Lily bentham Lily bentham - 21 days ago 8
C++ Question

Keeping part of a big number

I have wrote below program to extract the last five digits of n number that is the answer of function below:


n = 1^1 + 2^2 + ... + m^m


where m is given by the user. The program works all right for small number but it will not work for m as big as 100^100.

#include <iostream>
#include <math.h>
using namespace std;

int main()
{
int n;

cin>>n;
intmax_t a[n],num,rem;
a[0]=0;
for (int i=1; i<=n; i++){

a[i] = a[i-1]+pow(i,i);
}

num=a[n];

int b[5];
for (int i = 1; i <=5; i++) {
rem = fmod(num,10);
b[i]=rem;
num = num/10;
}

for (int i = 1; i <=5; i++) {
cout<< b[i];

}
return 0;
}

Answer

"Get last five digits" mean mod 100000. In fact, 100^100 is really small. You don't need to use bignum in this case since (a*b) mod n = ((a mod n) * (b mod n)) mod n.

#include <iostream>
using namespace std;

int getLastDigits(int base, int pow, int numDigit) {
    int divisor = 1;
    for (int i = 0; i < numDigit; i++) 
        divisor *= 10;

    int retVal = 1;
    for (int i = 0; i < pow; i++) {
        retVal *= base;
        retVal %= divisor;
    }

    return retVal;
}

int main()
{
    int n;

    cin>>n;
    int res = 0;
    for (int i=1; i<=n; i++){
        int tmp = getLastDigits(i,i,5);
        //cout << tmp;
        res += tmp;
    }

    cout << res % 100000;
    return 0;
}

FOr really big n, you can look at https://en.wikipedia.org/wiki/Modular_exponentiation