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//! N-Queens Problem Solver
//!
//! This example demonstrates solving the classic N-Queens problem using AllDifferent constraints.
//! The N-Queens problem involves placing N queens on an N×N chessboard such that no two queens
//! attack each other (same row, column, or diagonal).
//!
//! This is an excellent test case for AllDifferent constraint optimization because:
//! - Multiple AllDifferent constraints with different variable connectivity patterns
//! - Diagonal constraints create asymmetric constraint graphs
//! - Scales well to test optimization effectiveness across problem sizes
//!
//! Problem formulation:
//! - Variables: queen_row[i] = row position of queen in column i (1-based)
//! - Constraints:
//! 1. AllDifferent(queen_row) - no two queens in same row
//! 2. AllDifferent(queen_row[i] + i) - no two queens on same ascending diagonal
//! 3. AllDifferent(queen_row[i] - i) - no two queens on same descending diagonal
use selen::prelude::*;
use std::time::Instant;
fn main() {
println!("👑 N-Queens Problem Solver");
println!("=========================\n");
// Test different board sizes to validate optimization across problem scales
let test_sizes = [4, 6, 8];
for &n in &test_sizes {
println!("🔍 Solving {}-Queens problem:", n);
println!("📋 Problem stats: {} queens, {} variables, {} AllDifferent constraints", n, n, 3);
let start = Instant::now();
match solve_n_queens(n) {
Some((solution, stats)) => {
let duration = start.elapsed();
println!("✅ Solution found in {:.3}ms!", duration.as_secs_f64() * 1000.0);
println!("📊 Statistics: {} propagations, {} nodes explored", stats.propagations, stats.nodes);
println!("🔍 Efficiency: {:.1} propagations/node", stats.propagations as f64 / stats.nodes.max(1) as f64);
print_board(&solution, n);
println!("");
}
None => {
println!("❌ No solution found for {}-Queens", n);
}
}
println!("──────────────────────────────────────────────────");
}
// Performance test with larger sizes
println!("\n🚀 Performance Testing:");
let performance_sizes = [10, 12, 20];
for &n in &performance_sizes {
println!("\n🔍 Performance test: {}-Queens", n);
let start = Instant::now();
match solve_n_queens(n) {
Some((_, stats)) => {
let duration = start.elapsed();
println!("✅ Solved in {:.3}ms", duration.as_secs_f64() * 1000.0);
println!("📊 {} propagations, {} nodes, {:.1} prop/node",
stats.propagations, stats.nodes,
stats.propagations as f64 / stats.nodes.max(1) as f64);
}
None => {
println!("❌ No solution found");
}
}
}
println!("\n✨ Summary:");
println!("N-Queens demonstrates AllDifferent optimization with:");
println!("• Multiple AllDifferent constraints with different connectivity patterns");
println!("• Row constraint: simple 1-to-1 variable mapping");
println!("• Diagonal constraints: transformed variables with different connectivity");
println!("• Universal optimization applies across all constraint types");
println!("• 🎯 Perfect test case for validating general-purpose heuristics!");
}
struct SolverStats {
propagations: usize,
nodes: usize,
}
fn solve_n_queens(n: usize) -> Option<(Vec<i32>, SolverStats)> {
let mut model = Model::default();
// Variables: queen_row[i] = row position of queen in column i
let queen_rows = model.ints(n, 1, n as i32);
// Constraint 1: All queens must be in different rows
// This is the most direct AllDifferent constraint
model.alldiff(&queen_rows.clone());
// Constraint 2: No two queens on the same ascending diagonal
// Ascending diagonal: queen_row[i] + i must be different for all i
let ascending_diagonals: Vec<_> = queen_rows.iter().enumerate()
.map(|(i, &queen_row)| {
let col_offset = model.int(i as i32, i as i32);
model.add(queen_row, col_offset)
})
.collect();
model.alldiff(&ascending_diagonals);
// Constraint 3: No two queens on the same descending diagonal
// Descending diagonal: queen_row[i] - i must be different for all i
let descending_diagonals: Vec<_> = queen_rows.iter().enumerate()
.map(|(i, &queen_row)| {
let col_offset = model.int(-(i as i32), -(i as i32));
model.add(queen_row, col_offset)
})
.collect();
model.alldiff(&descending_diagonals);
// Solve the model with statistics tracking
// Solve the model with embedded statistics
let solution = model.solve();
match solution {
Ok(sol) => {
// Access statistics from the solution
let propagation_count = sol.stats.propagation_count;
let node_count = sol.stats.node_count;
// Extract queen positions
let positions: Vec<i32> = queen_rows.iter()
.map(|&var| match sol[var] {
Val::ValI(row) => row,
_ => 0,
})
.collect();
// Get solver statistics
let stats = SolverStats {
propagations: propagation_count,
nodes: node_count,
};
Some((positions, stats))
}
Err(_) => None,
}
}
fn print_board(solution: &[i32], n: usize) {
println!("\n📋 Solution:");
// Print column numbers
print!(" ");
for col in 1..=n {
print!("{:2} ", col);
}
println!();
// Print the board
for row in 1..=n {
print!("{:2} ", row);
for col in 0..n {
if solution[col] == row as i32 {
print!(" ♛ ");
} else {
print!(" · ");
}
}
println!();
}
// Print solution in compact form
print!("🎯 Queen positions: ");
for (col, &row) in solution.iter().enumerate() {
print!("C{}R{}", col + 1, row);
if col < solution.len() - 1 {
print!(", ");
}
}
println!();
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_4_queens() {
let solution = solve_n_queens(4);
assert!(solution.is_some(), "4-Queens should have a solution");
if let Some((positions, _)) = solution {
// Verify solution validity
assert_eq!(positions.len(), 4);
// Check no two queens in same row
let mut rows = positions.clone();
rows.sort();
for i in 1..rows.len() {
assert_ne!(rows[i], rows[i-1], "Two queens in same row");
}
// Check diagonals
for i in 0..4 {
for j in i+1..4 {
// Ascending diagonal check
assert_ne!(positions[i] + i as i32, positions[j] + j as i32,
"Two queens on same ascending diagonal");
// Descending diagonal check
assert_ne!(positions[i] - i as i32, positions[j] - j as i32,
"Two queens on same descending diagonal");
}
}
}
}
#[test]
fn test_8_queens() {
let solution = solve_n_queens(8);
assert!(solution.is_some(), "8-Queens should have a solution");
if let Some((_, stats)) = solution {
// Performance sanity check - 8-Queens should solve reasonably quickly
assert!(stats.propagations < 10000, "Too many propagations for 8-Queens");
assert!(stats.nodes < 1000, "Too many nodes for 8-Queens");
}
}
#[test]
fn test_optimization_effectiveness() {
// This test validates that our AllDifferent optimization is working
// by ensuring reasonable performance on larger instances
let solution = solve_n_queens(10);
assert!(solution.is_some(), "10-Queens should have a solution");
if let Some((_, stats)) = solution {
// With good optimization, 10-Queens should be solvable efficiently
println!("10-Queens stats: {} propagations, {} nodes", stats.propagations, stats.nodes);
// These bounds are generous but validate that optimization is preventing exponential blowup
assert!(stats.propagations < 50000, "Optimization may not be working - too many propagations");
assert!(stats.nodes < 5000, "Optimization may not be working - too many nodes");
}
}
}