#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

int main() 
{
    int input;

    // Init triangle 2D vector
    vector<vector<int> > triangleVector {
        { 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, 4, 23 }
    };

    // Displaying the 2D vector 
    // for (int i = 0; i < triangleVector.size(); i++) { 
    //     for (int j = 0; j < triangleVector[i].size(); j++) 
    //         cout << triangleVector[i][j] << " "; 
    //     cout << endl; 
    // }

    // cout << endl; 

    // Upside-down access rows and Max(current index, next index) + next row index
    // Back tracking max number and sum next row -> dynamic programming!
    for (int i = triangleVector.size() - 1; i > 0; i--) { 
        for (int j = 0; j < triangleVector[i].size() - 1; j++) {
            triangleVector[i-1][j] = triangleVector[i-1][j] + max(triangleVector[i][j], triangleVector[i][j+1]);
        }
    }

    cout << triangleVector[0][0] << endl;

    cout << "To end of program, input any character and enter...";
    cin >> input;
    return 0;
}