Minimum Changes 2

For an array that is a permutation of distinct target values, sort pairs (value, originalIndex) by value. The sorted position i wants the element currently at the original index recorded by that pair, which creates a permutation of indices. Visit each unvisited cycle. A cycle of length L can be fixed in L-1 swaps by repeatedly bringing the correct element into one chosen position, and fewer swaps cannot work because each swap can increase the number of correctly placed cycle elements by at most one in the required way. Sum L-1 across cycles. An alternative mutates a value-to-index map while swapping elements into their target positions, also O(n log n) if target ordering comes from sorting. The common HackerRank version contains values 1..n, so direct index placement gives O(n), but do not assume that for arbitrary values. Test already sorted input, one long cycle, disjoint cycles, and clarify duplicate handling because cycles are not unique with duplicates.