1) Pictures are being hung on a long wall in a gallery. All pictures are hung at the same height, but are hung at various dierent horizontal coordinates. Wall sensors can protect any picture whose center is within 1.0 meters of the sensor.

Design a greedy algorithm that, given a set A of n positive real numbers (indicating the distance between each pictures center and the left edge of the wall), nds the smallest number of sensors that will protect all of the pictures. Prove the correctness of your algorithm.