18.js

// Maximum path sum I
// Problem 18
//
// 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.
//
// 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)

var maxTotalInTriangleMatrix = function (matrix) {
    for (var r = 0; r < matrix.length; r++) {
        for (var c = 0; c < matrix[r].length; c++) {
            matrix[r][c] += matrix[r - 1] ? Math.max(matrix[r - 1][c] || 0, matrix[r - 1][c - 1] || 0) : 0;
        }
    }
    var max = matrix.pop().reduce(function (x, y) {
        return Math.max(x, y);
    });
    console.log(max);
};

maxTotalInTriangleMatrix([
    [3],
    [7, 4],
    [2, 4, 6],
    [8, 5, 9, 3]
]);

maxTotalInTriangleMatrix([
    [75],
    [95, 64],
    [17, 47, 82],
    [18, 35, 87, 10],
    [20, 4, 82, 47, 65],
    [19, 1, 23, 75, 3, 34],
    [88, 2, 77, 73, 7, 63, 67],
    [99, 65, 4, 28, 6, 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, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
    [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]
]);