Valid Anagram

Check whether two strings contain the same letters with the same counts.

Start with the concrete trace below. It shows the state the algorithm must carry as it runs.

Problem trace

Valid Anagram: Two strings are anagrams exactly when their character-count maps are equal.

Input and goalCheck whether two strings contain the same letters with the same counts.

Initialize both countersCounter starts with no entries for either string; the divider separates first="aab" from second="aba".

count firsta0a1b2|3a4b5a6

examplefirst = "aab", second = "aba"mapLabelCounter(first) and Counter(second)

Counter(first) and Counter(second)empty

Recognize it

Order may differ, but the question asks whether two strings contain exactly the same characters with the same multiplicities.

Keep true

After each Counter scan step, the visible count for a character equals its occurrences in the processed prefix; complete equal maps are necessary and sufficient for anagrams.

Reuse it

Replace irrelevant order with a canonical frequency summary; the same idea supports ransom-note checks, multiset equality, permutation detection, and histogram comparison.

Pattern: Frequency map.

Simple idea: Anagrams have the same letter count. Counter builds that count map.

from collections import Counter

def is_anagram(first: str, second: str) -> bool:
   return Counter(first) == Counter(second)

Cost: $O(n)$ time and $O(k)$ space, where $k$ is the number of different characters.