# Sort three numbers using only if-statements

Beginner here, trying to make a small program that sorts three numbers from smallest to largest only by using ifs. Any thoughts on how to improve this?

#include <iostream>

using namespace std;
int main ()
{
int num1, num2, num3;
int smallest, middle, biggest;
cin >> num1 >> num2 >> num3;

cout << endl;

if ((num1 < num2) && (num1 < num3))
{
smallest = num1;
if (num2 > num3)
{
biggest = num2;
middle = num3;
}
}
if ((num1 < num2) && (num3 << num1))
{
smallest = num1;
if (num2 < num3)
{
middle = num2;
biggest = num3;
}
}
if ((num1 > num2) && (num3 > num1))
{
middle = num1;
if (num2 < num3)
{
smallest = num2;
biggest = num3;
}
}
if ((num1 < num2) && (num3 < num1))
{
middle = num1;
if (num2 > num3)
{
biggest = num2;
smallest = num3;
}
}
if ((num1 > num2) && (num1 > num3))
{
biggest = num1;
if (num3 > num2)
{
middle = num3;
smallest = num2;
}
}

if ((num1 > num2) && (num1 > num3))
{
biggest = num1;
if (num2 > num3)
{
middle = num2;
smallest = num3;
}
}

cout << smallest << ", " << middle << ", " << biggest << endl;

return 0;
}

• Why the requirement of only using if? You might discover new things by trying other tools too :) – Morwenn May 27 '15 at 9:54
• I still haven't reached that part of the book :) – liquid3 May 27 '15 at 9:58
• If someone is interested in this problem further, a good solution would be to implement a sorting network. They are very efficient for very small N. – IEatBagels Sep 23 '19 at 20:25

I will try to take several things into account but to keep things simple. A few remarks:

• First, it seems that you have a typo here:

if ((num1 < num2) && (num3 << num1))


I think that you meant num3 < num1 instead of num3 << num1 in your second condition.

• As @Josay says, you better write small functions. I would add that you better separate the input/output operations (that you can keep in main) and the sorting function. In my opinion, this would be a good enough signature for the sorting function:

void sort3(int& a, int& b, int& c);


You would give three variables to it and it would sort them in-place so that you end up with $a \le b \le c$.

• Now, let's choose an algorithm. For three values, the easiest is to implement a bubble sort which shouldn't be really slower than other algorithms (when you want to sort more values, it becomes horribly slower though).

void sort3(int& a, int& b, int& c)
{
if (a > b)
{
std::swap(a, b);
}
if (b > c)
{
std::swap(b, c);
}
if (a > b)
{
std::swap(a, b);
}
}


Most sorting algorithms heavily rely on swapping values. The one I just implemented sorts your values with only three comparisons and at most three swaps and is, in my opinion, far simpler to understand than what you had.

Note that there are more efficient algorithms but I deliberately chose to present one that is not that bad while easy to understand.

• This is not a problem in your case, but we can't stress out enough that using namespace std; is often considered bad practice. It is the case when used in a header file, especially in a library header file since it will pollute the global namespace of every file including it. That's not a problem for you since you're probably doing everything in a .cpp file but it's better to keep that in mind.

• You don't need to return 0; at the end of main. If the compiler reaches the end of the main function without having encountered a return statement, it automagically adds a return 0; for you. Note that it only works with main though. Dropping this line is an interesting way to document that your program cannot return error codes and that it will only ever return 0.

• Thanks for your answers, i'm afraid i can't give thumbs up because i need more rep – liquid3 May 27 '15 at 10:50
• why did you test if a > b twice? – Ritchie Shatter May 27 '15 at 12:33
• @RitchieShatter If the values are $3, 2, 1$ the first two swaps will make the values $2, 1, 3$ so you need to swap a and b again. – Morwenn May 27 '15 at 12:37
• @RitchieShatter - don't know if this helps, but if you've studied how bubble sort works, think of this code as a bubble sort with the loops unrolled; the smallest values bubble down from the top. – Pete Becker May 27 '15 at 20:41
• "You don't need to return 0; at the end of main"â€”technically correct, of course, but is it really advisable not to? Nothing good will come of not returning zeroâ€¦a careless port to C (not C++), for example, will cause the exit status to be undefined. – wchargin May 27 '15 at 22:40

• write small functions you can test

• write tests

I did it for you and discovered problems quickly :

#include <iostream>

using namespace std;

void sort(int num1, int num2, int num3, int* smallest, int* middle, int* biggest)
{
if ((num1 < num2) && (num1 < num3))
{
*smallest = num1;
if (num2 > num3)
{
*biggest = num2;
*middle = num3;
}
}
if ((num1 < num2) && (num3 << num1))
{
*smallest = num1;
if (num2 < num3)
{
*middle = num2;
*biggest = num3;
}
}
if ((num1 > num2) && (num3 > num1))
{
*middle = num1;
if (num2 < num3)
{
*smallest = num2;
*biggest = num3;
}
}
if ((num1 < num2) && (num3 < num1))
{
*middle = num1;
if (num2 > num3)
{
*biggest = num2;
*smallest = num3;
}
}
if ((num1 > num2) && (num1 > num3))
{
*biggest = num1;
if (num3 > num2)
{
*middle = num3;
*smallest = num2;
}
}

if ((num1 > num2) && (num1 > num3))
{
*biggest = num1;
if (num2 > num3)
{
*middle = num2;
*smallest = num3;
}
}

