1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
/// 773. Sliding Puzzle (Hard)
///
/// On an 2 x 3 board, there are five tiles labeled from 1 to 5, and an empty
/// square represented by 0. A *move* consists of choosing 0 and a
/// 4-directionally adjacent number and swapping it.
///
/// The state of the board is solved if and only if the board is
/// [[1,2,3],[4,5,0]].
///
/// Given the puzzle board board, return the least number of moves required so
/// that the state of the board is solved. If it is impossible for the state of
/// the board to be solved, return -1.
///
/// *Example 1:*
///
/// *Input:* board = [[1,2,3],[4,0,5]]
/// *Output:* 1
/// *Explanation:* Swap the 0 and the 5 in one move.
///
/// *Example 2:*
///
/// *Input:* board = [[1,2,3],[5,4,0]]
/// *Output:* -1
/// *Explanation:* No number of moves will make the board solved.
///
/// *Example 3:*
///
/// *Input:* board = [[4,1,2],[5,0,3]]
/// *Output:* 5
/// *Explanation:* 5 is the smallest number of moves that solves the board.
/// An example path:
/// After move 0: [[4,1,2],[5,0,3]]
/// After move 1: [[4,1,2],[0,5,3]]
/// After move 2: [[0,1,2],[4,5,3]]
/// After move 3: [[1,0,2],[4,5,3]]
/// After move 4: [[1,2,0],[4,5,3]]
/// After move 5: [[1,2,3],[4,5,0]]
///
/// *Constraints:*
///
/// * board.length == 2
/// * board[i].length == 3
/// * 0 <= board[i][j] <= 5
/// * Each value board[i][j] is *unique*.
///
use leetcode::*;
use std::cmp::Ordering;
use std::collections::hash_map;
use std::collections::{BinaryHeap, HashMap};
type Board = [u8; 6];
const FINAL: Board = [1, 2, 3, 4, 5, 0];
#[derive(Clone, Eq)]
struct State {
board: Board,
pos: u8,
dist: u32,
cost: u32,
}
impl State {
fn new(board: Board, pos: u8) -> Self {
Self {
board,
pos,
dist: 0,
cost: Self::board_cost(board),
}
}
fn swap(&self, pos: u8) -> Self {
let mut board = self.board;
board.swap(self.pos as usize, pos as usize);
Self {
board,
dist: self.dist + 1,
cost: self.dist + 1 + Self::board_cost(board),
pos,
}
}
fn board_cost(board: Board) -> u32 {
(0..6)
.filter(|i| board[*i] > 0)
.map(|i| (i as u32).abs_diff(board[i] as u32 - 1))
.sum()
}
}
impl PartialEq for State {
fn eq(&self, other: &Self) -> bool {
self.cost == other.cost
}
}
impl Ord for State {
fn cmp(&self, other: &Self) -> Ordering {
other.cost.cmp(&self.cost)
}
}
impl PartialOrd for State {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
struct Solution {}
impl Solution {
fn push_swap(
queue: &mut BinaryHeap<State>,
distmap: &mut HashMap<Board, u32>,
state: &State,
pos: u8,
) {
let nstate = state.swap(pos);
match distmap.entry(nstate.board) {
hash_map::Entry::Occupied(mut entry) => {
let prev_dist = entry.get_mut();
if nstate.dist < *prev_dist {
*prev_dist = nstate.dist;
queue.push(nstate);
}
}
hash_map::Entry::Vacant(entry) => {
entry.insert(nstate.dist);
queue.push(nstate);
}
};
}
pub fn sliding_puzzle(board: Vec<Vec<i32>>) -> i32 {
let board: Board = (0..6)
.map(|i| board[i / 3][i % 3] as u8)
.collect::<Vec<_>>()
.try_into()
.unwrap();
let pos = board.iter().enumerate().find(|(_, v)| **v == 0).unwrap().0 as u8;
let mut queue = BinaryHeap::new();
let mut distmap = HashMap::new();
queue.push(State::new(board, pos));
while let Some(state) = queue.pop() {
if state.board == FINAL {
return state.dist as i32;
}
Self::push_swap(&mut queue, &mut distmap, &state, (state.pos + 3) % 6);
if (state.pos % 3) > 0 {
Self::push_swap(&mut queue, &mut distmap, &state, state.pos - 1);
}
if (state.pos % 3) < 2 {
Self::push_swap(&mut queue, &mut distmap, &state, state.pos + 1);
}
}
-1
}
}
pub fn main() {
println!("{}", Solution::sliding_puzzle(arg_into(1)));
}
#[cfg(test)]
mod tests {
use crate::Solution;
use leetcode::vvi;
#[test]
fn test() {
assert_eq!(Solution::sliding_puzzle(vvi("[[1,2,3],[4,0,5]]")), 1);
assert_eq!(Solution::sliding_puzzle(vvi("[[1,2,3],[5,4,0]]")), -1);
assert_eq!(Solution::sliding_puzzle(vvi("[[4,1,2],[5,0,3]]")), 5);
}
}
|
