#899529 (Rust) No.2405 Minimal Matrix Decomposition

• 問題: No.2405 Minimal Matrix Decomposition
• ユーザー: koba-e964
• 提出日時: 2023-08-08 01:01:59
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 1,284 ms / 2,000 ms
• コード長: 5,411 bytes
• コンパイル時間: 15,509 ms
• コンパイル使用メモリ: 379,500 KB
• 実行使用メモリ: 6,912 KB
• 最終ジャッジ日時: 2024-11-08 06:40:01
• 合計ジャッジ時間: 25,912 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	1 ms; 5,248 KB
testcase_04	AC	16 ms; 5,248 KB
testcase_05	AC	1,284 ms; 6,912 KB
testcase_06	AC	1 ms; 5,248 KB
testcase_07	AC	1 ms; 5,248 KB
testcase_08	AC	1 ms; 5,248 KB
testcase_09	AC	1 ms; 5,248 KB
testcase_10	AC	359 ms; 5,248 KB
testcase_11	AC	439 ms; 5,248 KB
testcase_12	AC	4 ms; 5,248 KB
testcase_13	AC	67 ms; 5,248 KB
testcase_14	AC	79 ms; 5,248 KB
testcase_15	AC	21 ms; 5,248 KB
testcase_16	AC	15 ms; 5,248 KB
testcase_17	AC	161 ms; 5,248 KB
testcase_18	AC	104 ms; 5,248 KB
testcase_19	AC	106 ms; 5,248 KB
testcase_20	AC	3 ms; 5,248 KB
testcase_21	AC	14 ms; 5,248 KB
testcase_22	AC	337 ms; 5,248 KB
testcase_23	AC	2 ms; 5,248 KB
testcase_24	AC	2 ms; 5,248 KB
testcase_25	AC	8 ms; 5,248 KB
testcase_26	AC	233 ms; 5,248 KB
testcase_27	AC	55 ms; 5,248 KB
testcase_28	AC	227 ms; 5,248 KB
testcase_29	AC	39 ms; 5,248 KB
testcase_30	AC	276 ms; 5,248 KB
testcase_31	AC	96 ms; 5,248 KB
testcase_32	AC	7 ms; 5,248 KB
testcase_33	AC	216 ms; 5,248 KB
testcase_34	AC	29 ms; 5,248 KB
testcase_35	AC	1 ms; 5,248 KB
testcase_36	AC	53 ms; 5,248 KB
testcase_37	AC	109 ms; 5,248 KB
testcase_38	AC	129 ms; 5,248 KB
testcase_39	AC	242 ms; 5,248 KB
testcase_40	AC	77 ms; 5,248 KB
testcase_41	AC	7 ms; 5,248 KB
testcase_42	AC	285 ms; 5,248 KB
testcase_43	AC	46 ms; 5,248 KB
testcase_44	AC	47 ms; 5,248 KB
testcase_45	AC	14 ms; 5,248 KB
testcase_46	AC	47 ms; 5,248 KB
testcase_47	AC	63 ms; 5,248 KB
testcase_48	AC	17 ms; 5,248 KB
testcase_49	AC	3 ms; 5,248 KB

コンパイルメッセージ

warning: call to `.clone()` on a reference in this situation does nothing
  --> src/main.rs:71:17
   |
71 |     let aold = a.clone();
   |                 ^^^^^^^^ help: remove this redundant call
   |
   = note: the type `[Vec<i64>]` does not implement `Clone`, so calling `clone` on `&[Vec<i64>]` copies the reference, which does not do anything and can be removed
   = note: `#[warn(noop_method_call)]` on by default

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Write, BufWriter};
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr,) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        read_value!($next, [$t; len])
    }};
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }
impl<T: PartialOrd> Change for T {
    fn chmax(&mut self, x: T) { if *self < x { *self = x; } }
    fn chmin(&mut self, x: T) { if *self > x { *self = x; } }
}

fn powmod(x: i64, mut e: i64, m: i64) -> i64 {
    let mut sum = 1;
    let mut cur = x % m;
    while e > 0 {
        if e % 2 != 0 {
            sum = sum * cur % m;
        }
        cur = cur * cur % m;
        e /= 2;
    }
    sum
}

// p must be prime.
// Returns (B, H) where HB = A, rows(B) = rank(A)
// A: n * m, B: r * m, H: n * r
fn find_basis_mod_p(a: &[Vec<i64>], p: i64) -> (Vec<Vec<i64>>, Vec<Vec<i64>>) {
    let n = a.len();
    let m = a[0].len();
    let aold = a.clone();
    let mut a = a.to_vec();
    let mut pos = vec![];
    let mut r = 0;
    for i in 0..n {
        for j in 0..r {
            let idx = pos[j];
            assert_eq!(a[j][idx], 1);
            let val = a[i][idx];
            for k in 0..m {
                a[i][k] -= a[j][k] * val % p;
                if a[i][k] < 0 {
                    a[i][k] += p;
                }
            }
        }
        let mut c = 0;
        while c < m && a[i][c] == 0 {
            c += 1;
        }
        if c >= m {
            continue;
        }
        a.swap(r, i);
        pos.push(c);
        let aic = a[r][c];
        let aicinv = powmod(aic, p - 2, p);
        a[r][c] = 1.into();
        for j in c + 1..m {
            a[r][j] *= aicinv;
            a[r][j] %= p;
        }
        for j in r + 1..n {
            let ajc = a[j][c];
            a[j][c] = 0;
            for k in c + 1..m {
                let val = ajc * a[r][k] % p;
                a[j][k] -= val;
                if a[j][k] < 0 {
                    a[j][k] += p;
                }
            }
        }
        r += 1;
    }
    let mut tr = vec![vec![0; r]; n];
    for i in 0..n {
        let mut cur = aold[i].clone();
        for j in 0..r {
            let idx = pos[j];
            let val = cur[idx];
            tr[i][j] = val;
            for k in idx..m {
                cur[k] -= val * a[j][k] % p;
                if cur[k] < 0 {
                    cur[k] += p;
                }
            }
        }
        assert!(cur.iter().all(|&x| x == 0), "{:?} {:?} {:?}", cur, a, aold);
    }
    (a[..r].to_vec(), tr)
}

// https://yukicoder.me/problems/no/2405 (3.5)
// 行列のランクを r としたとき、最適値は NM あるいは r(N + M) のどちらかと思われる。(つまり行列 1 個か 2 個)
// -> WA。ランクが 0 のとき (行列がゼロのとき) にも 1 行は必要。
// Tags: rank-of-matrices
fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    #[allow(unused)]
    macro_rules! putvec {
        ($v:expr) => {
            for i in 0..$v.len() {
                puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "});
            }
        }
    }
    input! {
        p: i64,
        n: usize, m: usize,
        a: [[i64; m]; n],
    }
    let (b, h) = find_basis_mod_p(&a, p);
    let r = b.len();
    if r * (m + n) > n * m || (r == 0 && m + n > n * m) {
        puts!("1\n{} {}\n", n, m);
        for i in 0..n {
            putvec!(a[i]);
        }
        return;
    }
    if r == 0 {
        puts!("2\n{} {}\n", n, 1);
        for _ in 0..n {
            puts!("0\n");
        }
        puts!("{} {}\n", 1, m);
        let v = vec![0; m];
        putvec!(v);
        return;
    }
    puts!("2\n{} {}\n", n, r);
    for i in 0..n {
        putvec!(h[i]);
    }
    puts!("{} {}\n", r, m);
    for i in 0..r {
        putvec!(b[i]);
    }
}