}

//==========================================================================
int main ()
{
int num1, num2, num3;
int smallest, middle, biggest;

//cin >> num1 >> num2 >> num3;
//sort(num1, num2, num3, &smallest, &middle, &biggest);
//cout << endl;
//cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 1; num2 = 2; num3 = 3;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 4; num2 = 4; num3 = 4;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 5; num2 = 5; num3 = 6;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 7; num2 = 8; num3 = 7;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 9; num2 = 10; num3 = 10;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 11; num2 = 13; num3 = 12;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 15; num2 = 14; num3 = 16;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 19; num2 = 18; num3 = 17;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 21; num2 = 22; num3 = 20;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

num1 = 25; num2 = 23; num3 = 24;
sort(num1, num2, num3, &smallest, &middle, &biggest);
cout << smallest << ", " << middle << ", " << biggest << endl;

return 0;
}


gives :

1, 2, 3
1, 2, 3
1, 2, 3
7, 2, 3
9, 2, 3
11, 12, 13
14, 15, 16
17, 18, 19
20, 21, 22
23, 24, 25

• Thanks for the answer, the problem is when i type 2 same numbers – liquid3 May 27 '15 at 10:13

Assuming you define min and max (or use std::min, std::max), you can do this:

int low, mid, high;
// Find the minimum of number 1 and the minimum of number 2 and number 3.
low = std::min(num1, std::min(num2, num3));
// Find the maximum of the minimum of number 1 and number 2 and the minimum of number 2 and number 3.
mid = std::max(std::min(num1, num2), std::min(num2, num3));
// Find the maximum of number 1 and the maximum of number 2 and number 3.
high = std::max(num1, std:max(num2, num3));


Which basically moves all of your if-else logic into standard library calls.

By the way, a popular method for switching numbers in place without a temporary integer goes as follows:

x = x ^ y;
y = y ^ x;
x = x ^ y;


Which replaces the need for a temp variable. Try it out and see.

if(a > b) {
a = a ^ b;
b = b ^ a;
a = a ^ b;
}
if(b > c) {
b = b ^ c;
c = c ^ b;
b = b ^ c;
}
if(a > b) {
a = a ^ b;
b = b ^ a;
a = a ^ b;
}


Of course, you could instead use std::swap. However, given all the alternatives, if performance was a non-issue (e.g. absolute clock cycle count was unimportant), I'd impress simply using std::min and std::max.

• I don't think that's a useful "popular method". It's more of a gimmick for a particular kind of puzzle (usually applicable to machine language); it's much clearer and usually more efficient to implement std::swap() using a temporary variable. – Toby Speight Sep 24 '19 at 8:23

Your code compiles, but your program is not exactly small. I like what you are trying to do. When I learn something new, I like to write a program to help showcase it. The problem is you need to bring the correct tools for the job. Analogously You probably could hammer a nail with a screwdriver, but I wouldn't recommend it.

There are multiple ways you could get this code under 10 lines. use of "else" and "else if" may help. however you will make your life considerably easier using logical operators. For example

#define max(x,y) ( x > y ? x : y )


EDIT

The above define is often used but can be dangerous as mentioned below. A better, significantly more safe way of doing this is like this:

#define max(a,b) \
({ typeof (a) _a = (a); \
typeof (b) _b = (b); \
_a > _b ? _a : _b; })


You could also use the c++ methods mentioned below.

you can make a simple preprocessor command that will give you the maximum value.

The logic for that command would read as if x is greater than y the answer is x, otherwise it's y.

The swap command mentioned above would work well to. I highly recommend before limiting yourself to one statement you read a little about c++ operators. Try here.

http://www.cplusplus.com/doc/tutorial/operators/

• You can get into some rather dangerous waters with that max macro if you do things such as max(foo + 1, bar). Code golf is great for people who understand the full set of tricks for the language, but code that is understandable to the coder(or next person) is often something to strive for. Clever code needs you to be more clever to debug it - and if the code is at your edge of cleverness this can cause problems. – user22048 May 27 '15 at 14:06
• Why define a max macro when there is already the safer std::max in the standard library? :( – Morwenn May 27 '15 at 14:07
• Interesting. I wasn't aware of std::max. nor std::swap. I guess I need to look through the std libraries at some point. MichaelT, your point is well taken. However, I still feel that a strong understanding of operators should be an early fundamental for learning c/c++ – mreff555 May 27 '15 at 17:12