new variant sentences with reference to the given text and a set of synonyms and synonym pairs? This problem not only makes it easier to understand the flexible use of language but has practical applications in areas related to paraphrasing, machine translation, and semantic analysis. Now let’s focus on how this problem can be solved and let me show you an example that will help the understanding of the solution.

Problem Description

You are given a list of equivalent string pairs synonyms where synonyms[i] = [si, ti] indicates that si and ti are equivalent strings. You are also given a sentence text.

Return all possible synonymous sentences sorted lexicographically.

Example:

Input: synonyms = [["happy","joy"],["cheerful","glad"]], text = "I am happy today but was sad yesterday"

Output: ["I am happy today but was sad yesterday","I am joy today but was sad yesterday"]

Constraints:

• 0 <= synonyms.length <= 10
• synonyms[i].length == 2
• 1 <= si.length, ti.length <= 10
• si != ti
• text consists of at most 10 words.
• All the pairs of synonyms are unique.
• The words of text are separated by single spaces.

Approach for Synonymous Sentences

To solve the problem of generating all possible synonymous sentences, we follow these main steps: use Union-Find to manage synonym groups, create a dictionary for fast synonym look-up, and utilize Depth-First Search (DFS) to generate sentences recursively.

Step-by-Step Approach

Union-Find Structure for Synonym Groups:

• Initialization: Initialize a Union-Find structure to manage synonym groups efficiently.
• Mapping Words to Indices: Assign a unique index to each word for easy management in the Union-Find structure.
• Union Operations: For each pair of synonyms, perform union operations to group them together.

Building Synonym Groups:

• Extract and Sort Groups: After all unions are performed, extract synonym groups from the Union-Find structure and sort them lexicographically.

DFS for Sentence Generation:

• Word-by-Word Processing: Split the given sentence into words and process each word to either use its synonyms or leave it unchanged if it has no synonyms.
• Recursive Generation: Use DFS to explore all combinations of synonyms. For each word, if it's a synonym, replace it with each word in its synonym group and recursively generate the rest of the sentence.

Sorting and Returning Results:

• Lexicographical Sorting: Once all possible sentences are generated, sort them lexicographically.
• Return the Sorted List: Return the sorted list of sentences as the final output.

Code:

Python

from collections import defaultdict
from typing import List, Dict

class UnionFind:
    def __init__(self, n: int):
        self.parent = list(range(n))
        self.rank = [1] * n

    def find(self, x: int) -> int:
        if self.parent[x] != x:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]

    def union(self, x: int, y: int):
        rootX = self.find(x)
        rootY = self.find(y)
        if rootX != rootY:
            if self.rank[rootX] > self.rank[rootY]:
                self.parent[rootY] = rootX
            elif self.rank[rootX] < self.rank[rootY]:
                self.parent[rootX] = rootY
            else:
                self.parent[rootY] = rootX
                self.rank[rootX] += 1

def generateSentences(synonyms: List[List[str]], text: str) -> List[str]:
    word_map = {}
    words = set()
    for a, b in synonyms:
        words.add(a)
        words.add(b)

    words = sorted(words)
    word_map = {word: idx for idx, word in enumerate(words)}
    uf = UnionFind(len(words))

    for a, b in synonyms:
        uf.union(word_map[a], word_map[b])

    synonym_groups = defaultdict(list)
    for word in words:
        root = uf.find(word_map[word])
        synonym_groups[root].append(word)

    for group in synonym_groups.values():
        group.sort()

    def dfs(index: int, path: List[str], results: List[str], words_in_sentence: List[str], word_map: Dict[str, int], synonym_groups: Dict[int, List[str]]):
        if index == len(words_in_sentence):
            results.append(" ".join(path))
            return

        word = words_in_sentence[index]
        if word in word_map:
            root = uf.find(word_map[word])
            for synonym in synonym_groups[root]:
                dfs(index + 1, path + [synonym], results, words_in_sentence, word_map, synonym_groups)
        else:
            dfs(index + 1, path + [word], results, words_in_sentence, word_map, synonym_groups)

    words_in_sentence = text.split()
    results = []
    dfs(0, [], results, words_in_sentence, word_map, synonym_groups)

    return sorted(results)

# Example usage:
synonyms = [["happy","joy"],["sad","sorrow"],["joy","cheerful"]]
text = "I am happy today but was sad yesterday"
print(generateSentences(synonyms, text))

synonyms = [["happy","joy"],["cheerful","glad"]]
text = "I am happy today but was sad yesterday"
print(generateSentences(synonyms, text))

Output

['I am cheerful today but was sad yesterday', 'I am cheerful today but was sorrow yesterday', 'I am happy today but was sad yesterday', 'I am happy today but was sorrow yesterday', 'I am joy today but...

Explanation

• Union-Find Structure: This is used to group synonyms. Each word is assigned a unique index and added to the Union-Find structure.
• Mapping Words to Indices: A dictionary maps each word to its corresponding index.
• Union of Synonyms: The union method is used to group words that are synonyms.
• Grouping and Sorting Synonyms: The synonym groups are extracted and sorted lexicographically.
• DFS for Sentence Generation: A recursive function explores all combinations of synonyms for each word in the sentence, building possible sentences.
• Lexicographical Sorting: The final list of sentences is sorted lexicographically before being returned.

Conclusion

The problem of generating all possible synonymous sentences is effectively solved using a combination of the Union-Find data structure and Depth-First Search (DFS). The Union-Find structure helps efficiently group synonyms, while DFS explores all possible combinations of words to form valid sentences.