ninthlargest

Ninthlargest is a term used in computing and mathematics to refer to the ninth-largest element in a set or sequence. In practice, it often appears as a named function, variable, or concept in programming tasks where the goal is to determine the element with rank nine among the values.

If a list of numbers is sorted in descending order, the ninthlargest is the element at position 9. If the list contains fewer than nine elements, or if the notion of ninth largest is undefined in context, the result may be undefined or require special handling. Some contexts distinguish between counting duplicates (the ninth item in the sorted sequence) and counting distinct values (the ninth distinct largest).

Algorithms for finding the ninthlargest include several approaches. A simple method is to sort the list, which runs in O(n log n) time. A more efficient approach uses a min-heap of size nine to track the top nine values, operating in O(n log 9). Another option is a selection algorithm such as quickselect to find the kth largest with expected linear time, O(n).

In code, ninthlargest is commonly represented as a function name like kth_largest with k set to 9. The lowercase concatenated form ninthlargest is possible but less conventional. The concept is related to order statistics and is part of problems known as the kth largest problem.

See also: kth largest, order statistics, quickselect, heap-based selection.