fourthlargest

Fourthlargest is a term used to describe the element that ranks fourth when a collection of values is ordered from largest to smallest. In practice, there are two common interpretations of what counts as the “fourth largest,” depending on whether duplicates are treated as separate items or as a single distinct value.

If duplicates are counted (the standard interpretation in many programming problems), the fourth largest is the element at position four in a descending sort of all elements. If duplicates are ignored and only distinct values are considered, the fourth largest is the fourth element in the descending sequence of unique values (the fourth distinct largest).

Computing the fourth largest can be done in several ways. A straightforward method is to sort the data in descending order and pick the fourth position, which runs in O(n log n) time. A more efficient approach for large datasets is to use a min-heap of size k (here k = 4) to maintain the top four values as you scan the data, giving an O(n log k) algorithm. For average-case linear time, a Quickselect selection algorithm can locate the k-th largest in O(n) expected time. When seeking the fourth distinct largest, you would first extract unique values (for example, by using a set) and then apply the same methods to the resulting smaller collection.

Example: with the numbers [9, 7, 9, 5, 3, 7, 4], the fourth largest including duplicates is 7, while the fourth largest distinct value is 4. Questions of definition matter for ties and for datasets with fewer than four elements.

See also k-th largest element, order statistics, and Quickselect.