Project Euler Problem 18

Problem 18

31 May 2002

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)

Answer: 1074

 

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

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

        static void Main(string[] args) {
            // go backward
            for (int i = nums.Length - 2; i >= 0; i--) {
                for (int j = 0; j <= nums[i].Length - 1; j++) {                    
                    nums[i][j] += Math.Max(nums[i + 1][j], nums[i + 1][j + 1]);
                }
            }
            Console.WriteLine(nums[0][0]);

            Console.ReadKey();
        }
    }
}

Racket

 

(define nums
  (vector
   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))

(define (triangle-yx->x y x)
  (+ (/ (* y (+ 1 y)) 2) x))

(define (problem18)
  (for* ([i (in-range (- 15 2) -1 -1)]
         [j (in-range 0 (+ 1 i))])
    (vector-set! nums
                 (triangle-yx->x i j)
                 (+ (vector-ref nums (triangle-yx->x i j)) (max (vector-ref nums (triangle-yx->x (+ 1 i) j))
                                                                (vector-ref nums (triangle-yx->x (+ 1 i) (+ 1 j)))))))
  (display (vector-ref nums 0)))

(problem18)

 

 

Javascript

 

var nums = [
    [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]
    ];

function main() {
    // go backward
    for (var i = nums.length - 2; i >= 0; i--) {
        for (var j = 0; j <= nums[i].length - 1; j++) {                   
            nums[i][j] += Math.max(nums[i + 1][j], nums[i + 1][j + 1]);
        }
    }
    alert(nums[0][0]);
}
main();