By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3 7 4 2 4 6 8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

#include <iostream>
#include <cassert>
 
     // assert()
#include <cstdarg>     // va_start() and va_end()
#include <algorithm>   // max()
#include <ctime>       // clock()

using namespace std;

int triangle4x4[4][4] = {
  {3},
  {7,4},
  {2,4,6},
  {8,5,9,3}
};

int triangle15x15[15+1][15+1] = {
{75},
{95,64},
{17,47,82},
{18,
 
35,87,10},
{20,04,82,47,65},
{19,01,23,75,03,34},
{88,02,77,73,07,63,67},
{99,65,04,28,06,16,70,92},
{41,41,26,56,83,40,80,70,33},
{41,48,72,33,47,32,37,16,94,29},
{53,71,44,65,25,43,91,52,97,51,14},
{70,11,33,28,77,73,17,78,39,68,17,57},
{91,71,52,38,17,14,91,43,58,50,27,29,48},
{63,66,04,68,89,53,67,30,73,16,69,87,40,31},
{04,62,98,27,23, 9,70,98,73,93,38,53,60,04,23}
};


class PE0018
{
private:
    static const int MAX_SIZE = 15;
    int m_triangle[MAX_SIZE+1][MAX_SIZE];

    int m_maxTotal;
    int m_routesSum;
    
    int m_routesStack[MAX_SIZE]; 
    int m_routesRow[MAX_SIZE]; 
    int m_routesCol[MAX_SIZE]; 

    void debugPrintf(const char *format, ...);

public:
    int getMaximumTotal(int dimension);
    void tryNext(int row, int col, int step, int n);
};

// #define DEBUG

int main()
{
    clock_t start = clock(); 

    PE0018 pe0018;

    assert(23 == pe0018.getMaximumTotal(4));

    cout << "The maximum total from top to bottom of the triangle is " ;
    cout << pe0018.getMaximumTotal(15) << endl;

    clock_t finish = clock();
    double duration=(double)(finish - start) / CLOCKS_PER_SEC;
    cout << "C/C++ application running time: " << duration << " seconds" << endl;

    return 0;
}

int PE0018::getMaximumTotal(int dimension)
{
    m_maxTotal  = 0;
    m_routesSum = 0;

    for(int row=0; row<dimension; row++)
    {
        for(int col=0; col<=row; col++)
        {
            if (4 == dimension)
            {
                m_triangle[row][col] = triangle4x4[row][col];
            }
            else
            {
                m_triangle[row][col] = triangle15x15[row][col];
            }
        }
    }

    tryNext(0, 0, 0, dimension); // parameters row, col and step starts from 0

    return m_maxTotal;
}

void PE0018::tryNext(int row, int col, int step, int n)
{
    m_routesStack[step] = m_triangle[row][col];
    m_routesRow[step]   = row;
    m_routesCol[step]   = col;

    if (row >= col && row < n)
    {
        if (row+1 < n)
        {
            tryNext(row+1, col, step+1, n);
        }
        if (row+1<n && col+1<n)
        {
            tryNext(row+1, col+1, step+1, n);
        }
    }
    
    if (n-1 == row && n-1 == step)
    {
        m_routesSum++;

        int total = 0;
        for (int i=0; i<=step; i++)
        {
            total += m_routesStack[i];
            debugPrintf("Step %2d : %2d (%2d, %2d)\n", i+1, 
                        m_routesStack[i], m_routesRow[i], m_routesCol[i]);
        }
        
        m_maxTotal = max(total, m_maxTotal);

        debugPrintf("==> m_routesSum = %d, m_maxTotal = %d\n\n", 
                    m_routesSum, m_maxTotal);
    } 
}

void PE0018::debugPrintf(const char *format, ...)
{
#ifdef DEBUG
    va_list args;
    char buffer[512];   // it can change with the allowed max size

    va_start (args, format);
    (void)vsprintf (buffer, format, args);
    va_end(args);

    printf (buffer);
#endif
}