How do you solve Sum of Largest Prime Substrings on LeetCode?

Sum of Largest Prime Substrings (LeetCode #3556) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Unique substrings can generate multiple primes.

What is the time complexity of Sum of Largest Prime Substrings?

The optimal solution for Sum of Largest Prime Substrings runs in O(n) time and uses O(n) space. The complexity is reduced by precomputing primes and efficiently generating substrings.

What is the brute force solution for Sum of Largest Prime Substrings?

The brute force approach for Sum of Largest Prime Substrings is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all possible substrings and check each for primality. This method is straightforward but inefficient due to the number of substrings. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Sum of Largest Prime Substrings?

Sum of Largest Prime Substrings uses the following concepts: Hash Table, Math, String, Sorting, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Sum of Largest Prime Substrings?

Explain your thought process clearly. Discuss time and space complexity upfront. Consider edge cases and constraints.

What are common mistakes when solving Sum of Largest Prime Substrings?

Not handling leading zeros correctly. Forgetting to check for unique primes.

#3556

Sum of Largest Prime Substrings

Medium

Hash TableMathStringSortingNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Use a sliding window to generate substrings efficiently and a sieve to precompute primes up to a certain limit.

⚙️

Algorithm

3 steps

1Step 1: Precompute all primes up to 9999999999 using the Sieve of Eratosthenes.
2Step 2: Generate unique substrings, convert to integers, and check against the precomputed primes.
3Step 3: Collect unique primes and return the sum of the three largest.

solution.py17 lines

1def sieve_of_eratosthenes(limit):
2    is_prime = [True] * (limit + 1)
3    for i in range(2, int(limit**0.5) + 1):
4        if is_prime[i]:
5            for j in range(i * i, limit + 1, i):
6                is_prime[j] = False
7    return {i for i in range(2, limit + 1) if is_prime[i]}
8
9def sum_of_largest_primes(s):
10    primes = sieve_of_eratosthenes(9999999999)
11    unique_primes = set()
12    for i in range(len(s)):
13        for j in range(i + 1, len(s) + 1):
14            num = int(s[i:j])
15            if num in primes:
16                unique_primes.add(num)
17    return sum(sorted(unique_primes, reverse=True)[:3])

ℹ

Complexity note: The complexity is reduced by precomputing primes and efficiently generating substrings.

1Unique substrings can generate multiple primes.
2Primality testing can be optimized with precomputation.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.