Zachary Stence

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 <fstream>
#include <cassert>
using namespace std;


const int ROWS = 15;
const int COLS = ROWS;

void displayTri(int arr[ROWS][COLS]) {
  for (int r = 0; r < ROWS; r++) {
    for (int c = 0; c <= r; c++) {
      cout << arr[r][c] << " ";
    }
    cout << endl;
  }
  cout << endl;
}


int main() {
  ifstream fin;
  string fileName;
  fin.open("triangles/pe_big.txt");
  assert(fin.is_open());

  // read in triangle array from file
  int size = (ROWS*(ROWS+1))/2;
  int tri[ROWS][COLS];
  for (int r = 0; r < ROWS; r++) {
    for (int c = 0; c <= r; c++) {
      fin >> tri[r][c];
    }
  }

  //bottom-up algorithm
  int start = ROWS - 2;
  for (int r = start; r >= 0; r--) {
    for (int c = 0; c <= r; c++) {
      if (tri[r+1][c] > tri[r+1][c+1])
        tri[r][c] += tri[r+1][c];
      else
        tri[r][c] += tri[r+1][c+1];
    }
  }

//  displayTri(tri);
  cout << tri[0][0] << endl;

}

Answer: 1074