Comp 1572, Winter 2002
Pencil-and-Paper Assignment 2
Assigned Friday, January 11, 2002
Due Friday, January 18, 2002 (At the beginning of class)

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Solutions
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1.  Problem 4.8 from Deitel and Deitel:
    Write C++ statements to accomplish each of the following:
    a) Display the value of the seventh element of character array f
       ANS: cout << f[6] << endl;
    b) Input a value into element 4 of floating-point array b.
       ANS: The question is ambiguous; do they mean the element numbered 4
       or do they mean the fourth element?  If they meant the former, then
       cin >> b[4];  
       otherwise
       cin >> b[4];
    c) Initialize each of the 5 elements of single-subscripted integer
       array g to 8.
       ANS: int g[5] = {8,8,8,8,8};
       or
          for (int j = 0; j < 5; j++)
              g[j] = 8; 
    d) Total and print the elements of floating-point array c of 100 elements.
       ANS:
           for (int k = 0; k < 100; k++) {
               total += c[k]  // assume total is declared and initialized to 0
               cout << c[k] << endl;
           }
           cout << "Total is " << total;
    e) Copy array a into the first portion of array b. Assume
       double a[ 11 ], b[ 34 ];
       ANS: for (int i = 0; i <= 10; i++)
                b[i] = a[i];
    f) Determine and print the smallest and largest values contained in
       99-element floating-point array w.
       ANS:
           // assume all variables declared and initialized
           // in particular, initialize smallest to w[0]
           for (int j = 0; j < 99; j++) {
             if (w[j] < smallest)
                 smallest = w[j];
             if (w[j] > largest)
                 largest = w[j];
           }
           cout << "Largest value is " << largest << endl;
           cout << "Smallest value is " << smallest << endl;

2.  Problem 4.13(a)-(c) from Deitel and Deitel:
    Find the error(s) in each of the following statements:
    a) Assume that: char str[ 5 ];
       cin >> str; // User types hello
       ANS: We need a slot at the end of the array for the null character,
       so we need 6 slots - not enough space in the variables str
    b) Assume that: int a[ 3 ];
       cout << a[ 1 ] << " " << a[ 2 ] << " " << a[ 3 ] << endl;
       ANS: If they meant to print the three numbers in the array,
       then they should have used a[0], a[1], a[2] - array subscripts
       begin at 0. 
    c) double f[ 3 ] = { 1.1, 10.01, 100.001, 1000.0001 };
       ANS: Too many initializers - at most 3 if they've declared f[3]

3.  Problem 3.31 from Deitel and Deitel:
    Write a function that takes an integer value and returns the number
    with its digits reversed. For example, given the number 7631,
    the function should return 1367.
    ANS:  This solution assumes that the integers is positive
    int reverse_digits(int num)
    {
        int ans(0);
        while (num > 0) {
            ans = ans*10+num%10;
            num /= 10;
        }
        return(ans);
    }

4.  Write a function that takes as input an array of floats and the length
    of the array and returns the average (arithmetic mean) of the numbers
    in the array.  Use this function to write a program that
    inputs 5 numbers from the user, then prints them out on one line,
    and prints their average on the next line.
    ANS:
    #include <iostream>
    using namespace std;

    float array_average(float [], int);

    int main()
    {
        float a[5];  // store input from the user here

        // input 5 floating point numbers from user
        for (int i=0; i < 5; i++) {
            cout << "Please enter a number: ";
            cin >> a[i];
        }
        // calculate average of 5 numbers and display it
        cout << array_average(a, 5);
    }

    // Calculate the average of the elements of b
    // len gives the number of numbers in the array
    float array_average(float b[], int len)
    {
        float total(0);
        for (int i=0; i < len; i++)
             total += b[i];
        return total/len;
    }

5.  Write a function that takes an array of integers and the length
    of the array as parameters, then modifies the array by getting
    rid of the first element (the other numbers will have to shift
    forwards).
    ANS:
    void shift_array(int arr[], int len)
    {
        for (int i = 0; i < len-1; i++)
            arr[i] = arr[i+1];
    }
 
6.  Problem 3.40 from Deitel and Deitel:
    Write a recursive function power( base, exponent ) that, when invoked,
    returns the value of base^exponent.  For example,
    power( 3, 4 ) = 3 * 3 * 3 * 3. Assume that exponent is an integer
    greater than or equal to 1. Hint: The recursion step would use the
    relationship base^exponent = base x base^(exponent - 1)
    and the terminating condition occurs when exponent is equal to 1
    because base^1 = base.
    ANS: Assume that exp is a positive integer, notice that base can be negative
    int integer_power(int base, int exp)
    {
        if (exp==1) return base;
        else return base*integer_power(base, exp-1);
    }

7.  A palindrome is a string that is spelled the same forward and backward 
    (e.g., "mom" and "racecar").  Its recursive structure is as follows: 
    Let c be a single character, and w be a string.
     -- Basis: string cc is a palindrome.
               a string of a single character c is a palindrome.
     -- Recursive step: if string w is a palindrome, then cwc is a palindrome.

    Given the function prototype below, write a recursive function isPalindrome
    that returns true if a string is a palindrome.

    bool isPalindrome(string w);
    ANS:
    bool isPalindrome(string w)
    {
        
        if (w.length() == 0 || w.length()==1)   // if it's empty or 1 char long
            return true;                        // it's a palindrome
        else if (w.at(0) != w.at(w.length()-1)) // if first and last don't match
            return false;                       // it's not a palindrome
        // Now first and last are the same, so strip them off the string
        // and check that what remains is a palindrome:
        else return isPalindrome(w.substr(1, w.length()-2));
    }