Copy from Wikipedia
Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.
Why does cycle sort have minimum write times (or minimum swap times)? I can't find such a claim in the paper Cycle-Sort: A Linear Sorting Method. I have met different variants of cyclesort, so I want to know the specific proof method.
Edited: I misunderstood minimum write times with minimum swap times, so the premise of the problem is wrong.