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Count Special Quadruplets

Difficulty: Easy

Problem Description

Given a 0-indexed integer array nums, return the number of distinct quadruplets (a, b, c, d) such that:

  • nums[a] + nums[b] + nums[c] == nums[d], and
  • a < b < c < d

Key Insights

  • The problem requires checking combinations of four indices in the array.
  • We need to ensure the indices are distinct and in increasing order.
  • The sum of the first three elements must equal the fourth element.
  • The constraints allow for a straightforward brute-force approach due to the limited size of the array (maximum length of 50).

Space and Time Complexity

Time Complexity: O(n^3)
Space Complexity: O(1)

Solution

To solve the problem, we can use a brute-force approach by iterating through all possible combinations of indices a, b, c, and d. We will use three nested loops to select indices a, b, and c, and then use a fourth loop to find d such that the condition nums[a] + nums[b] + nums[c] == nums[d] holds true. This algorithm leverages the fact that the size of nums is manageable, allowing us to check each combination without performance concerns.

Code Solutions

def countQuadruplets(nums):
    count = 0
    n = len(nums)
    for a in range(n):
        for b in range(a + 1, n):
            for c in range(b + 1, n):
                for d in range(c + 1, n):
                    if nums[a] + nums[b] + nums[c] == nums[d]:
                        count += 1
    return count
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