1. algorithm

2. proof of correctness.

1 Star Wars In a galaxy far, far away, the Empire has builtn Death Satellites to attack n planets controlled by the rebels (each satellite will attack exactly one planet). The Rebels have installed a defensive shield in each planet. Thei-th satellite has power fi, while the shield on planet j can tolerate up to si power. A successful attack on the i-th planet brings benefit b to the Empire. That is, if planet is attacked by the j-th satellite and fi > Si, then the Empire will receive benefit bi; otherwise, it will receive benefit 0. Match satellites to planets to maximize the Empire's benefit in O (n logn) time, using a greedy algorithm. Hint: Make one or more heaps