Write a c program to find max of 2 numbers

help
,
1

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
2

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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3

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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4

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. :slight_smile:

3 Likes
5

@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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6

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

7

Thanks, it helped me to understand the concept.!

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8

can anyone tell me s for what? I can not understand. is it third number of three numbers? or it means any constant value? please explain

9

abs() is a function

10

#include<studio.h>
int main()
{
int a,b;
printf(“Enter two no.”);
scanf("%d %d",&a,&b);
if(a>b)
printf(“greater is %d”,a);
else
printf(“greater is %d”,b);
return 0;
}

1 Like
11

By considering cases a>b

and a≤b, it’s easy to see that

|a−b|=max(a,b)−min(a,b),(note:|a−b|=|b−a|)

and

a+b=max(a,b)+min(a,b).
now put value of min(a,b) from above