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```/*
Author: Joseph Lee
Date: 05/15/23
*/

#include <iostream>

using namespace std;

cout << "1. Output the median\n";
cout << "2. Get the next permutation\n";
cout << "3. Sort in descending order\n";
cout << "4. Simplify the numbers\n";
cout << "Enter your choice (1-4), Q to quit: ";
cin >> times;
if (times == 'q' || times == 'Q'){
}
}

int median(int a, int b, int c){
int value;
//the following comments will show what the order of the value of the integers would be in order to calculate the median
if (b < a && a < c){ //b a c
value = a;
}
if (c < a && a < b){ // c a b
value = a;
}
if (a < b && b < c){ //a b c
value = b;
}
if (c < b && b < a){ // c b a
value =b;
}
if (a < c && c < b){ // a c b
value = c;
}
if (b < c && c < a){ // b c a
value = c;
}
if (a == b || b == c) { // if there are duplictes, then the duplicate value will always be the median
value = b;
}
if (a == c) { //if there are duplicates, then the duplicate value will always be the median
value = c;
}

return value;
}

void myPermutation(int& a, int& b, int& c){
int x, y, z; // create integers for the placeholders for the integer's values
x = a; // x now holds a's value
y = b; // y now holds b's value
z = c; // z now holds c's value
//now we will "reorder" (basically re-value) the integers in the following way
c = y;
a = z;
b = x;

cout << "After one permutation: " << a << " " << b << " " << c << endl << endl;
}

void mySort(int& a, int& b, int& c){
cout << "After sorting: ";
if (b < a && a < c){ //b a c
cout << c << " " << a << " " << b << endl;
}
if (c < a && a < b){ // c a b
cout << b << " " << a << " " << c << endl;
}
if (a < b && b < c){ //a b c
cout << c << " " << b << " " << a << endl;
}
if (c < b && b < a){ // c b a
cout << a << " " << b << " " << c << endl;
}
if (a < c && c < b){ // a c b
cout << b << " " << c << " " << a << endl;
}
if (b < c && c < a){ // b c a
cout << a << " " << c << " " << b << endl;
}
if (b == a && a < c){ //  b a c (a and b are the same value)
cout << c << " " << a << " " << b << endl;
}
if (b == a && c < a){ // b a c
cout << a << " " << b << " " << c << endl;
}
if (a == c && c < b){ // a c b
cout << b << " " << a << " " << c << endl;
}
if (a == c && b < c){ // b a c
cout << c << " " << a << " " << b << endl;
}
if (b == c && c < a){ // b c a
cout << a << " " << b << " " << c << endl;
}
if (b == c && a < c){ // a b c
cout << c << " " << b << " " << a << endl;
}

}

void mySimplify(int& a, int& b, int& c){
for (int i = 2; a%i == 0 && b%i == 0 && c%i == 0; i++){
a /= i;
b /= i;
c /= i;
cout << "After one permutation: " << a << " " << b << " " << c << endl << endl;
}
}

int main() {
int integer1, integer2, integer3;
bool validInput = false;
do
{
cout << "Enter your three positive integers: ";
cin >> integer1 >> integer2 >> integer3;
if (cin.fail ()) {
cin.clear(); // Clear the fail state of cin
cin.ignore(9999, '\n');
cout << "Error: non positive integer recieved." << endl << endl;
}
else if (integer1 < 0 || integer2 < 0 || integer3 < 0) {
cout << "Error: non positive integer recieved." << endl << endl;
}
else {
validInput = true;
}
}
while (!validInput);

int input, number;
number = 0;
while (validInput){
number++;
cout << "================== MENU " << number << " ==================\n";
if (input == 1) {
cout << "The median among the three is: " << median (integer1, integer2, integer3) << endl << endl;
}
if (input == 2) {
myPermutation(integer1, integer2, integer3);
}
if (input == 3) {
mySort(integer1, integer2, integer3);
}
if (input == 4){
mySimplify(integer1, integer2, integer3);
}
if (input == 'q' || input == 'Q') { //CHECK ON THIS
break;
}
if (cin.fail ()) {
cin.clear(); // Clear the fail state of cin
cin.ignore(9999, '\n');
}
}

return 0;
}
```