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Finding Possible Triangles from Array Elements Based on Side Length Conditions

Problem Overview
The challenge is to count the number of possible triangles that can be formed using three different elements from a given integer array.
A triangle is valid if the sum of any two sides is greater than the third side, as per the triangle inequality theorem.

Triangle Validity Conditions
For three sides a, b, and c (where (a != b l= c), the condition (a + bゝ c) must hold true to form a valid triangle.
Examples of invalid combinations include (1, 2, 3) and (3, 4, 7), where the sum of the two smaller sides equals or is less than the largest side.
The need to assess all triplet combinations emphasizes understanding the conditions under which triangles can be formed.

Algorithm Approach
An algorithm with a time complexity of O(N^2) is proposed for solving the problem, where N is the number of elements in the array.
The algorithm involves sorting the array first, which allows for efficient checking of triangle conditions by pruning unnecessary comparisons.
A nested loop structure is used to evaluate pairs of sides, while a third pointer checks for valid combinations that satisfy the triangle inequality.

Optimization Techniques
The sorted nature of the array enables early termination of the search for the third side once a length is found that does not meet the triangle conditions.
This optimization prevents unnecessary computations by ensuring that if a number fails the triangle condition, all subsequent numbers will also fail.
The algorithm can count valid triangles incrementally as it iterates through potential side combinations.

Complexity Considerations
Despite the O(N^2) complexity, in this case it is deemed acceptable due to the manageable input size and specific problem constraints.

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