Array Nesting

Treat the permutation as a directed functional graph: each index has one outgoing edge to nums[i]. Because nums is a permutation, every component is a cycle, and the desired nesting length is that cycle size. Maintain visited globally. For each index not yet visited, follow current = nums[current], marking nodes and incrementing a local count until current is already visited. Update the answer with the local count. Global marking is the key: starting a new traversal from every index without it repeats the same cycle and becomes O(n squared). A variant can mark visited entries in place with a sentinel only if mutation is allowed and values cannot equal that sentinel. Test one large cycle, several disjoint cycles, and length one. Every index is entered once, so the runtime is O(n) and the visited array uses O(n) space; in-place marking can reduce auxiliary space to O(1).