 # GVR - Editorial

Practice

Author: arnie8991
Tester: horsbug98
Editorialist: arnie8991

EASY

# PREREQUISITES:

Rabin Miller primalty test

# EXPLANATION:

The best approach to solve this problem quickly is to use the rabin miller primalty test to check which numbers are prime and then keep the count.
You can read more about the Rabin Miller algorithm for primalty check and other similar algorithms from here.
We have to individually count how many primes are there in the first half and the second half of the array and then decide whether the conditions are met or not.

# SOLUTIONS:

Setter's Solution
``````def check_composite(n, a, d, s):
x = pow(a, d, n)
if x==1 or x==n-1:
return False
for r in range(1, s):
x = x * x % n
if x==n-1:
return False
return True

def miller_rabin(n):
if n<2:
return 0
r = 0
d = n-1
while((d&1)==0):
d >>=1
r += 1
base = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
for a in base:
if n==a:
return 1
if check_composite(n, a, d, r):
return 0
return 1

n = int(input())
input_array = [int(x) for x in input().split()]

first_prime = -2
last_prime = -2

leftCount = 0
rightCount = 0

for i in range(n//2):
if (miller_rabin(input_array[i]) == 1):
if first_prime == -2:
first_prime = input_array[i]
leftCount+=1

for i in range(n//2,n):
if (miller_rabin(input_array[i]) == 1):
last_prime = input_array[i]
rightCount+=1

if (leftCount == rightCount and first_prime>last_prime):
print('PERFECT')
else:
print('IMPERFECT')
``````
2 Likes

Can someone please explain which primalty test should we used…
Correct me if I’m wrong that is for finding primes in ranges we used drive but for individual no we use Rabin…

Why this solution got accepted?
https://www.codechef.com/viewsolution/27644424

According to constraints 1<=a[i]<=10^14, then how n*sqrt(a[i]) solution passes ?

@codeguptaji the test cases for this was weak(My bad). @akshay1_2 the highest prime in the test cases was somewhere around 10^12… so a root N solution also works for this. Again, sorry for the weak test cases…The original intention was for the question to pass only miller rabin solutions.