Merge pull request #43 from manta1130/feature/twosat

Implement twosat

Author: qryxip

src/lib.rs

@@ -32,3 +32,4 @@ pub use string::{
     lcp_array, lcp_array_arbitrary, suffix_array, suffix_array_arbitrary, suffix_array_manual,
     z_algorithm, z_algorithm_arbitrary,
 };
+pub use twosat::TwoSat;

src/twosat.rs

@@ -1 +1,114 @@
+use crate::internal_scc;
 
+pub struct TwoSat {
+    n: usize,
+    scc: internal_scc::SccGraph,
+    answer: Vec<bool>,
+}
+impl TwoSat {
+    pub fn new(n: usize) -> Self {
+        TwoSat {
+            n,
+            answer: vec![false; n],
+            scc: internal_scc::SccGraph::new(2 * n),
+        }
+    }
+    pub fn add_clause(&mut self, i: usize, f: bool, j: usize, g: bool) {
+        assert!(i < self.n && j < self.n);
+        self.scc.add_edge(2 * i + !f as usize, 2 * j + g as usize);
+        self.scc.add_edge(2 * j + !g as usize, 2 * i + f as usize);
+    }
+    pub fn satisfiable(&mut self) -> bool {
+        let id = self.scc.scc_ids().1;
+        for i in 0..self.n {
+            if id[2 * i] == id[2 * i + 1] {
+                return false;
+            }
+            self.answer[i] = id[2 * i] < id[2 * i + 1];
+        }
+        true
+    }
+    pub fn answer(&self) -> &[bool] {
+        &self.answer
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #![allow(clippy::many_single_char_names)]
+    use super::*;
+    #[test]
+    fn solve_alpc_h_sample1() {
+        // https://atcoder.jp/contests/practice2/tasks/practice2_h
+
+        let (n, d) = (3, 2);
+        let x = [1, 2, 0i32];
+        let y = [4, 5, 6];
+
+        let mut t = TwoSat::new(n);
+
+        for i in 0..n {
+            for j in i + 1..n {
+                if (x[i] - x[j]).abs() < d {
+                    t.add_clause(i, false, j, false);
+                }
+                if (x[i] - y[j]).abs() < d {
+                    t.add_clause(i, false, j, true);
+                }
+                if (y[i] - x[j]).abs() < d {
+                    t.add_clause(i, true, j, false);
+                }
+                if (y[i] - y[j]).abs() < d {
+                    t.add_clause(i, true, j, true);
+                }
+            }
+        }
+        assert!(t.satisfiable());
+        let answer = t.answer();
+        let mut res = vec![];
+        for (i, &v) in answer.iter().enumerate() {
+            if v {
+                res.push(x[i])
+            } else {
+                res.push(y[i]);
+            }
+        }
+
+        //Check the min distance between flags
+        res.sort();
+        let mut min_distance = i32::max_value();
+        for i in 1..res.len() {
+            min_distance = std::cmp::min(min_distance, res[i] - res[i - 1]);
+        }
+        assert!(min_distance >= d);
+    }
+
+    #[test]
+    fn solve_alpc_h_sample2() {
+        // https://atcoder.jp/contests/practice2/tasks/practice2_h
+
+        let (n, d) = (3, 3);
+        let x = [1, 2, 0i32];
+        let y = [4, 5, 6];
+
+        let mut t = TwoSat::new(n);
+
+        for i in 0..n {
+            for j in i + 1..n {
+                if (x[i] - x[j]).abs() < d {
+                    t.add_clause(i, false, j, false);
+                }
+                if (x[i] - y[j]).abs() < d {
+                    t.add_clause(i, false, j, true);
+                }
+                if (y[i] - x[j]).abs() < d {
+                    t.add_clause(i, true, j, false);
+                }
+                if (y[i] - y[j]).abs() < d {
+                    t.add_clause(i, true, j, true);
+                }
+            }
+        }
+        assert!(!t.satisfiable());
+    }
+}