# AFK - Editorial

Practice

Author: Misha Chorniy

Tester: Lewin Gan

Easy

None

## PROBLEM:

You are given three integers A,B and C. You need to find the minimum no. of operations required to make the sequence A,B,C an arithmetic progression. In one operation you can choose one of the numbers A,B,C and either add 1 to it or subtract -1 from it.

## EXPLANATION:

For A,B,C to be in arithmetic progression, they must satisfy 2B = A+C. We need to make both side of the expression equal. Observe that in right hand side, you need to do the same type of operation on A,C. You canâ€™t add 1 on A and subtract -1 from C because it will only increase the number of operations. Observe that left hand side of the expression can be increased by 2 or reduced by 2 in one operation. Hence, in order to minimize the number of operation we must first operate on left hand side and try to make the equation as balance as possible.

The only case in which we can not make the equation balance by operating on left hand side is when right hand side is odd. In this case we can either add 1 or subtract 1 from right hand side and try to find the minimum operation which results from both the cases. A pseudo-code to illustrate this:

``````def g(B,sum):
return abs(B-sum/2)

def f(A,B,C):
if (A+C)%2 != 0:
return min(g(B,A+C-1),g(B,A+C+1))
else:
return g(B,A+C)
``````

Function g(B,sum) here tries to find minimum number of operation required to balance the expression 2.B = sum, where changes can only be done in left hand side. Say, you operate on B by x here, then 2.(B+x) = sum. Now, x can be computed as sum/2-B and the number of operations will be abs(B-sum/2).

## Time Complexity:

O(1) per test case.

## AUTHORâ€™S AND TESTERâ€™S SOLUTIONS

Setterâ€™s solution

Testerâ€™s solution

3 Likes

Video solution can be found here: https://youtu.be/B_PcaHnqxn8?t=7m14s

2 Likes

Can anyone please tell why my code is giving WA?
https://code.hackerearth.com/121a4em

1 Like

Cannot open your code. Alternatively share using ideone.

1
-51 -23 -10

Thanks man

Still getting WA for some other case

Btw instead of floor((float)(a+c)/2) you can simply write (a+c)/2 both will give same result.

I am gettting WA. Can anyone help? https://ideone.com/TKvPMi

1

No, if we have (-61)/2 â€¦ here floor will give answer -31 and normal division will give -30

1 Like

Also Iâ€™ve used double in place of float, still the error persists.Can you identify some other test case will will fail here

Yes, @jatin_12345 you are right.

@jatin_12345 If you can deal with +ve, -ve separately Then It might be good. Because converting to float and double results in round off. This might be case for failing at large input.

Test case found
1
0 -1 -5