How do you solve Split Array by Prime Indices on LeetCode?

Split Array by Prime Indices (LeetCode #3618) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log log n) time complexity and O(n) space complexity. Key insight: Understanding prime numbers is crucial.

What is the time complexity of Split Array by Prime Indices?

The optimal solution for Split Array by Prime Indices runs in O(n log log n) time and uses O(n) space. Sieve of Eratosthenes runs in O(n log log n) and we traverse nums once, making it efficient.

What is the brute force solution for Split Array by Prime Indices?

The brute force approach for Split Array by Prime Indices is Brute Force, with O(n²) time complexity and O(1) space complexity. Check each index to see if it's prime, then split the array accordingly. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n log log n).

What algorithm or data structure is used to solve Split Array by Prime Indices?

Split Array by Prime Indices uses the following concepts: Array, Math, Number Theory. The recommended patterns to study are: Sieve of Eratosthenes, Array.

What are the interview tips for Split Array by Prime Indices?

Explain your thought process clearly. Use examples to illustrate your approach. Practice coding under time constraints.

What are common mistakes when solving Split Array by Prime Indices?

Not checking for edge cases like small arrays. Misunderstanding prime index calculations.

#3618

Split Array by Prime Indices

Medium

ArrayMathNumber TheorySieve of EratosthenesArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log log n)Space O(n)

Use the Sieve of Eratosthenes to find all prime indices efficiently, then split the array in a single pass.

⚙️

Algorithm

3 steps

1Step 1: Generate a list of prime indices using the Sieve of Eratosthenes.
2Step 2: Iterate through nums, adding to sumA for prime indices and sumB for others.
3Step 3: Return |sumA - sumB|.

solution.py15 lines

1def split_array(nums):
2    n = len(nums)
3    is_prime = [True] * n
4    is_prime[0] = is_prime[1] = False
5    for i in range(2, int(n**0.5) + 1):
6        if is_prime[i]:
7            for j in range(i*i, n, i):
8                is_prime[j] = False
9    sumA, sumB = 0, 0
10    for i in range(n):
11        if is_prime[i]:
12            sumA += nums[i]
13        else:
14            sumB += nums[i]
15    return abs(sumA - sumB)

ℹ

Complexity note: Sieve of Eratosthenes runs in O(n log log n) and we traverse nums once, making it efficient.

1Understanding prime numbers is crucial.
2Efficient algorithms can significantly reduce complexity.

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