Some test cases wrong

#1
#2

as a is very large b is also very large
hence a^b is very very large so you have to take mod at each step
otherwise data overflow
and after that no use of taking mod

use this code

i hope this helps
if yes hit a like and don’t forgot to mark doubt as resolved :grinning:
if you have more doubts regarding this feel free to ask

#3

this question is before the topic of recursion so i will come back to this quesion later
is it right

#4

No!
There is no need to do it after recusion (yes we can also do it by recursion)
But one can use while loop to calculate the modular exponentiation , I have done that!!

#5

if you want to do it iterative
yes you can obviously do that
using this

#include<bits/stdc++.h>
using namespace std;
#define int long long int
int ModularExponentiationIter(int a,int b,int c){
	a=a%c;
	int ans=1;
	for(int i=1;i<=b;i++){
		ans=(ans*a)%c;
	}
	return ans;
}
int32_t main(){
	// freopen("input.txt","r",stdin);
	int a,b,c;
	cin>>a>>b>>c;
	cout<<ModularExponentiationIter(a,b,c);
	return 0;
}

but the recursive one is more optimised

i hope this helps
if yes hit a like and don’t forgot to mark doubt as resolved :grinning:
if you have more doubts regarding this feel free to ask

#6

I was not talking of this variant, it is O(n)
But following is O(logn)

int power( int x, unsigned int y, int p)

{

int res = 1; // Initialize result

x = x % p; // Update x if it is more than or

// equal to p

if (x == 0) return 0; // In case x is divisible by p;

while (y > 0)

{

// If y is odd, multiply x with result

if (y & 1)

res = (res*x) % p;

// y must be even now

y = y>>1; // y = y/2

x = (x*x) % p;

}

return res;

}

#7

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