Number of Distinct Substrings in String
A medium Trie problem included in Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Trie
- Sheets
- 1
- Core for
- 7 roles
- Platform
- GeeksforGeeks
The problem
Given a string, count the total number of distinct non-empty substrings it contains.
Example 1
- Input
- s = "aab"
- Output
- 5
- Why
- The distinct substrings are: 'a', 'aa', 'aab', 'ab', 'b'.
Example 2
- Input
- s = "abc"
- Output
- 6
- Why
- The distinct substrings are: 'a', 'ab', 'abc', 'b', 'bc', 'c'.
Constraints
- 1 <= s.length <= 500
- s consists of lowercase English letters
How to think about it
Updated 2026-09-09Every contiguous segment of a string is uniquely identified by which character starts it and where it terminates. Overlapping characters mean duplicate substrings share the same path from the root of a prefix tree built from all suffixes; counting nodes created along the way directly yields the unique substring count without string storage.
Approaches, worst first
Explicit substring set
time O(n^3) · space O(n^3)
Extract every substring using two pointers and record each in a hash set. Measuring the resulting set size is conceptually direct, but copying strings causes excessive memory consumption and polynomial hashing costs.
Incremental suffix trie insertionWrite this one
time O(n^2) · space O(n^2 * 26)
Iterate every starting index i and stream trailing characters into a trie. Every time a child pointer is absent, create the node and increment an accumulator. Because each node represents one distinct prefix of some suffix, the tally is exact.
Where people lose marks · 2
- Including the empty string in the final count; the trie root node corresponds to the empty prefix and should not be counted.
- Re-allocating the trie for every starting index instead of continuing insertions into the single shared trie structure.
The theory behind it
Trie — the ground this problem stands on. All Trie problems
What Trie is
A trie, also called a prefix tree, is a tree structured for storing words character by character. Instead of storing entire words in individual nodes, each step down a branch represents a single letter. Words that share the same beginning, like car, card, and care, share the exact same starting path down the tree. A special boolean marker sits at the end of each valid word to show that a complete word terminates at that letter.
When to reach for it
Reach for a trie when questions involve prefix lookups, dictionary word searches, autocomplete engines, or matching prefixes against a body of text. Prompts asking whether any word in a dictionary begins with a given prefix, or searching for words on a Boggle board grid, point directly to a trie. It also applies to bitwise tasks, such as finding the maximum XOR pair among integers by treating numbers as binary prefixes.
How the pattern works
Represent each trie node with an array or hash map of child links, plus a boolean flag marking if a complete word ends at that node. When inserting, start at the root and walk down character by character, creating new child nodes whenever a path does not exist yet, then mark the final node as a word ending. When searching, follow the characters; if any child link is missing, the word or prefix does not exist. If all characters match, check the boolean flag to distinguish between a full word and a partial prefix.
What each operation costs
| Operation | Time |
|---|---|
| insert word of length l into trie | O(l) |
| search for full word of length l | O(l) |
| check if any word begins with prefix of length l | O(l) |
What usually goes wrong with Trie
- Confusing prefix matches with full word matches by returning true when characters exist but the end-of-word flag on the final node was never set.
- Allocating fixed 26-slot arrays for child pointers without verifying that all input characters are strictly lowercase English letters.
- Forgetting to prune unvisited branches during board searches, leading to time limit exceeded errors on grids with large word sets.
Which roles need this problem
Trie is a core topic for these 7 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 2 more roles, including Information Retrieval Engineer, Storage Engineer.
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