Add test: Magic Square.

magicsquare_3x3: 873 guesses.
magicsquare_4x4: 13475456 guesses (all solutions).

tests/magicsquare.rs

@@ -0,0 +1,68 @@
+//! Magic Square.
+//!
+//! https://en.wikipedia.org/wiki/Magic_square
+
+extern crate puzzle_solver;
+
+use puzzle_solver::{LinExpr,Puzzle,Solution,Val,VarToken};
+
+fn make_magic_square(n: usize) -> (Puzzle, Vec<Vec<VarToken>>, VarToken) {
+    let mut sys = Puzzle::new();
+    let digits: Vec<Val> = (1..(n * n + 1) as Val).collect();
+    let vars = sys.new_vars_with_candidates_2d(n, n, &digits);
+
+    // Calculate the range of the total (in a dumb way).
+    let min = digits.iter().take(n).sum();
+    let max = digits.iter().rev().take(n).sum();
+    let total = sys.new_var_with_candidates(&(min..max).collect::<Vec<Val>>());
+
+    sys.all_different(vars.iter().flat_map(|it| it));
+
+    for y in 0..n {
+        sys.equals(total, vars[y].iter().fold(LinExpr::from(0), |sum, &x| sum + x));
+    }
+
+    for x in 0..n {
+        sys.equals(total, vars.iter().fold(LinExpr::from(0), |sum, row| sum + row[x]));
+    }
+
+    {
+        sys.equals(total, (0..n).fold(LinExpr::from(0), |sum, i| sum + vars[i][i]));
+        sys.equals(total, (0..n).fold(LinExpr::from(0), |sum, i| sum + vars[i][n - i - 1]));
+    }
+
+    // Sum of all digits = sum of all rows (columns) = total * n.
+    sys.equals(total * (n as Val), digits.iter().sum::<Val>());
+
+    (sys, vars, total)
+}
+
+fn print_magic_square(dict: &Solution, vars: &Vec<Vec<VarToken>>) {
+    for row in vars.iter() {
+        for &var in row.iter() {
+            print!(" {:2}", dict[var]);
+        }
+        println!();
+    }
+}
+
+#[test]
+fn magicsquare_3x3() {
+    let (mut sys, vars, total) = make_magic_square(3);
+    let solutions = sys.solve_all();
+    assert_eq!(solutions.len(), 8);
+
+    print_magic_square(&solutions[0], &vars);
+    for dict in solutions.iter() {
+        assert_eq!(dict[total], 15);
+    }
+    println!("magicsquare_3x3: {} guesses", sys.num_guesses());
+}
+
+#[test]
+fn magicsquare_4x4() {
+    let (mut sys, vars, total) = make_magic_square(4);
+    let dict = sys.solve_any().expect("solution");
+    print_magic_square(&dict, &vars);
+    assert_eq!(dict[total], 34);
+}