Minimum Swaps to Sort Descending

Given an array, compute the minimum number of swaps needed to sort it in decreasing order. Requirements Input: an array of integers. Return the minimum number of swaps required to reorder it into descending order. Clarify duplicate handling. If duplicates exist, stable target positions or value-index pairs are needed to avoid ambiguous swaps. Notes Sort value-index pairs by value descending to compute each element's target position, then count cycles in the permutation. Each cycle of length k contributes k - 1 swaps. If all values are distinct, the implementation is straightforward. If duplicates are allowed, pair each value with its original index to make target positions deterministic. Preparation Implement cycle counting from a target-position permutation. Test already-sorted descending input, ascending input, duplicates, and a single long cycle.