algorithms-edu 0.2.7

Algorithms for pedagogical demonstration
Documentation 
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

//! The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
//!
//! Given an integer n, return all distinct solutions to the n-queens puzzle.
//!
//! Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
//!
//! # See also
//!
//! - [Leetcode](https://leetcode.com/problems/n-queens/)

use std::collections::HashSet;

pub fn solve_n_queens(n: i32) -> Vec<Vec<String>> {
    Board::new(n as usize).solve()
}

struct Board {
    matrix: Vec<Vec<char>>,
    n: usize,
    solutions: HashSet<Vec<String>>,
}

impl Board {
    pub fn new(n: usize) -> Self {
        Self {
            matrix: vec![vec!['.'; n]; n],
            n,
            solutions: HashSet::new(),
        }
    }
    pub fn solve(mut self) -> Vec<Vec<String>> {
        self._solve(0, 0);
        self.solutions.into_iter().collect()
    }
    fn _solve(&mut self, i: usize, count: usize) {
        if count == self.n {
            self.add_solution();
        } else if i == self.n {
        } else {
            for col in 0..self.n {
                if self.safe(i, col) {
                    self.matrix[i][col] = 'Q';
                    self._solve(i + 1, count + 1);
                    self.matrix[i][col] = '.';
                }
            }
        }
    }
    fn add_solution(&mut self) {
        self.solutions.insert(
            self.matrix
                .iter()
                .map(|x| x.iter().copied().collect())
                .collect(),
        );
    }

    fn safe(&self, i: usize, j: usize) -> bool {
        for j_ in 0..self.n {
            if self.matrix[i][j_] == 'Q' {
                return false;
            }
        }
        for i_ in 0..self.n {
            if self.matrix[i_][j] == 'Q' {
                return false;
            }
        }
        let (mut i_, mut j_) = (i + 1, j + 1);
        while i_ > 0 && j_ > 0 {
            i_ -= 1;
            j_ -= 1;
            if self.matrix[i_][j_] == 'Q' {
                return false;
            }
        }
        let (mut i_, mut j_) = (i, j + 1);
        while i_ < self.n && j_ > 0 {
            j_ -= 1;
            if self.matrix[i_][j_] == 'Q' {
                return false;
            }
            i_ += 1;
        }
        let (mut i_, mut j_) = (i, j);
        while i_ < self.n && j_ < self.n {
            if self.matrix[i_][j_] == 'Q' {
                return false;
            }
            i_ += 1;
            j_ += 1;
        }
        let (mut i_, mut j_) = (i + 1, j);
        while i_ > 0 && j_ < self.n {
            i_ -= 1;
            if self.matrix[i_][j_] == 'Q' {
                return false;
            }
            j_ += 1;
        }
        true
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_n_queens() {
        let n1 = solve_n_queens(1);
        assert_eq!(n1, vec![vec!["Q".to_string()]]);

        let n2 = solve_n_queens(2);
        assert!(n2.is_empty());

        let n3 = solve_n_queens(3);
        assert!(n3.is_empty());

        let mut n4 = solve_n_queens(4);
        n4.sort();
        assert_eq!(
            n4,
            make_solution(&[
                &["..Q.", "Q...", "...Q", ".Q.."],
                &[".Q..", "...Q", "Q...", "..Q."],
            ])
        );

        let mut n5 = solve_n_queens(5);
        let mut n5_expected = make_solution(&[
            &["..Q..", "....Q", ".Q...", "...Q.", "Q...."],
            &["...Q.", "Q....", "..Q..", "....Q", ".Q..."],
            &["....Q", ".Q...", "...Q.", "Q....", "..Q.."],
            &["Q....", "...Q.", ".Q...", "....Q", "..Q.."],
            &[".Q...", "....Q", "..Q..", "Q....", "...Q."],
            &["....Q", "..Q..", "Q....", "...Q.", ".Q..."],
            &[".Q...", "...Q.", "Q....", "..Q..", "....Q"],
            &["..Q..", "Q....", "...Q.", ".Q...", "....Q"],
            &["...Q.", ".Q...", "....Q", "..Q..", "Q...."],
            &["Q....", "..Q..", "....Q", ".Q...", "...Q."],
        ]);
        n5.sort();
        n5_expected.sort();
        assert_eq!(n5, n5_expected);

        let n8 = solve_n_queens(8);
        assert_eq!(n8.len(), 92);
    }

    fn make_solution(sol: &[&[&'static str]]) -> Vec<Vec<String>> {
        sol.iter()
            .map(|&x| x.iter().map(|&s| s.to_owned()).collect())
            .collect()
    }
}