Maximum-Path-Sum-I.js

/*
Description: 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! 

maximumPathSumI(testTriangle) should return 23;
*/

function maximumPathSumI(triangle) {
    //compute the length of the triangle
    const size = triangle.length
    //then create a dummy array full of zeroes
    const dummy = new Array(size).fill(0).map(() => new Array(size).fill(0));
    //copy the last line of the original triangle
    dummy[size - 1] = triangle[size - 1].slice();
    //starting from the last line of the triangle compute the maximum sum using dp
    for(let i=size-2;i>=0;i--){
      for(let j=0;j<=i;j++){
        dummy[i][j] = triangle[i][j] + Math.max(dummy[i+1][j],dummy[i+1][j+1])
      }
    }
    return dummy[0][0];
  }
  
  const testTriangle = [[3, 0, 0, 0],
                        [7, 4, 0, 0],
                        [2, 4, 6, 0],
                        [8, 5, 9, 3]];
  
  maximumPathSumI(testTriangle);