Watch 9 video solutions for Split Array by Prime Indices, a medium level problem involving Array, Math, Number Theory. This walkthrough by ExpertFunda has 265 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
You are given an integer array nums.
Split nums into two arrays A and B using the following rule:
nums must go into array A.B.Return the absolute difference between the sums of the two arrays: |sum(A) - sum(B)|.
Note: An empty array has a sum of 0.
Example 1:
Input: nums = [2,3,4]
Output: 1
Explanation:
nums[2] = 4 is placed in array A.nums[0] = 2 and nums[1] = 3 are placed in array B.sum(A) = 4, sum(B) = 2 + 3 = 5.|4 - 5| = 1.Example 2:
Input: nums = [-1,5,7,0]
Output: 3
Explanation:
nums[2] = 7 and nums[3] = 0 are placed in array A.nums[0] = -1 and nums[1] = 5 are placed in array B.sum(A) = 7 + 0 = 7, sum(B) = -1 + 5 = 4.|7 - 4| = 3.
Constraints:
1 <= nums.length <= 105-109 <= nums[i] <= 109Problem Overview: You are given an array and need to split or process its elements based on whether their indices are prime numbers. The core task is identifying prime indices efficiently and then simulating the required split or aggregation using those indices.
Approach 1: Naive Prime Check + Simulation (O(n * sqrt(n)) time, O(1) space)
The straightforward approach checks whether each index is prime by testing divisibility from 2 to sqrt(i). For every array index, run the prime check and then place or process the element accordingly. This method works for small inputs but becomes inefficient because each index requires a separate primality test. The algorithm repeatedly performs expensive checks even though many results could be reused.
Approach 2: Sieve of Eratosthenes + Simulation (O(n log log n) time, O(n) space)
The efficient solution precomputes all prime indices up to n - 1 using the Sieve of Eratosthenes. Create a boolean array where each position indicates whether the index is prime. Start by marking multiples of each prime number as non‑prime, which builds the complete prime table in O(n log log n) time. After building the sieve, iterate through the array once and check the precomputed prime flag for each index.
If the index is prime, process the element in the "prime index" group; otherwise place it in the "non‑prime index" group. The simulation step is linear and consists of simple array iteration and conditional checks. Because primality is already computed, each lookup is O(1), making the total runtime dominated by the sieve preprocessing.
This pattern frequently appears in problems combining array traversal with math utilities. Precomputing primes with a sieve is a standard optimization in number theory tasks where repeated prime checks are required.
Recommended for interviews: The Sieve of Eratosthenes + simulation approach is the expected solution. Interviewers want to see that you avoid repeated primality checks and instead precompute primes efficiently. Mentioning the naive method shows you understand the baseline, but using the sieve demonstrates stronger algorithmic optimization and familiarity with number‑theory preprocessing techniques.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Naive Prime Check + Simulation | O(n * sqrt(n)) | O(1) | When constraints are small or when demonstrating baseline logic before optimization |
| Sieve of Eratosthenes + Simulation | O(n log log n) | O(n) | General case for large arrays where many prime index checks are required |