project05
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// file project05.cpp
// date 09/17/2007
// author AOU

#include <iostream>
#include <ctime>
using namespace std;

/*
Problem:
  Write a function that will find the highest two
  values out of the three values given

  given: x, y, z
  expected: a, b such that a and b are top two values of x, y, z
      and a>=b


Examples:
  Input (3,1,2) => (3,2)
  Input (1,1,2) => (2,1)
  Input (5,5,5) => (5,5)

Algorithm:
  input x,y,z 
  output a,b

  option1: use any sort to put x,y,z in increasing order, a=z,b=y
    if x>y then swap(x,y)
    if x>z then swap(x,z)
    if y>z then swap(y,z)
    a=z
    b=y

  option2: compare values 9x,y,z) and calculate a,b
    if x>=y and x>=z then 
        a=x
        if y>=z then b=y else b=z
      else if y>=x and y>=z then
        a=y
        if x>=z then b=x else b=z
      else 
        a=z
        if x>=y then b=x else b=y
      end if

  option3: use any sort to put x,y,z in increasing order, a=z,b=y
    do the following 2 times
      if x>y then swap(x,y)
      if y>z then swap(y,z)
      end do

    a=z
    b=y

*/

/////////////////////////////////////////////////////
//Assignment #1 9/17/2007 due 9/21/2007
//Prepare a 1-2 page summary of chapter 3
/////////////////////////////////////////////////////


/////////////////////////////////////////////////////
//Assignment #2 9/17/2007 due 9/24/2007
//Implement the checkMax2 function
/////////////////////////////////////////////////////

/*
Problem:
Develop a function that will make sure that a and b 
are the top two values from x,y,z and a>=b.

bool checkMax2(int x, int y, int z, int a, int b)

make sure [a, b] is a subset of [x, y, z]
make sure a >= b
make sure a is max of [x,y,z]
make sure b is max of [x,y,z]-[a]

Examples:
  (1,2,3,3,2) => true
  (1,2,3,3,1) => false
  (1,2,3,3,3) => false
  (1,2,3,4,3) => false
  (1,2,3,1,3) => false


Algorithm:
  make sure [a, b] is a subset of [x, y, z]:
    if a<>x and a<>y and a<>z then return false
    if b<>x and b<>y and b<>z then return false

  make sure a >= b:
    if b>a then return false
    
  make sure a is max of [x,y,z]:
    if a<x or a<y or a<z then return false

  make sure b is max of [x,y,z]-{v=a}:
    if a=x then swap(x,z)
    if a=y then swap(y,z)
    if b<x or b<y then return false
           
  return true

  end of algorithm
*/


/*
  Notes for the book:
    make sure b is max of [x,y,z]-[a]:

    plan1: put x,y,z in an array array[0:2], 
           delete the value from array[] that matches with a
           make sure b is highest of the remaining values in array[]

    plan2: if a=x then make sure b is highest of [y,z]
           if a=y then make sure b is highest of [x,z]
           if a=z then make sure b is highest of [x,y]

    plan3: if a=x then swap(x,z)
           if a=y then swap(y,z)
           if b<x or b<y then return false
           

*/

void findMax2(int x, int y, int z, int &a, int &b);
void findMax2v2(int x, int y, int z, int &a, int &b);
void findMax2v3(int x, int y, int z, int &a, int &b);
void swap(int &p, int &q);

void main(void)
  {
  cout << time(NULL) << endl;

  srand(time(NULL));

  int x, y, z;
  int v1, v2;

  for (int i=1; i<=100; i++)
    {
    x = rand()%100;
    y = rand()%100;
    z = rand()%100;

    findMax2(x,y,z,v1,v2);
    cout << "(x, y, z)=" << "(" << x << ", " << y << ", " << z << ")\n";
    cout << "  (v1, v2) =" << "(" << v1 << ", " << v2 << ")\n";

    findMax2v2(x,y,z,v1,v2);
    cout << "  (v1, v2) =" << "(" << v1 << ", " << v2 << ")\n";

    findMax2v3(x,y,z,v1,v2);
    cout << "  (v1, v2) =" << "(" << v1 << ", " << v2 << ")\n";
    cout << endl;
    }
  
  }

void findMax2(int x, int y, int z, int &a, int &b)
  // based on option3
  {
  for (int i=1; i<=2; i++)
    {
    if (x>y) swap(x,y);
    if (y>z) swap(y,z);
    }

  a=z;
  b=y;
  }

void swap(int &p, int &q)
  {
  int temp = p;
  p = q;
  q = temp;
  }

void findMax2v2(int x, int y, int z, int &a, int &b)
  {
  if (x>y) swap(x,y);
  if (x>z) swap(x,z);
  if (y>z) swap(y,z);
  a=z;
  b=y;
  }

void findMax2v3(int x, int y, int z, int &a, int &b)
  {
  a=911;
  b=911;
  if ((x>=y) && (x>=z))  
      {
      a=x;
      if (y>=z) b=y; else b=z;
      }
    else if ((y>=x) && (y>=z)) 
      {
      a=y;
      if (x>=z) b=x; else b=z;
      }
    else
      {
      a=z;
      if (x>=y) b=x; else b=y;
      }

  }


/*
bool checkMax2(int x, int y, int z, int a, int b)

make sure [a, b] is a subset of [x, y, z]
make sure a >= b
make sure a is max of [x,y,z]
make sure b is max of [x,y,z]-[a]
*/