Fast Phil works the late shift and leaves his company's parking lot at precisely 2:00 AM every morning. His route home is by a straight road which has one or more traffic signals. Phil has always wondered if, given the locations and cycles of each of the traffic signals, are there velocities he can travel home without ever having to speed up or slow down on account of a red light. You are to write a program to satisfy his curiosity.
Your program should find all integer speeds (in miles per hour) which can be used for Phil's trip home. Each speed is a rate (in miles per hour) he can maintain the moment he leaves the parking lot at 2:00 AM until he arrives home (we assume Phil has a long driveway in which to decelerate) such that he never passes through a red signal. He is allowed to pass throgh a signal at the exact moment it turns from yellow to red, or at the exact moment a red signal turns green. Since Phil is a relatively law-abiding citizen, you need only consider speeds less than or equal to 60 mph. Likewise, Phil isn't interested in travelling too slowly, so you should not consider speeds lower than 30 mph.
Hare the lowest and highest speeds for the interval. Intervals of the form
L-L(that is, an interval of length 1) shold just be written as
L. Intervals should be separated by commas. If there are no valid speeds, you program should display the phrase
No acceptable speeds.The Expected Output below illustrates this format.
1 5.5 40 8 25 3 10.7 10 2 75 12.5 12 5 57 17.93 15 4 67 -1
Case 1: 30, 32-33, 36-38, 41-45, 48-54, 59-60 Case 2: No acceptable speeds.