Ruudukko

use std::collections::hash_map::Entry;
use std::collections::HashMap;
use std::io;
 
const MOD: u32 = (10_i32.pow(9) + 7) as u32;
 
fn main() {
    let dimension = {
        let mut input: String = String::new();
        io::stdin().read_line(&mut input).unwrap();
        input.strip_suffix("\n").unwrap().parse::<u16>().unwrap()
    };
 
    let mut rows: Vec<Vec<Cell>> = Vec::with_capacity(dimension as usize);
    let mut coordinates_by_value: HashMap<u32, Vec<(u16, u16)>> = HashMap::new();
 
    for y in 0..dimension {
        let mut input: String = String::new();
        io::stdin().read_line(&mut input).unwrap();
 
        let mut row: Vec<Cell> = Vec::with_capacity(dimension as usize);
 
        let mut x: u16 = 0;
        for str in input.split_whitespace() {
            let value = str.parse::<u32>().unwrap();
            row.push(Cell {
                value,
                possible_paths: 0
            });
 
            match coordinates_by_value.entry(value) {
                Entry::Occupied(entry) => { entry.into_mut().push((y, x)); }
                Entry::Vacant(entry) => { entry.insert(vec![(y, x)]); }
            }
 
            x += 1;
        }
 
        rows.push(row);
    }
 
    let mut values_sorted = coordinates_by_value.keys().collect::<Vec<&u32>>();
    values_sorted.sort();
    let mut sum: u32 = 0;
    let last_value = values_sorted.last().unwrap();
    for value in &values_sorted {
        if **value <= 1 { continue; }
        for (y, x) in &coordinates_by_value[value] {
            let x = *x as usize;
            let y = *y as usize;
            let mut path_counter = 0;
 
            // Vertical matches
            for (yi, row) in rows.iter().enumerate() {
                if yi == y { continue; }
                let cell = row.get(x).unwrap();
                if cell.value < **value {
                    path_counter = (path_counter + 1 + cell.possible_paths) % MOD;
                }
            }
 
            // Horizontal matches
            let column = rows.get(y).unwrap();
            for (xi, cell) in column.iter().enumerate() {
                if xi == x { continue; }
                if cell.value < **value {
                    path_counter = (path_counter + 1 + cell.possible_paths) % MOD;
                }
            }
 
            if value != last_value {
                rows.get_mut(y).unwrap().get_mut(x).unwrap().possible_paths = path_counter;
            }
            sum = (sum + path_counter) % MOD;
        }
    }
 
    sum = (sum + (dimension as u32 * dimension as u32)) % MOD;
 
    println!("{}", sum);
}
 
struct Cell {
    value: u32,
    possible_paths: u32,
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 2, 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: ACCEPTED

Test 6

Group: 2, 3

Verdict: ACCEPTED

Test 7

Group: 3

Verdict: ACCEPTED

Test 8

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 9

Group: 3

Verdict: TIME LIMIT EXCEEDED