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89 lines
2.3 KiB
89 lines
2.3 KiB
// Problem 81:
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//
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// In the 5 by 5 matrix below, the minimal path sum from the top left to the
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// bottom right, by only moving to the right and down, is indicated in brackets
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// and is equal to 2427.
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//
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// [131] 673 234 103 018
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// [201] [096] [342] 965 150
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// 630 803 [746] [422] 111
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// 537 699 497 [121] 956
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// 805 732 524 [037] [331]
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//
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// Find the minimal path sum from the top left to the bottom right by only
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// moving right and down in matrix.txt, a 31K text file containing an 80x80
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// matrix.
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// https://projecteuler.net/project/resources/p081_matrix.txt
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use std::collections::HashMap;
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use std::io;
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use std::io::prelude::*;
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use std::io::BufReader;
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fn parse<T: Read>(reader: T) -> io::Result<Vec<Vec<i32>>> {
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let mut mat = Vec::new();
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for line in BufReader::new(reader).lines() {
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let row = line?
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.trim()
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.split(',')
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.filter_map(|s| s.parse::<i32>().ok())
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.collect();
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mat.push(row);
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}
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Ok(mat)
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}
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fn compute(matrix: &[Vec<i32>], mut memo: &mut HashMap<(usize, usize), i32>, x: usize, y: usize) -> i32 {
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let (w, h) = (matrix[0].len(), matrix.len());
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// memoize
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if let Some(ret) = memo.get(&(x, y)) {
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return *ret;
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}
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// base cases
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if (x, y) == (w - 1, h - 1) {
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return matrix[y][x];
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} else if x == w - 1 {
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return matrix[y][x] + compute(matrix, &mut memo, x, y + 1);
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} else if y == h - 1 {
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return matrix[y][x] + compute(matrix, &mut memo, x + 1, y);
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}
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let ret = matrix[y][x] + {
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let bottom = compute(matrix, &mut memo, x, y + 1);
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let right = compute(matrix, &mut memo, x + 1, y);
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if bottom < right {
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bottom
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} else {
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right
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}
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};
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memo.insert((x, y), ret);
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ret
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}
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fn main() {
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let mat = parse(io::stdin());
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if let Ok(data) = mat {
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println!(
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"the minimal path sum is: {}",
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compute(&data, &mut HashMap::new(), 0, 0)
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);
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}
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}
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#[test]
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fn five_by_five() {
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let mat = vec![
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vec![131, 673, 234, 103, 18],
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vec![201, 96, 342, 965, 150],
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vec![630, 803, 746, 422, 111],
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vec![537, 699, 497, 121, 956],
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vec![805, 732, 524, 37, 331],
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];
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assert_eq!(2427, compute(&mat, &mut HashMap::new(), 0, 0));
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}
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