Question

Here’s the problem statement.

The series, 1^1 + 2^2 + 3^3 + … + 10^10 = 10405071317.

Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + … + 1000^1000?

The question’s pretty straightforward.
The code which I’ve written can correctly find all the individual numbers(ie (1^1,2^2,…997^997 etc and they’re all correct because I checked using WolframAlpha) 🙂
The glitch occurs when i try to add all these numbers. My program always outputs 0.
I’ve read through it many times and somehow can’t manage to find the error.

PS-Since the numbers here are too large, I’ve stored the individual digits in an array.
Code

#include<stdio.h>
int n[1001][3001]={};
int sum[3001]={};
int raisedto(int q)
{
    int i,j;    
    //int digit;
    int carry=0;
    int carry1=0;
    n[q][0]=q;
    for(i=0;i<q-1;i++)
    {

    for(j=0;j<3001;j++)
    {
        carry=(q*n[q][j]+carry1)/10;
        n[q][j]=((q*n[q][j])+carry1)%10;
        carry1=carry;
    }
    carry1=0;
    carry=0;
    }
return(0);      
}
int sumof()
{
    int i,j,carry=0,carry1=0;
    for(i=0;i<1001;i=i+2)
    {
        for(j=0;j<3001;j++)
        {
            carry=(n[i][j]+n[i+1][j]+carry1)/10;
            sum[j]=(n[i][j]+n[i+1][j]+carry1)%10;
            carry1=carry;
        }   
        carry1=0;
        carry=0;

    }   
    return(0);
}       
int main(void)
{
    int j,i;
    for(i=0;i<1001;i++)
    {
    printf("%d",i);
    raisedto(i);
    }
    printf("\n");
    sumof();

    for(j=0;j<3001;j++)
    {
        printf("%d",sum[j]);
    }   
    printf("done");
    return(0);
}

Answer 1

You were correct, your sumof() function was wrong…

int sumof()
{
    int i,j,carry=0,s = 0;
    for(i=0;i<3001;i++) //iterate each column (as in digit)
    {
        s = carry;
        for(j=0;j<1000;j++) //sum all the columns  (ie add all units places, then tenths place)
        {
            s+=n[j][i];
        }   
        carry = s / 10; //store carry
        sum[i] = s % 10; //store last digit as the sum
    }   
    return(0);
}       

This is essentially what you needed.

Do try and solve using the method i suggested, it’ll help you for advanced problems of Euler.

And the answer checks out. 🙂