Pascal Programming Exercises

For each program you should:

• try to figure out what is required;
• if you can't write the code from existing knowledge look at the answer and try to understand that;
• go back to the compiler and try to write the code again without looking at the answer;
• keep trying to write the code until you succeed;
• pay particular attention to the variable types used in the program; the links are to definitions which are part of the specification.

It may seem hard at first but practice is the main thing that is required so that the keywords and the syntax become more familiar and ingrained into your mind. We will go through many of the exercises during the course. Don't panic at this stage if you find it hard to get started; it takes time to absorb everything that you need to know and it may take you a while to pick up.

1: Read & Write Variables

1. (Program, begin, end, writeln, readln, type char) Write a program which outputs one or more numbers and literal strings. Answer
    
2. (Type integer, arithmetic operators, integer operators) Write a program which reads two integers and then displays a) their product and b) their quotient when the first is divided by the second. Answer
    
3. (Type real, format descriptor) Write a program which accepts three real numbers, computes their sum and outputs the result. Amend the program so that the result is output to 2 dp. Answer
   
   
4. Write a program that takes in the width, length and height of a room in metres and returns the volume of the room in cubic metres. Give the answer in centimetres as well. Choose integer or real as you think fit.
    
5. (Format descriptor) Write a program which accepts two real numbers, a value for the number of decimal places, calculates the sum and outputs the result. Try entering a real number for the number of decimal places. Answer
    
6. (Format descriptor) Write a program which accepts a sequence of real numbers and then outputs them in the following formats: a) decimal points in line; b) left justified; c) right justified. (Two of these are the same - can you see which ones?) Answer
   
   
7. Write a program which takes an amount of money in £ and then gives the minimum number of notes or coins that could make up this number e.g. £34 = 1x£20, 1x£10, 4x£1. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code.
   
   
8. Write a program which finds the roots of a quadratic equation from the three coefficients (a, b, c) using the formula roots= (-b +- sqrt(b ^2 -4ac)) / 2a. (a is the coefficient for x² b for x and c for the numeric part.) (PG) Answer

2: Selection with If

1. (If) Rewrite Exercise 5 to allow a choice between left and right justification of the numbers. Answer
   
   
2. Write a program that takes a temperature for water in either degrees F or C and outputs whether the water is freezing or boiling or neither.
    
3. (If..then, transformation) Write a program which accepts a temperature value for water and then offers the user a choice between converting from C to F or from F to C. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
    
4. (Pre-defined functions, round, trunc, typecast, if..then, type char, transformation) Write a program which accepts two real numbers, asks whether the user requires a rounded or truncated result and then outputs their product in the form requested. Answer
    
5. Write a program that accepts input for number of hours worked in a week and hourly rate of pay. Hours worked over 40 should be paid at 1.5 times the base rate.
   
   
6. Write a program that accepts a mark for an exam out of 60, converts it to a percentage and outputs a grade based on the score. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code.
   

3: Constants

1. (Constants, fixed value, transformation) Write a program which takes the radius of a circle as input and returns its area and circumference (pi = 3.14159). Answer
    
2. (Constants, fixed value, transformation) Write a program which sets up a constant for base rate tax, inputs the gross pay and returns the net pay. Answer
    
3. (Constants, fixed value) Write a program which sets up constants for base rate and higher rate tax (try 20% and 40%) and the tax thresholds for basic and higher rates (try £5,000 and £30,000). After inputting the gross pay the program should return the net pay according to the thresholds and rates. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer

4: Loops (For, Repeat, While)

1. (If, Repeat..until, and, most recent holder, transformation) Rewrite Exercise 1.2 so that only three-digit integers are accepted. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
    
2. (If, Repeat..until, and, most recent holder, transformation) Rewrite Exercise 1.3 so that only values in the range -100 to +100 are accepted. Answer
    
3. (If, odd, Repeat..until, most recent holder, transformation) Rewrite Exercise 1.3 so that only even numbers are accepted for the number of decimal places to be displayed. Answer
   
   
4. (Repeat, stepper, gatherer) Write a program which accepts a sequence of numbers and calculates their sum and mean average. Ask the user to enter the number of values in the sequence. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
    
5. (for loop, stepper, most recent holder) Write a program which outputs the multiplication table of the user's choice. Each line should read, for example, "3 x 13 = 39", where 13 was the number entered by the user. Answer
    
