Write a c ++ program . Q1. Modified Programming Exercise 6.37 (page 260) (20 marks)

( Financial: credit card number validation, loop, char to digit conversion, digits extraction from a number )

Credit card numbers follow certain patters. A credit card must have between 13 to 16 digits. The number must starts with the following (prefix):

4 for visa cards

5 for MasterCard cards

37 for American Express cards

6 for Discover cards

In 195 4, Hans Luhn of IBM proposed an algorithm (known as Luhn check or the Mod 10 check ) for validating credit card numbers. For illustration, given a card number: 4388576018402626

a) Double every second digit (highlighted below with green shade) from right to left. If doubling of a digit results in a two - digit number, add the two digits to get a single digit number.

4

3

8

8

5

7

6

0

1

8

4

0

2

6

2

6

2 x 2 = 4

2 x 2 = 4

4 x 2 = 8

1 x 2 = 2

6 x 2 = 12 (1 + 2 = 3)

5 x 2 = 10 (1 + 0 = 1)

8 x 2 = 16 (1 + 6 = 7)

4 X 2 = 8

b) Now add all single - digit numbers from Step a).

4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37

c) Add all digits in the odd places from right to left in the card number.

6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38

d) Sum the results from Step b) and Step c).

37 + 38 = 75

e) If the result from Step d) is divisible by 10, the card number is valid; otherwise, it is invalid. For example, the above number is inva lid. You may check your own credit card numbers to verify that they are valid.

Write a program that prompts the user to enter a credit card number as a string. Display whether the number is valid. Design your program to use the following functions:

// Return true if the card number is valid

bool isValid( const string& cardNumber )

// Get the result from Step b)

int sumOfDoubleEvenPlace( const string& cardNumber )

// Return this number if it is a single digit, otherwise

// return the sum of two digits

int getDigit( int number )

// Return sum of odd - place digit in the card number

int sumOfOddPlace( const string& cardNumber )

// Return true if substr is the p refix for card number

bool startWith( const string& cardNumber, const string& substr )