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1. A palindrome is a word that reads the same forwards and backwards, likelevel” orsees ordeified. Write a recursive function that checks whether a single word supplied by the user is a palindrome. Dont worry about upper and lowercase issues. Here is a prototype:

bool is_palindrome(unsigned int a, unsigned int b, const string& s)

You may want to #include <string>; this library is useful because it contains a function length(), which tells you how long the string is.

Hint: there are two variants of the base case: consider the case for tot” or toot, both of which are palindromes. Do not use any local variables.

EXAMPLES:

ABCDEFGFEDCBA” is a palindrome ABCDEFGGFEDCBA” is a palindrome ABCDEFGEDCBA is not a palindrome

2. Write a recursive function that takes an integer and prints it out as a binary one. Here is the prototype:

void binary_print(ostream& outs, unsigned int n);

The function prints the value of n as a BINARY number to the ostream outs. If n is zero, then a single zero is printed; otherwise no leading zeros are printed in the output. The \ncharacter is NOT printed at the end of the output. Do not use any local variables. EXAMPLES:

n=0 Output:0 n=4 Output:100 n=27 Output:11011

3. Examine this fractal pattern of asterisks and blanks, and write a recursive method that can generate patterns such as this:

*

* *

*

* * * *

*

* *

*

* * * * * * * *

*

* *

*

* * * *

*

* *

*

With recursive thinking, the method needs only seven or eight lines of code (including

two recursive calls). Your method should look like this:

void pattern(ostream& outs, int n, int i)

// Precondition: n is a power of 2 greater than zero.

// Postcondition: A pattern based on the above example has been

// printed. The longest line of the pattern has

// n stars beginning in column i of the output. For example,

// the above pattern is produced by the call pattern(8, 0).

Hints: You do not need to check the precondition. Think about how the pattern is a fractal. Can you find two smaller versions of the pattern within the large pattern? Here is some code that may be useful within your method:

// A loop to print exactly i spaces:

for (k = 0; k < i; k++) outs << ;

// A loop to print n asterisks:

for (k = 0; k < n; k++) outs << *;