The best method of sorting 3 values using if-statement

Question

I've found an exercise in "Programming principles and practice by B. Stroustrup's" that asks to write a program to sort 3 integer values using if-else statement.

• I've tried a lot and found myself the swapping method although later on I've found it already done on the internet:

  int x = 3, y = 5, z = 1;
  if(y < x)
     swap(x, y);
  if(y < z)
     swap(y, z);
  if(y < x)
      swap(x, y);
  

• Although it works just fine but that simple line function-call (swap(A, B)) has a significant cost behind the curtain: A temporary and Copy:

   if(y < x){
      auto tmp = x;
      x = y;
      y = tmp;
   }
  

As you can see it is called at least 2 times in the worst cases like 5 2 7.

• I've tried a lot and written down all possible permutations until I've discovered this solution:

1- Declare three integer values, let's say min, mid, max.

2- Set min to value of x, max to y's and mid to z.

3- mid (z) initial value has 6 possibilities: 2 correct and 4 wrong:

2 7 5 -> mid = 5 correct
7 2 5 -> mid = 5 correct
2 5 7 -> mid = 7 incorrect -> mid has max value
5 2 7 -> mid = 7 incorrect -> mid has max value
5 7 2 -> mid = 2 incorrect -> mid has min value
7 5 2 -> mid = 2 incorrect -> mid has min value

• So The first thing we do is to check whether min and max of x and y are correct otherwise swap min and max:

  if(y < x){
      min = y;
      max = x;
  }
  

• Now we have correct min and max.

• Check whether z is (previous value of mid) greater than max and if so we swap max and mid (z):

   if(max < z){
       mid = max; // update mid to the previous value of max
       max = z; // update max to the previous value of mid (z)
   }
  

• Check whether z (previous value of mid) is less than min and if so we swap min and mid (z):

  if(z < min){
      mid = min;
      min = z;
  }
  

• Now everything works fine. Here is the full example:

    int main(){
  
        int x = 2, y = 5, z = 7;
        int min = x, max = y, mid = z; 
  
        if(y < x){
            min = y;
            max = x;
        }
        if(max < z){ 
            mid = max;
            max = z;
        }
        if(z < min){
            mid = min;
            min = z;
        }
  
        std::cout << min << ", " << mid << ", " << max << '\n';
  
    }
  

• Is my analysis rational? Is my program efficient? Can we depend on it as the best implementation of sorting three values? Any Tip, comment is highly appreciated.

• Input:

  2 5 7
  2 7 5
  5 2 7
  5 7 2
  7 2 5
  7 5 2
  

• Output:

  2, 5, 7
  2, 5, 7
  2, 5, 7
  2, 5, 7   
  2, 5, 7