Interval covering

Given several real numbers x₁, …, x_(n), we want to find the smallest
possible set of closed intervals of length 1 that cover those real
numbers. In other words, we must find a set of intervals
{[y₁, y₁ + 1], …, [y_(m), y_(m) + 1]} such that

- for every x_(i), there exists some j such that
  x_(i) ∈ [y_(j), y_(j) + 1];

- m is minimum.

For instance, if the x_(i)’s are 1.4, 1.9, 2.3 i 2.7, a possible
solution is {[1.2, 2.2], [1.8, 2.8]}, because every x_(i) is inside of
(at least) one of the two intervals, and it is not possible to cover the
four real numbers with only one interval.

Input

Input consists of several cases, each with a number n followed by n
different real numbers. Assume n ≤ 10⁵.

Output

For every case, print the minimum number of closed intervals of length 1
that cover the given real numbers.

Problem information

Author: Unknown
Translator: Amalia Duch

Generation: 2026-01-25T10:35:14.480Z

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