secondhighest

Second highest is a term used to describe the value that is immediately below the maximum in a collection of numbers, when the values are arranged in descending order. In many contexts, it refers to the second largest distinct value—the next value that differs from the maximum. If all elements are equal or if only one unique value exists, there is no second highest distinct value.

Distinguishing between interpretations is important. When duplicates are allowed, counting by position in a sorted list yields the second element, which may be equal to the maximum if the maximum occurs more than once. By contrast, the second highest distinct value ignores duplicates and looks for the greatest value strictly less than the maximum. This distinction matters for tasks such as ranking or statistical reporting.

Common algorithms focus on finding the second largest value in a single pass. A typical approach maintains two variables, max and second, initialized to negative infinity. As each number is processed, max and second are updated to preserve the largest and the second largest (or the second largest distinct) values. Special care is needed to handle duplicates if the goal is the distinct interpretation.

Applications of the concept include sports standings, performance analytics, and programming challenges that require order statistics. Understanding the second highest helps in determining runner-up positions and in calculations that depend on thresholds or breakpoints.

See also: maximum, second maximum, runner-up, top-k, order statistics.