The following problems all concern an input array of integers, possibly with duplicate entries. Which of them can be solved using a single invocation of a sorting subroutine followed by a single pass over the sorted array? You are allowed to use a constant amount of space for variables. Please explain your answer on a high level, i.e., how would such an algorithm accomplish the task at hand.

1. Compute the minimum gap between any pair of array elements.

2. Compute the number of distinct integers contained in the array.

3. Compute a de-duplicated version of the input array, meaning generate an output array that contains exactly one copy of the distinct integers in the input array. 4. Compute the mode (the most frequently appearing integer) in the array. If there is a tie, return any of the tied entries.