Start by iterating through all possible substrings of the input string to generate candidate numbers. Use a hash table to store unique primes and check each number for primality with math optimizations. Sum the three largest primes or all available primes if fewer than three exist, returning 0 if no primes are found.
Problem Statement
Given a string of digits, identify all distinct prime numbers formed by any of its contiguous substrings. Leading zeros are ignored, and each prime is counted only once regardless of duplicates in different substrings.
Return the sum of the three largest unique prime numbers discovered. If fewer than three unique primes exist, sum all available primes. If no prime numbers can be formed, return 0. Ensure efficient handling for strings up to length 10 using hash table and math-based primality checks.
Examples
Example 1
Input: s = "12234"
Output: 1469
Example 2
Input: s = "111"
Output: 11
Constraints
- 1 <= s.length <= 10
- s consists of only digits.
Solution Approach
Generate Substrings and Convert
Iterate through all possible substrings of the input string. Convert each substring to an integer while ignoring leading zeros, and collect potential candidate numbers for primality testing.
Check Primality Efficiently
Use a math-based primality test for each candidate number. Store confirmed primes in a hash table to maintain uniqueness and avoid counting duplicates from multiple substrings.
Sum the Largest Primes
Sort the unique primes stored in the hash table in descending order and sum the top three. If fewer than three primes exist, sum all available ones. Return 0 if no primes are found.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is roughly O(n^3) due to generating all substrings and checking each for primality. Space complexity is O(k) where k is the number of unique prime numbers stored in the hash table.
What Interviewers Usually Probe
- Focus on hash table usage to prevent duplicate prime counting from overlapping substrings.
- Expect efficient math checks for primality due to potential large numeric substrings.
- Clarify handling of leading zeros and small input strings.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to ignore leading zeros when converting substrings to integers.
- Counting the same prime multiple times if it appears in different substrings.
- Inefficient primality checks causing timeouts on larger numeric substrings.
Follow-up variants
- Return the sum of the k largest unique prime substrings instead of three.
- Count primes formed only by substrings of a fixed length.
- Compute the product instead of the sum of the largest prime substrings.
How GhostInterview Helps
- GhostInterview highlights candidate substrings and identifies unique primes quickly.
- The solver ensures math-based primality checks are applied efficiently to all numbers.
- It automatically aggregates and sums the top primes, reducing manual sorting and logic errors.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What exactly is a prime substring in this problem?
A prime substring is any contiguous sequence of digits from the input string that converts to a prime number, ignoring leading zeros.
How should I handle repeated primes from different substrings?
Store primes in a hash table to count each prime only once, even if it appears in multiple substrings.
Can I use GhostInterview to quickly generate candidate numbers?
Yes, GhostInterview iterates over all substrings efficiently and tracks unique candidates for primality checking.
What if there are fewer than three primes?
Return the sum of all available unique primes. If none exist, return 0.
Does the Hash Table plus Math pattern apply here?
Absolutely, hash tables handle uniqueness while math functions efficiently test for primality across substrings.
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Count Beautiful Substrings II focuses on finding beautiful substrings with hash tables and number theory techniques.
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