PROBLEM LINK:

Practice
Contest

Author:Roman Rubanenko
Tester:Sergey Kulik
Editorialist:Lalit Kundu

DIFFICULTY:

SIMPLE

PREREQUISITES:

AD-HOC

PROBLEM:

K times, following operation is done on a array A₁,A₂...A_N:
Choose maximum from array A, say MAX. Do A_i=MAX-A_i, for every 1 ≤ i ≤ N.
Print the final array.
0 ≤ K ≤ 10⁹
1 ≤ N ≤ 10⁵

QUICK EXPLANATION:

There will a cycle of size not greater than 2. After that we can easily simulate the operations.

EXPLANATION:

We can prove that there wouldn't be cycle of size greater than 2 (proof is left as an exercise to reader). Means, that states of array will repeat after a maximum of 2 operations.

Pseudo code:

if k==0:    
    print Array A    
    return

if k%2==1: k=1    
else: k=2

for i=1 to k:   
    mx=A[0]    
    for j=1 to N-1:    
        mx=max(mx,A[j])   
    for j=0 to N-1:    
        A[j]=mx-A[j]   
print array A.

Complexity: O(N)

AUTHOR'S AND TESTER'S SOLUTIONS:

Author's solution
Setter's solution