Problem 18 "Maximum path sum I"

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)

問 「最大経路の和 その1」

以下の三角形の頂点から下の行の隣接する数字を通って下まで移動するとき, その数値の和の最大値は23になる.

この例では 3 + 7 + 4 + 9 = 23.

以下の三角形を頂点から下まで移動するとき, その最大の和を求めよ.

''注:'' ここではたかだか 16384 通りのルートしかないので, すべてのパターンを試すこともできる. Problem 67 は同じ問題だが100行あるので, 総当りでは解けない. もっと賢い方法が必要である.

fn main() {
    let mut triangle: Vec<Vec<u16>> = vec![
        vec![75],
        vec![95, 64],
        vec![17, 47, 82],
        vec![18, 35, 87, 10],
        vec![20, 4, 82, 47, 65],
        vec![19, 1, 23, 75, 3, 34],
        vec![88, 2, 77, 73, 7, 63, 67],
        vec![99, 65, 4, 28, 6, 16, 70, 92],
        vec![41, 41, 26, 56, 83, 40, 80, 70, 33],
        vec![41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
        vec![53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
        vec![70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
        vec![91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
        vec![63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
        vec![4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23],
    ];
    triangle.push(vec![0; triangle.last().unwrap().len() + 1]);
    for y in (0..triangle.len() - 1).rev() {
        for x in 0..triangle[y].len() {
            let a = triangle[y + 1][x];
            let b = triangle[y + 1][x + 1];
            triangle[y][x] += std::cmp::max(a, b);
        }
    }
    let sum = triangle[0][0];

    println!("{}", sum);
    assert_eq!(sum, 1074);
}