6. (for loop, stepper, most recent holder) Write a program which outputs the first 10 triangle numbers: 1, 3, 6, 10, 15, etc. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
    
7. (Nested for loop, stepper,most recent holder) Write a program which takes two integer values from the user and outputs the multiplication tables between the first and second numbers. (e.g. 4 and 7 will output the 4 times table, the 5 times table, the 6 times table and the 7 times table). Answer
    
8. (for loop, stepper, gatherer) Write a program which sums the terms of the harmonic series (1 + 1/2 + 1/3 + 1/4...) up to a limit supplied by the user. Output the values as floating point and as a fraction.(PG)
   
   
9. (for loop, stepper, gatherer) Write a program that uses the following formula to calculate pi: pi=4(1 - 1/3 + 1/5 - 1/7 + 1/9...).
   
   
10. (For, downto, run time errors, try-except, stepper) Write a program which divides a number by a successively smaller number of values. Try to extend the range of values from, say, 5 to -5 and observe the result. Provide a suitable error trapping routine to prevent this error from happening. Answer.
     
11. (if..then..else) Write a program which outputs part of a sequence of numbers on the screen and then invites the user to enter the next number (e.g. 2,4,6,8,? answer 10 - this is an easy example). The formula for finding the next number will be in the for loop e.g. next := next * 3. Display messages according to the success achieved. A BIO question asked for the next number in the sequence 1 2 4 8 16 23 28 38 49. This is tricky to spot and trickier to code than 1, 4, 9, 16, 25, 36, etc. And how about this one: 1; 11; 21; 1211; 111221; 312211...?
     
12. (Nested for loop) Write a program which finds and displays the 'perfect numbers' up to a user-supplied value. (A perfect number is one whose factors add up to the number itself, eg 6 = 1+2+3.) Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
    
    
13. (single, double, extended) Write a program that calculates the frequency of notes on a piano. The ratio of two musical notes a semitone apart is the 12th root of 2 (take the square root of 2 twelve times - keep pressing the calculator button until 1.059463094). Middle A is 44 cycles per second, the lowest note is 4 octaves below this. There are 88 notes on a concert piano.  (PG) Answer
    
    
14. Write a program that examines a set of integers (including negative ones) and determines whether there is a sub-set of the numbers that sums to zero e.g. {−7, −3, −2, 5, 8} Look here.
    

5: Pre-defined Functions

1. (Ord, chr, ANSI) Write a program which uses two methods to print the ANSI sequence from 'space' (chr(32) or ' ') to 'z' (chr(122)), one using ord and the other using chr. Answer
    
2. (Ord, chr, length(), UpCase, string) Write a program that takes a string such as a name and encrypts it by finding the numerical value of each character and adding 1 to this (or any other value). The code should convert the altered numeric value to the corresponding character and build a copy of the encrypted string. Extension: convert the encrypted characters to upper case. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Can you think of a more effective algorithm for encrypting characters?
     
3. (odd, mod, loop) Write a program that takes a single input value and then applies these rules until the answer is 1: if the number is even divide by 2; if the number is odd multiply by 3 and add 1. Output the numbers produced. Is there a pattern in the output? Will all input numbers eventually reach 1? (The odd function takes the form odd(n) and returns a Boolean; so if n=1 or 3 or 5 etc. then odd(n) returns true while if n=2 or 4 or 6 etc then odd(n) returns false).
   

6: User-Defined Functions

1. (Case, function) Write a program which takes two values from the user and then offers a choice between the four basic arithmetic operations to be performed. Use a menu, case and a function for each operation. Answer
   
   
2. (function, for loop, stepper, follower, initialisation) Write a program which includes one function to calculate a Fibonacci number from the previous two numbers and another function to calculate the golden ratio from two Fibonacci numbers. The program should take a user-supplied value and display the Fibonacci sequence up to that value, along with the golden ratio for the current value divided by the previous one. Answer
   
   
3. Write a program that includes a function to calculate the greatest common divisor of two numbers. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code.
    
4. (function, gatherer) Write a program that calculates n! using a function. Answer
    
5. (function) Write a program that includes a function to calculate m to the power n. Use this function to illustrate the difference between n to the power 2, 3, etc. and 2 to the power n, where n is 2, 3, 4, etc. The first of these is a quadratic function (n²) while the second is exponential (2ⁿ). Explain the difference between these functions. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code.
   
