What is the brute force approach and complexity for Sort Characters By Frequency?

Count the characters, then sort the string by (count high to low, character low to high) with time complexity O(N log N) and space complexity O(1).

What is the optimal approach and complexity for Sort Characters By Frequency?

Count the characters; bucket them by count; walk from n down, writing each block with optimal time complexity O(N) and space complexity O(N).

Sort Characters By Frequency

Q: How do you identify the pattern for Sort Characters By Frequency?

Look for key signals in the prompt: "sort by frequency" indicates Count first. The key is the count, not the character.; "decreasing order" indicates Highest count first: a bucket walk from n down, or a max-heap.; "same characters together" indicates Each character is one block of copies, written in one go.; "return any of them" indicates Ties may come in any order, so check the rules, not one exact string..

Medium·LeetCode #451 Pro OnlyBasic Reinforcement

LeetCode

Problem Statement

You get a string s. Reorder its characters so that the most frequent character comes first, then the next most frequent, and so on. All copies of one character must sit next to each other.

If two characters appear the same number of times, either one may come first. Return the new string.

Input

A string s.

Output

A string with the same characters, where each character's copies are together and characters with more copies come first.

Example 1

Input: s = "tree"

Output: "eert"

e appears twice, so it comes first. r and t appear once each, so they may come in either order. eetr is also accepted.

Example 2

Input: s = "cccaaa"

Output: "aaaccc"

c and a both appear three times, so either can come first. cacaca is wrong, because all copies of a character must be together.

Example 3

Input: s = "Aabb"

Output: "bbAa"

A and a are different characters, and each appears once. b appears twice, so it must come first. Aabb is wrong for the same reason.

Constraints

• 1 ≤ s.length ≤ 5 · 10^5
• `s` consists of uppercase letters, lowercase letters and digits only.

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“sort by frequency”

→ Count first. The key is the count, not the character.

“decreasing order”

→ Highest count first: a bucket walk from n down, or a max-heap.

“same characters together”

→ Each character is one block of copies, written in one go.

“return any of them”

→ Ties may come in any order, so check the rules, not one exact string.

Approach Complexity Ladder

Brute Force — count, then sort the charactersO(N log N)O(1)

Count the characters, then sort the string by (count high to low, character low to high)

Better — max-heap of (count, char), write all copiesO(N + D log D)O(N)

Count the characters; pop from a max-heap of (count, char) and write all copies of each

Optimal — bucket the characters by count, walk downO(N)O(N)

Count the characters; bucket them by count; walk from n down, writing each block

Brute Force Intuition

Count each character. Then sort the string itself with a comparator: a character with more copies goes first. When the counts are equal, compare the characters, so copies of one letter stay together.

Recognition rule for this sub-pattern:

Count first, then keep the K most frequent in a heap (or bucket by count).

Remember this · Heap — Top K

Trigger

"K largest / smallest / most frequent / closest", kth element, streaming top-K.

Think

Do I really need everything sorted, or only the best K?

Key question

Min-heap or max-heap of size K — which one lets me kick out the worst candidate?

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