# Write a c program to find max of 2 numbers

write a c program to find max of two number and number taken from user
you can use only operators +,-,abs,division and number should be integer

1 Like

it’s easy. the max between A and B can be considered as the value
located at |A-B|/2 distance from the middle (A+B)/2, to the right.
thus, the formula is : (A+B+abs(A-B))/2. you only use +, -, abs and
division. it only works for non-negative integers, obviously.

``````int max(int A, int B)
{
return (A + B + abs(A - B)) / 2;
}
``````
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the formula is perfect…!!
But can you just explain it in another simpler way…I am sort of not getting how that formula was derived.

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Let B be the max.

```                            |A-B|/2
|
|-----------|
v           v
----------- A ---------------------- B --------------
^
|
(A+B)/2
```

As you can see, the formula is reversible, meaning if A is the max, the expression remains :

```* (A+B) / 2 = (B+A) / 2
* |A-B| / 2 = |B-A| / 2
```

Thus, max(A, B) = middle_position + gap_between_both / 2
= (A+B) / 2 + |A-B| / 2
= (A + B + abs(A - B)) / 2

Hope this helps.

2 Likes

@cool_techie It is pretty simple to understand. It follows from the definition of abs.

``````if A=B
abs(A-B) = 0
A+B+abs(A-B) = 2A
if A>B
abs(A-B) = A-B
A+B+abs(A-B) = 2A
if B>A
abs(A-B) = B-A
A+B+abs(A-B) = 2B
``````

This is not dependent on the sign of the numbers as @cyberax pointed out. But yes it has troubles with overflow and underflow.

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“This is not dependent on the sign of the numbers as @cyberax pointed out.”
true ! my bad. i was tired

Thanks, it helped me to understand the concept.!

1 Like
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