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binary_exponentiation.c
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binary_exponentiation.c
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#include <stdio.h>
// returns base * base * base ... (exponent times) modulo modulus
// (base ^ exponent)%modulus recursively
long long recursive_exponentiation(long long base, long long exponent, long long modulus){
// a number power 0 is 1
if (exponent == 0){
return 1;
}
long long result = recursive_exponentiation(base, exponent / 2, modulus);
if (exponent % 2){ // if the exponent is not divisible by 2
result = (result * result * base) % modulus;
} else {
result = (result * result) % modulus;
}
return result;
}
// returns base * base * base ... (exponent times) modulo modulus
// (base ^ exponent)%modulus iteratively
long long iterative_exponentiation(long long base, long long exponent, long long modulus){
long long result = 1;
while (exponent > 0){
if (exponent & 1){ // if exponent not divisible by 2
result = (result * base) % modulus;
}
base = (base * base) % modulus;
exponent >>= 1;
}
return result;
}
int main(){
printf("%lld\n", recursive_exponentiation(2, 6, __INT_MAX__));
printf("%lld\n", recursive_exponentiation(5, 4, __INT_MAX__));
}