Finding largest product in a series

Question

I am trying to solve the following problem: https://projecteuler.net/problem=8

Basically I am going through the 2D array and getting the 13 digit product from each of the eight directions (N, NW, NE, E, W, S, SW, SE) and setting the return value to the largest one (if there is one).

But I am getting an answer of 64497254400, which is incorrect. Any hints as to what I could possibly be doing wrong?

Following is my straightforward, inefficient solution:

#include <stdio.h>
#include <iostream>
#include <fstream>

using namespace std;

long long int MAX(long long int a, long long int b)
{
    if (a > b)
    {
        return a;
    }
    else
    {
        return b;
    }
}

void largest_product_in_series(int param)
{
    char filename[] = "8_.txt";
    char my_character ;
    int column = 0; int row = 0;
    int c = 0; int r = 0; int cc = 0; int rr = 0;
    int list[100][100];
    int num = param - 1;

    ifstream fin;
    fin.open(filename, ios::in);

    while (!fin.eof() ) 
    {
        fin.get(my_character);
        if (my_character == '\n')
        {
            row++;
            r++;
            c = 0;
            cout << endl;
        }
        else
        {
            if (row == 0)
            {
                column++;
            }
            list[r][c] = (my_character - '0');
            cout << list[r][c];
            c++;
        }
    }

    cout << "Column: " << column << endl;
    cout << "Row: " << row << endl;

    long long int greatest_product = 0;

    long long int product = 0;

    for (rr = 0; rr < row; rr++)
    {
        for (cc = 0; cc < column; cc++)
        {
            //cout << "Column: " << cc << " Row: " << rr << endl;
            if (rr >= num)
            {
                r = rr;
                c = cc;
                product = list[r--][c];

                for (int i = 0; i < num; i++)
                {
                    product *= list[r--][c];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if ((rr + num) <= row)
            {
                r = rr;
                c = cc;
                product = list[r++][c];

                for (int i = 0; i < num; i++)
                {
                    product *= list[r++][c];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if (cc >= num)
            {
                r = rr;
                c = cc;
                product = list[r][c--];

                for (int i = 0; i < num; i++)
                {
                    product *= list[r][c--];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if ((cc + num) <= column)
            {
                r = rr;
                c = cc;
                product = list[r][c++];

                for (int i = 0; i < num; i++)
                {
                    product *= list[r][c++];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if ((rr >= num) && (cc >= num)) // NW
            {
                r = rr;
                c = cc;
                product = list[r--][c--];
                for (int i = 0; i < num; i++)
                {
                    product = list[r--][c--];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if ((rr >= num) && ((cc + num) <= column)) // NE
            {
                r = rr;
                c = cc;
                product = list[r--][c++];
                for (int i = 0; i < num; i++)
                {
                    product = list[r--][c++];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if (((rr + num) <= row) && ((cc >= num))) // SW
            {
                r = rr;
                c = cc;
                product = list[r++][c--];
                for (int i = 0; i < num; i++)
                {
                    product = list[r++][c--];
                }
                greatest_product = MAX(greatest_product, product);
            }
            if (((rr + num) <= row) && ((cc + num) <= column)) // SE
            {
                r = rr;
                c = cc;
                product = list[r++][c++];
                for (int i = 0; i < num; i++)
                {
                    product = list[r++][c++];
                }
                greatest_product = MAX(greatest_product, product);
            }
            //cout << "G: " << greatest_product << endl;
        }
    }
    cout << "Greatest Product: " << greatest_product << endl;
}

int main(void)
{
    largest_product_in_series(13);
    return 0;
}

Answer 1

When I run your code, it says the column is 50, and the row is 21. That seems a little odd, since it should be a 20x50 array, not a 21x50 array, that would be a 1050-digit number. Best guess is that you're accidentally storing some unprintable characters in a 21st row and the product involves some of those.

Also, some of the loops have product = ... instead of product *= ...

And lastly, it wouldn't influence the answer, but multiplication is commutative, so if you get the product of some numbers forward and backward, the result will be the same. So you can simplify your solution a little by getting rid of everything with N xor W in the direction.