18.rs

/*
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)
*/

fn maximum_path_sum(triangle: Vec<Vec<usize>>) -> usize {
    let mut tri = triangle.clone();

    for row in (0..(triangle.len() - 1)).rev() {
        for col in 0..(row + 1) {
            tri[row][col] = tri[row][col] + std::cmp::max(tri[row + 1][col], tri[row + 1][col + 1]);
        }
    }

    return tri[0][0];
}

pub fn main() {
    let triangle: Vec<Vec<usize>> = 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],
    ];

    let sum = maximum_path_sum(triangle);

    println!("The maximum path sum of the triangle is {}!", sum);
}