Project Euler #11 in C/C++

Question

I have this code which is meant to solve the 11th problem from Project Euler, and it doesn't work further than printout(), after which it crashes with "stack overflow". I guess that something is wrong with my indices (probably in the next_elem function), but I don't see what. Please, give a hint.

#include "stdafx.h"
#include <iostream>


const int matrix[20][20]  = {
                             {8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
                             {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
                             {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
                             {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
                             {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
                             {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
                             {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
                             {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
                             {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
                             {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
                             {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
                             {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
                             {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
                             {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
                             {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
                             {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
                             {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
                             {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
                             {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
                             {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48},
                            };

unsigned long int rows[20][20], columns [20][20], diagslash[20][20], diagbackslash[20][20]; //create all necessary arrays of maximum possible dimensions

//a debugging function  -- to check that everything is right and that I'm working with indices correctly
void printout()
    {
    for(int i=0;i<20;++i)
    {
            {
                    for(int j=0;j<20;++j) 
                        std::cout << "a["<<i<<"],["<<j<<"] = " << matrix[i][j] << " " << "\n";
            }
        std::cout << "\n"; 
        }    
    }


// a function that calculates the next element from the previous one and some matrix elements
unsigned long int next_elem(int i,int j, unsigned long int array[][20])
    {
        if (matrix[i][j] == 0) // a zero in a sequence means we need to move 4 elements to the right
        {
            j+=4;
            next_elem(i,j,rows);
        }
        else if(matrix[i][j] > matrix[i][j-4])  // this condition is meant to put an increasing sequence of results into the 'rows' array
        {
            rows[i][j-4]=rows[i][j-5]*matrix[i][j-1]/matrix[i][j-1];
            next_elem(i,j,rows);
        }
        return 0;
    }



void check(int i, int j, unsigned long int array[][20]) 
    {
        if ((matrix[i][j] == 0) || (matrix[i][j+1] == 0) || (matrix[i][j+2] == 0) || (matrix[i][j+3] == 0)) //look for a zero
        {
            j+=4;
            check(i,j,rows);    
        }
        else  //no zero found, calculate the next element
        {
            rows[i][j] = matrix[i][j]*matrix[i][j+1]*matrix[i][j+2]*matrix[i][j+3]; 
            next_elem(i,j+4,rows); 
        }


    }

void sort()  //this function is meant to find maximums in 'rows', 'columns' and so on
{
    for (int i = 0; i<20;++i)
    {
        for (int j = 0;j < 17;++j)
        {
            check(i,j,rows);
            std::cout << "rows["<<i<<"]["<<j << "] = " << rows[i][j] << std::endl; //a debugging line -- to see what's going on
        }
    }
}

int main()
{
    printout();
    sort();
    return 0;
}

P.S. For those in doubt, this version is mostly in C. I'll re-write it in C++ once I get the hang of the algorithm.

Answer 1

// m is matrix
int max=0;
void update(int i){
    if(i>max)max=i;}
void main(){
    for(int i=0;i<17;i++){
        for(int j=0;j<17;j++){
            update(m[i][j]*m[i+1][j]*m[i+2][j]*m[i+3][j]);
            update(m[i][j]*m[i][j+2]*m[i][j+3]*m[i][j+4]);
            update(m[i][j]*m[i+1][j+1]*m[i+2][j+2]*m[i+3][j+3]);
            update(m[i][j+3]*m[i+1][j+2]*m[i+2][j+1]*m[i+3][j]);
        }
    }
    printf("%d\n",max);
}

Answer 2

You are seg faulting because:

for (int j = 0;j < 17;++j)

needs to be

for (int j = 0; j < 16; ++j)

Answer 3

Nothing is done to i or j or matrix in this situation:

else if(matrix[i][j] > matrix[i][j-4])  // this condition is meant to put an increasing sequence of results into the 'rows' array
{
    rows[i][j-4]=rows[i][j-5]*matrix[i][j-1]/matrix[i][j-1];
    next_elem(i,j,rows);
}

So it'll recurse forever, always with the same parameters, always passing through the same branch, eventually giving you a stack overflow; this would be my guess what's happening.

You need to step i or j along, or change either matrix[i][j] or matrix[i][j-4] so the condition will eventually be false, terminating the recursion.

Haven't analyzed the code or the problem further, so I don't know what you need to change :)

Answer 4

It is difficult to track all conditions but it is pretty clear that you can easily get out of bound:

void check(int i, int j, unsigned long int array[][20]) 
{
    if ((matrix[i][j] == 0) || (matrix[i][j+1] == 0) || (matrix[i][j+2] == 0) || (matrix[i][j+3] == 0)) //look for a zero
    {
        j+=4; // what if j was 16 here?
        check(i,j,rows); 
    }
}

So as the first step I would recommend to put assert to check that all parameters in range:

void check(int i, int j, unsigned long int array[][20]) 
{
    assert( i >= 0 && i < 20 && j >= 0 && j < 20 );
    ...
}

Do same for next_element compile with debug enabled and check.