Cannot understand comma expression - c++

Question

#include <iostream>
using namespace std;
int main()
{
int a, b, c, max;
cout<<"a="; cin>>a;
cout<<"b="; cin>>b;
cout<<"c="; cin>>c;
a>b?(max=a, a=b, b=max):a;
b>c?(max=b, b=c, c=max):a;
a>b?(max=a, a=b, b=max):a;
cout<<a<<" "<<b<<" "<<c;
}
This is a code where you can input 3 random numbers and it will put them in order. I don't understand this part, however:
a>b?(max=a, a=b, b=max):a;
b>c?(max=b, b=c, c=max):a;
a>b?(max=a, a=b, b=max):a;
How does it work, and why?
Let's say a = 6, b = 54, and c = 12.
a>b?(max=a, a=b, b=max):a; <-- sets max to 6, then a to 54, then 54=max. then compares 6 to 54 which is false and writes a (6) as the first number?
b>c?(max=b, b=c, c=max):a; <-- sets max to 54, b=12, 12=max. then compares 54 to 12 which is true in our case and writes c=12 as the second number?
a>b?(max=a, a=b, b=max):a; <-- sets max to 6, a=54, 54=max. then compares 6 to 54 which is false and writes 6 again, wtf?
The program itself works correctly. I just don't understand how the algorithm works.

Answer 1

This:
cond ? A : B
is roughly equivalent to this:
if (cond) {
A;
} else {
B;
}
This:
(X, Y, Z)
is roughly equivalent to this:
X;
Y;
Z;
i.e. each expression is evaluated completely, in turn.
Using these two rules, you should be able to trace the execution of your code. However, that code is grotesque, and should never have been written like that. So my recommendation is to just ignore it, and write the algorithm properly.

Answer 2

All the code's doing is abusing the comma operator's ability to do multiple things in one to swap values in one statement.
The first line finds the max of the first two numbers. The second finds the max of that and the third, so that it's now found the largest of the three. The third line sorts the other two in order afterwards.
It's about the same as this:
if (a > b)
swap (a, b); //b is max(a,b)
if (b > c)
swap (b, c); //c is max(max(a,b),c), which is largest
if (a > b)
swap (a, b); //b is max (a, b), so numbers are in order smallest to largest

Answer 3

a>b?(max=a, a=b, b=max):a
The final ":a" really doesn't do anything, it could just as easily have been ":0". It is essentially the statement that is to be carried out if the "a>b" is false. but since the a isn't assigned to anything, it doesn't do anything. so in this case
if(a > b){
max = a;
a = b;
b = max;
}
It uses the max variable to swap a and b; The SAME algorithm is used for the following two lines. So essentially
if a > b then swap them
now if b (which could hold a) > c then swap them
now if a (which could hold the older b) > b(which could hold the oldest c) then swap

Answer 4

Well, essentially I this is what happens.
a>b?(max=a, a=b, b=max):a;
the first section is just a normal comparison in the fashion of a tertiary if statement, so basically it checks if a>b, then ? is just equal to the first brackets set, so if its true, it evaluates the first section otherwise then the code after : is just like else and that is is evaluated.. The (max=a, a=b, b=max) basically evaluates each item in turn, so first max is set to a, then a = b and finally b = max; Same for the other two lines.
You can read more here: http://www.cplusplus.com/doc/tutorial/operators/
Hope this helped.