Exercise 1 — Jet Lag Calculator

How many days of rest do you need to recover from jet lag? The International Civil Avaiation Organization has a fomula for this:

1. Hours = number of hours of travel
2. Zones = number of time zones crossed
3. Depart =
   • 0, for departures between 8AM and noon
   • 1, for departures between noon and 6PM
   • 3, for departures between 6PM and 10PM
   • 4, for departures between 10PM and 1AM
   • 5, for departures between 1AM and 8AM
4. Arrive =
   • 4, for arrivals between 8AM and noon
   • 2, for arrivals between noon and 6PM
   • 0, for arrivals between 6PM and 10PM
   • 1, for arrivals between 10PM and 1AM
   • 3, for arrivals between 1AM and 8AM

The number of days you need to recover is:

days of recovery = (Hours/2 + (Zones-3) + Depart + Arrive)/10

For example, say that you are flying from New York Kennedy Airport to London Heathrow. Your flight leaves at 7AM (New York time) and arrives at 7PM (London time).

1. Hours = 7 (London time is New York time + 5)
2. Zones = 4
3. Depart = 5
4. Arrive = 0

days of recovery = (7/2 + (4-3) + 5 + 0)/10 = (3.5 + 1 + 5 + 0)/10 = 9.5/10 = 0.95 days

Write a program that asks the user for the number of hours of travel, the number of time zones crossed, the departure time, and the arrival time and then calculates the number of days needed for recovery. Let the user enter time using a 24 hour clock (so 6PM is 18).

(Formula from Darrell Huff, How to Figure It, Norton, 1996.

Exercise 2 — Adding up Squares and Cubes

Write a program that adds up the squares and adds up the cubes of integers from 1 to N, where N is entered by the user:

Upper Limit:
5
The sum of Squares is  55
The sum of Cubes   is  225

Do this by using just one loop that generates the integers. Of course, if you really needed to calculate these sums you would use the appropriate formulas:

12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6

13 + 23 + 33 + ... + n3 = n2(n+1)2/4

Add these formulas to your program and print out their results as well as that of the explicit summations.

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Exercise 3 — Power of a number

Write a program that computes XN where X is a floating point number and N is a positive integer. The program informs the user that N must be positive if the user enters a negative value. Of course,

XN = X * X * X * ... * X   
     --------------------
           N times

The user dialog will look something like this:

Enter X
1.3
Enter N
5

1.3 raised to the power 5 is:  3.71293

-------

Enter X
5.6
Enter N
-3

N must be a positive integer.

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Exercise 4 — Wedge of Stars

Write a program that writes a wedge of stars. The user enters the initial number of stars, and the program writes out lines of stars. Each line has one few star than the previous line:

Initial number of stars:
7

*******
******
*****
****
***
**
*

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Exercise 5 — Pine Tree

Write a program that writes a tree made of stars on the terminal:

       *
      ***
     *****
    *******
   *********
  ***********
 *************
***************
      ***
      ***
      ***

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