Class Examples
				   7/18/02

Example #1
----------
#include <iostream.h>

int f(int,int);
void g(int,int);

void main() {

  int i = 10;
  int j = 20;

  i = f(j,i);
  g(i,j);  

  cout << "I = " << i << endl;
  cout << "J = " << j << endl;
}

int f(int i,int j) {
  j = i - j;
  i = j - i;
  cout << "I = " << i << endl;
  cout << "J = " << j << endl;
  return i-j;
}

void g(int i,int j) {
  
  i = i + j;
  j = j - i;
  cout << "I = " << i << endl;
  cout << "J = " << j << endl;

}

Example #2
----------

#include <iostream.h>

const int SIZE = 4;
const double TIP_RATE = 0.15;

int Power(int, int);
int Triangle_Number(int);
int Fibonacci(int);
void Tip_Chart(int, int);
void Print_Triangle(int,char);
void Print_Line(int, char);
bool Search(int[], int, int, int);
int Num_Inc_Subseq(int[], int, int, int, int);

// Precondition: exponent is a non-negative integer.
// Postcondition: Function returns the value base^exponent.
int Power(int base, int exponent) {
  if (exponent == 0) 
    return 1;
  else
    return base*Power(base,exponent-1);
}

// Precondition: n is a non-negative integer.
// Postcondition: Function returns the nth triangle number.
int Triangle_Number(int n) {
  if (n == 0)
    return 0;
  else
    return n + Triangle_Number(n-1);
}

// Precondition: n is a non-negative integer.
// Postcondition: Function returns the nth Fibonacci number.
int Fibonacci(int n) {
  if (n<2)
    return n;
  else
    return Fibonacci(n-1)+Fibonacci(n-2);
}

// Precondition: Both first_val and last_val are positive.
// Postcondition: The function will print out a tip chart at 15% for each
//                dollar increment from the first_val to the last_val.
void Tip_Chart(int first_val, int last_val) {
  if (!(first_val > last_val)) {
    cout << "On a meal of $" << (double)first_val << " you should tip $";
    cout << first_val*TIP_RATE << endl;
    Tip_Chart(first_val+1, last_val);
  }
}

// Precondition: n is a non-negative integer.
// Postcondition: Will print a line of the character c, exactly n times,
//                followed by a new line character.
void Print_Line(int n, char c) {

  for (int i=0;i<n;i++)
    cout << c;
  cout << endl;
}

// Precondition: n is a non-negative integer.
// Postcondition: Will print a triangle out with the character c, with n lines.
void Print_Triangle(int n, char c) {
  
  if (n > 0) {
    Print_Triangle(n-1,c);
    Print_Line(n,c);
  }
}

// Precondition: low and high must be valid indices to the array list.
// Postcondition: The function will return true if value is stored in one
//                of the indices in the array, in between low and high,
//                inclusive.
bool Search(int list[],int low, int high, int value) {

  int midindex;

  // Check trivial case & assign the next "guess" for the search.
  if (high < low)
    return false;
  else 
    midindex = (high+low)/2;
    
  // Either return true if value is found, or narrow search accordingly.
  if (value == list[midindex])
    return true;
  else if (value > list[midindex])
    return Search(list, midindex+1, high, value);
  else 
    return Search(list, low, midindex-1, value);
  
}

// Precondition: low and high are valid indices to the array list, and
//               len must be a positive integer less than or equal to the
//               size of the array list.
// Postcondition: Returns the number of non-decreasing sequences of numbers
//                of length len in the array list in between the indices
//                of low and high, inclusive.
int Num_Inc_Subseq(int list[], int cur_val, int low, int high, int len) {

  // First take care of base cases.
  if (len == 0)
    return 1;
  else if (high < low)
    return 0;
  else {
    // Check to see if current value can create new sequences.
    int bonus = 0;
    if (list[low]>= cur_val) 
      bonus = Num_Inc_Subseq(list, list[low], low+1, high, len-1);
      
    // Add these to sequences found in the rest of the array.
    return Num_Inc_Subseq(list, cur_val, low+1, high, len) + bonus;
  }
}