Is Number of Single Divisor Triplets easy or hard?

The problem is rated Medium because the brute force logic is straightforward but the optimized solution requires careful counting and combinatorial reasoning. Handling duplicate values and computing the correct number of index permutations adds extra complexity.

Number of Single Divisor Triplets Python/Java solution

Most implementations build a frequency array, iterate through all possible value triples (a, b, c), compute the sum, and check how many of a, b, and c divide that sum. If exactly one divisor condition holds, multiply by the number of permutations derived from their frequencies. The same logic works in Python, Java, C++, Go, and TypeScript.

How to solve Number of Single Divisor Triplets in O(n)?

A strict O(n) algorithm is not typical for this problem because the divisor condition depends on combinations of three numbers. The common optimized solution uses a frequency array and enumerates value triples, achieving roughly O(U^3) time where U is the distinct value count. This is much faster than checking all n^3 index triplets when many numbers repeat.

What is the best approach for Number of Single Divisor Triplets?

The most efficient approach is counting + enumeration. First compute the frequency of each value in the array, then enumerate value triplets (a, b, c) instead of index triplets. For each combination, check whether exactly one value divides the sum a + b + c and multiply by the number of index permutations. This reduces repeated work and runs in about O(U^3) time where U is the number of distinct values.

Is Number of Single Divisor Triplets asked at Google/Amazon/Meta?

Problems involving combinatorics and divisibility conditions appear frequently in interviews at large tech companies. Variants that combine counting, enumeration, and modular arithmetic have shown up in interviews at companies like Amazon and Google. The question tests reasoning about arithmetic constraints and efficient counting.

What data structure is used in Number of Single Divisor Triplets?

The core data structure is a frequency map or fixed-size counting array. It stores how many times each number appears in the input. This allows the algorithm to enumerate unique value combinations and compute how many index triplets they represent using combinatorics.

What is the time complexity of Number of Single Divisor Triplets?

A direct brute force solution requires O(n^3) time because every triplet of indices must be checked. The optimized counting approach reduces the search space by enumerating value combinations instead of indices, giving O(U^3) time where U is the number of unique values. Space complexity is O(U) for storing frequencies.

Description Hints 2 Solution Video 15:17

2198. Number of Single Divisor Triplets

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You are given a 0-indexed array of positive integers nums. A triplet of three distinct indices (i, j, k) is called a single divisor triplet of nums if nums[i] + nums[j] + nums[k] is divisible by exactly one of nums[i], nums[j], or nums[k].

Return the number of single divisor triplets of nums.

Example 1:

Input: nums = [4,6,7,3,2]
Output: 12
Explanation:
The triplets (0, 3, 4), (0, 4, 3), (3, 0, 4), (3, 4, 0), (4, 0, 3), and (4, 3, 0) have the values of [4, 3, 2] (or a permutation of [4, 3, 2]).
4 + 3 + 2 = 9 which is only divisible by 3, so all such triplets are single divisor triplets.
The triplets (0, 2, 3), (0, 3, 2), (2, 0, 3), (2, 3, 0), (3, 0, 2), and (3, 2, 0) have the values of [4, 7, 3] (or a permutation of [4, 7, 3]).
4 + 7 + 3 = 14 which is only divisible by 7, so all such triplets are single divisor triplets.
There are 12 single divisor triplets in total.

Example 2:

Input: nums = [1,2,2]
Output: 6
Explanation:
The triplets (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), and (2, 1, 0) have the values of [1, 2, 2] (or a permutation of [1, 2, 2]).
1 + 2 + 2 = 5 which is only divisible by 1, so all such triplets are single divisor triplets.
There are 6 single divisor triplets in total.

Example 3:

Input: nums = [1,1,1]
Output: 0
Explanation:
There are no single divisor triplets.
Note that (0, 1, 2) is not a single divisor triplet because nums[0] + nums[1] + nums[2] = 3 and 3 is divisible by nums[0], nums[1], and nums[2].

Constraints:

3 <= nums.length <= 10⁵
1 <= nums[i] <= 100

Topics

Math

Hints open one at a time

Hint 1

The maximum value of nums.length is very large, but the maximum value of nums[i] is not.

Hint 2

Count the number of times each value appears in nums. Brute force through every possible combination of values and count how many single divisor triplets can be made with that combination of values.

15:17

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2198. Number of Single Divisor Triplets

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