   
6. (for loop) Write a program which displays the factors of a number (they do not have to be prime factors). Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
   
   
7. (Repeat, function, nested loop, algorithm, tracing) Write a program which reads an integer and outputs its prime factors or declares that the number is prime. Make sure the prime factor routine is in a function. Write the algorithm for this in pseudo-code and/or flowchart format before proceeding to the code. Answer
   
   
8. Write a program which converts between currencies. You could do this by asking the user for the two currencies, the amount and the exchange rate or you could store a range of currency exchange rates in an array or in a file that is read into an array at run-time. This would work well in a GUI program.
   
   
9. (for loop, stepper, gatherer) Writea program that calculates e from the formula 1 + 1 + 1/2! + 1/3! + 1/4!...
   
   
10. Write a program that takes the product of two prime numbers and then finds its factors. e.g. enter 77: factors are 7 and 11. Answer
    
    
11. Write a program that takes a number and finds the powers of 2 that sum to that number e.g. 25 = 1 + 8 + 16. Answer
    

1. Write a program that defines a procedure with two input parameters, one an integer, n, and the other a character, c. The procedure will output the character n times.
   
   
2. Write a program that defines a procedure that takes two input parameters and returns them in ascending order, either numeric or dictionary, according to whether you choose numeric or string variables.
   
   
3. Write a program that includes a procedure that takes an odd number as a parameter and prints an upside down triangle of stars that starts with the input value and decreases by 2 until the last row contains a single character.
   
   
4. (Boolean, string, if, procedures) Write a program which takes a date as three numbers and returns output in the form number/string/number eg 12th November 1992. Include error checking on the range of acceptable numbers for the day and month, and check that the numbers entered for the day are valid for the month (eg 30/2/99, or 31/6/02). Use an appropriate technique to explain the action of the program. Dry run the program with these dates: 1/4/76, 29/2/2008, 31/12/2005 and show what happens. Write out a test plan of 10 dates for testing the program, showing that it can handle both valid and invalid dates. Rewrite the code using procedures for reading the three values, finding the suffix for the day and finding the name of the month. Answer.
   
   
5. (procedure) Write a program which takes a rational number from the user as a numerator and a denominator. Write a procedure which removes common factors from this number, eg 15/24 = 5/8. To do this you will have to find the gcd of the two numbers and then divide the original values by this eg gcd of 15 & 24 is 3, 15/3=5, 24/3=8. (PG)
    
6. Extend the previous exercise to include a procedure to add two rational numbers, eg 2/7+1/6=12/42+7/42=19/42. Finally, use the procedures you now have to find partial sums of the harmonic series. For 1/1+1/2+1/3 we have: 6/6+3/6+2/6=11/6. Adding 1/4 we have 11/6+1/4=23/12+3/12=25/12, etc. (PG)

8: Arrays 

1. (Array) Write a program which fills an array with a sequence of numbers such as a multiplication table. The user should then be able to specify a value from the table by its index value. For example, if the table contains 5, 10, 15...50, the user should be able to input 6 and obtain the result 30 from the table (6x5). Extend this to a 12 x 12 table so the user can specify two values and retrieve the product. Answer
   
   
2. Take the Fibonacci program that you wrote earlier and store the Fibonacci numbers in a table so that a user could specify the nth Fibonacci value and the program will then look it up in the table. Extend this to store the golden section values as well.
    
3. (Array, linear search, stepper, most wanted holder). Write a program that populates a list with a range of values and then finds the largest and smallest values in the list. Answer
    
4. (Array, case, sorting, stepper) Write a program which inputs some strings (such as names) and outputs them in the same sequence, in reverse and in ascending order. Use a menu to allow the user to choose the option required. Answer and Sorting methods
    
5. (Array, concatenation) Write a program which accepts an integer from the user and outputs the equivalent in Roman numerals. Your program should allow input of numbers up to 3,999. Answer
   
   
6. Write a program that plays noughts and crosses with the user. The program should allow the user to choose who goes first and then play a game with the user. The program should check after each turn whether there is a winning position. The program should indicate the winner and whether a game was drawn.
    
7. (function) Write a program that calculates the values of m ^ n mod p for n = 1, 2, 4, 8, 16... Store the results in an array. e.g. 18 ^ 1 mod 55, 18^2 mod 55, 18^4 mod 55, 18^8 mod 55. Hence, using the previous program about sums of powers of 2, find a way to calculate e.g. 18^7 mod 55, which is 18^1 mod 55 x 18^2 mod 55 x 18^4 mod 55.