What is the brute force approach and complexity for Search Suggestions System?

For each typed prefix, keep the matching products, sort them and take the first three with time complexity O(m · (S + n log n · L)) and space complexity O(S).

What is the optimal approach and complexity for Search Suggestions System?

Insert sorted products into a trie; each node keeps up to three; one walk per typed letter with optimal time complexity O(n log n · L + S + m · L) and space complexity O(26 · S).

How do you identify the pattern for Search Suggestions System?

Look for key signals in the prompt: "suggest after each letter" indicates Each answer is for a prefix of the typed word, and the prefixes are nested. The node for each prefix is one step below the node before it.; "the three smallest" indicates Sort first, so the alphabetically smallest products come first, and keep at most three at each node.; "products with a common prefix" indicates Products that share a prefix share the trie nodes for that prefix, so each node can hold its own short list..

Search Suggestions System

Medium·LeetCode #1268 Pro OnlyInterview-Level

LeetCode

Problem Statement

You get a list of product names, products, and a word, searchWord, that the user types one letter at a time. After each letter, suggest up to three products that start with everything typed so far. If more than three products match, suggest the three that come first in alphabetical order.

Return one list of suggestions for each letter typed.

Input

products, a list of product names, and searchWord, the word the user types.

Output

A list of lists. The list at position i holds the suggestions after the first i + 1 letters of searchWord are typed.

Example 1

Input: products = ["mobile", "mouse", "moneypot", "monitor", "mousepad"], searchWord = "mouse"

Output: [["mobile", "moneypot", "monitor"], ["mobile", "moneypot", "monitor"], ["mouse", "mousepad"], ["mouse", "mousepad"], ["mouse", "mousepad"]]

Sorted, the products are mobile, moneypot, monitor, mouse, mousepad. After m and mo, all five products match, so the first three in alphabetical order are shown. After mou, mous and mouse, only mouse and mousepad match.

Example 2

Input: products = ["havana"], searchWord = "havana"

Output: [["havana"], ["havana"], ["havana"], ["havana"], ["havana"], ["havana"]]

havana is the only product, and every typed prefix of it matches, so it is suggested after every letter.

Constraints

• 1 ≤ products.length ≤ 1000
• 1 ≤ products[i].length ≤ 3000
• 1 ≤ sum of all products[i].length ≤ 2 · 10^4
• All strings in products are unique
• products[i] uses only lowercase letters
• 1 ≤ searchWord.length ≤ 1000
• searchWord uses only lowercase letters

Pattern Recognition Clues

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

“suggest after each letter”

→ Each answer is for a prefix of the typed word, and the prefixes are nested. The node for each prefix is one step below the node before it.

“the three smallest”

→ Sort first, so the alphabetically smallest products come first, and keep at most three at each node.

“products with a common prefix”

→ Products that share a prefix share the trie nodes for that prefix, so each node can hold its own short list.

Approach Complexity Ladder

Brute Force — filter, sort, take three, for each prefixO(m · (S + n log n · L))O(S)

For each typed prefix, keep the matching products, sort them and take the first three

Better — sort once, then lower_bound for each prefixO(n log n · L + m · L · log n)O(S)

Sort the products once; for each prefix, binary-search the first match and take the next three that still match

Optimal — trie that stores the three best at each nodeO(n log n · L + S + m · L)O(26 · S)

Insert sorted products into a trie; each node keeps up to three; one walk per typed letter

Brute Force Intuition

For each prefix of searchWord (length 1, 2, 3 and so on), scan all products and keep the ones that start with the prefix. Sort the kept products and take at most three. Repeat for the next letter.

Recognition rule for this sub-pattern:

Insert each word letter by letter; search by walking the same path.

Remember this · Trie

Trigger

Many words + prefix search, autocomplete, word dictionary with wildcards, maximum XOR.

Think

Do many queries share prefixes that I keep re-checking?

Key question

What does each node store (children, end-of-word, count)?

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Beyond The LeetCode Problem

How this concept connects to System Design & C++ Systems

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LLD Practice

Autocomplete & Search Engine

Prefix query caching, ranking, and memory-efficient trie compaction.

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Memory Alignment & Struct Padding

Minimizing pointer overhead and cache misses across 26-ary trie nodes.

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