Standing Ovation

Design a hardware module that simulates an auditorium where audience members give a standing ovation. Each person i will stand only if at least i people have already stood up. Given the initial shyness levels, calculate the minimum number of additional people needed to guarantee everyone eventually stands.

Example: For audience with counts [1,1,1,1,1] and smax=4, calculate the minimum number of additional people needed.

Source: Google Code Jam 2015 Qualification Round - Problem A: Standing Ovation