Coding questions · ByteDance
Count Special Subarrays by Modular Frequency
This question evaluates the ability to apply modular arithmetic, frequency tracking, and prefix-count reasoning to efficiently count subarrays that satisfy a congruence condition, testing algorithmic problem-solving and scalable complexity management.
You are given an integer array nums, and two integers modulo and target, where 0 <= target < modulo.
Call an index i special if nums[i] % modulo == target.
A contiguous subarray nums[l..r] is considered valid if the number of special indices inside the subarray has remainder target when divided by modulo.
Return the number of valid subarrays.
Example
nums = [3, 1, 9, 6], modulo = 3, target = 0
Special indices are those whose values are divisible by 3: indices 0, 2, and 3.
Valid subarrays are those where the count of special elements is congruent to 0 mod 3.
Requirements
- Design an efficient algorithm.
- The array may be large, so an
O(n^2)enumeration of all subarrays is not acceptable. - Return the count as a 64-bit integer.
Count Special Subarrays by Modular Frequency
Constraints
- 0 <= len(nums) <= 200000
- 1 <= modulo <= 1000000000
- 0 <= target < modulo
- -1000000000 <= nums[i] <= 1000000000
- Use the mathematical non-negative remainder for modulo comparisons
Hints
- Convert the array into a sequence of 0s and 1s, where 1 means the index is special.
- For each prefix count modulo modulo, count how many previous prefix remainders would make the subarray's special count congruent to target.