When working with strings that need to be grouped by shared characteristics, one powerful technique is creating signatures - unique identifiers that capture the essential properties we care about while ignoring irrelevant differences.
The key insight is that anagrams share the same letters with the same frequencies, just in different orders. If we can create an identifier that's identical for all anagrams but different for non-anagrams, we can use it as a grouping key.
One effective approach is character sorting. When we sort the characters in any word alphabetically, anagrams will always produce the same sorted result. For example:
This creates natural groups where words with identical signatures belong together.
Dictionary-based grouping is the standard pattern for this type of problem. We iterate through our data once, compute each item's signature, and use the signature as a dictionary key. Items with the same signature get added to the same list.
This pattern appears frequently in data processing: grouping database records by category, organizing files by type, clustering similar items, or partitioning data for parallel processing. The signature can be anything that captures the grouping criteria - sorted characters, hash values, extracted features, or computed properties.
The time complexity is typically O(n × k) where n is the number of items and k is the cost of computing each signature. For character sorting, k is the length of each string, making this approach quite efficient for most practical purposes.
1# Grouping students by their grade level
2def group_students_by_grade(students):
3 grade_groups = {}
4
5 for student in students:
6 grade = student['grade'] # This is our signature
7
8 if grade in grade_groups:
9 grade_groups[grade].append(student)
10 else:
11 grade_groups[grade] = [student]
12
13 return list(grade_groups.values())
14
15# Example usage
16students = [
17 {'name': 'Alice', 'grade': 10},
18 {'name': 'Bob', 'grade': 11},
19 {'name': 'Carol', 'grade': 10}
20]
21result = group_students_by_grade(students)
22# Returns: [[{'name': 'Alice', 'grade': 10}, {'name': 'Carol', 'grade': 10}],
23# [{'name': 'Bob', 'grade': 11}]]