Full solution calculation

src/lib.rs

@@ -1,6 +1,8 @@
 use itertools::Itertools;
 
 pub type Variable = usize;
+pub type Block = Vec<(Variable, Output)>;
+pub type BlockRef<'a> = &'a [(Variable, Output)];
 
 pub const A: Variable = 1 << 0;
 pub const B: Variable = 1 << 1;
@@ -66,7 +68,7 @@ pub fn find_groups(func: &FunctionSpec, vars: &[Variable], typ: Output) -> Vec<V
 				}
 				let mut fits = true;
 				for input in 0..func.len() {
-					if input | mask == input && input & inv_mask == input {
+					if check_mask(input, mask, inv_mask) {
 						if func[input] == typ.invert() {
 							fits = false;
 							break;
@@ -82,10 +84,10 @@ pub fn find_groups(func: &FunctionSpec, vars: &[Variable], typ: Output) -> Vec<V
 	groups
 }
 
-pub fn find_prime<'a>(func: &FunctionSpec, vars: &[Variable], typ: Output, blocks: &'a [Vec<(Variable, Output)>]) -> Vec<&'a [(Variable, Output)]> {
+pub fn find_prime<'a>(func: &FunctionSpec, vars: &[Variable], typ: Output, blocks: &'a [Block]) -> Vec<&'a [(Variable, Output)]> {
 	assert_eq!(func.len(), 2usize.pow(vars.len() as u32));
 
-	let block_masks = blocks.iter().map(|x| &**x)
+	let block_masks = blocks.iter()
 		.map(block_to_mask)
 		.collect::<Vec<_>>();
 
@@ -95,8 +97,8 @@ pub fn find_prime<'a>(func: &FunctionSpec, vars: &[Variable], typ: Output, block
 			continue;
 		}
 		let mut matched = None;
-		for (i, (mask, inv_mask)) in block_masks.iter().enumerate() {
+		for (i, &(mask, inv_mask)) in block_masks.iter().enumerate() {
-			if input | mask == input && input & inv_mask == input {
+			if check_mask(input, mask, inv_mask) {
 				if matched.is_none() {
 					matched = Some(i);
 				} else {
@@ -111,21 +113,83 @@ pub fn find_prime<'a>(func: &FunctionSpec, vars: &[Variable], typ: Output, block
 	prime.into_iter().enumerate().filter(|&(_, prime)| prime).map(|(i, _)| &*blocks[i]).collect()
 }
 
+pub fn all_solutions(mut func: FunctionSpec, vars: &[Variable], typ: Output, prime: &[BlockRef], other: &[Block]) -> Vec<Vec<Block>> {
+	assert_eq!(func.len(), 2usize.pow(vars.len() as u32));
+
+	// first mark all inputs covered by prime blocks as Any
+	let prime_masks = prime.iter()
+		.map(block_to_mask)
+		.collect::<Vec<_>>();
+	'input: for input in 0..func.len() {
+		if func[input] != typ {
+			continue;
+		}
+		for &(mask, inv_mask) in prime_masks.iter() {
+			if check_mask(input, mask, inv_mask) {
+				func[input] = Any;
+				continue 'input;
+			}
+		}
+	}
+	// then start recursive search
+	let other_masks = other.iter()
+		.map(block_to_mask)
+		.collect::<Vec<_>>();
+	all_recursive(func, vars, typ, other, &other_masks)
+}
+
+fn all_recursive(func: FunctionSpec, vars: &[Variable], typ: Output, other: &[Block], other_masks: &[(Variable, Variable)]) -> Vec<Vec<Block>> {
+	let mut all = Vec::new();
+	for i in 0..other.len() {
+		let block = &other[i];
+		let (mask, inv_mask) = other_masks[i];
+		for input in 0..func.len() {
+			if func[input] != typ {
+				continue;
+			}
+			if check_mask(input, mask, inv_mask) {
+				// this block is useful
+				// mark inputs as done
+				let mut func = func.clone();
+				for input in 0..func.len() {
+					if check_mask(input, mask, inv_mask) {
+						func[input] = Any;
+					}
+				}
+				let extensions = all_recursive(func, vars, typ, other, other_masks);
+				if extensions.is_empty() {
+					all.push(vec![block.clone()]);
+				}
+				for mut extension in extensions {
+					extension.push(block.clone());
+					all.push(extension);
+				}
+			}
+		}
+	}
+	all
+}
+
 /// a ⊆ b
 fn subset_of<T: Eq>(a: &[T], b: &[T]) -> bool {
 	a.iter().all(|x| b.contains(x))
 }
 
-fn block_to_mask(block: &[(Variable, Output)]) -> (Variable, Variable) {
+fn block_to_mask<T: AsRef<[(Variable, Output)]>>(block: T) -> (Variable, Variable) {
 	let mut mask = 0;
 	let mut inv_mask = !0;
-	for &(var, out) in block {
+	for &(var, out) in block.as_ref() {
 		mask |= if out == One { var } else { 0 };
 		inv_mask ^= if out == Zero { var } else { 0 };
 	}
 	(mask, inv_mask)
 }
 
+#[inline(always)]
+fn check_mask(input: usize, mask: usize, inv_mask: usize) -> bool {
+	input | mask == input && input & inv_mask == input
+}
+
 pub fn print_implicate(vars: &[(Variable, Output)]) -> String {
 	let mut s = String::new();
 	for i in 0..vars.len() {
@@ -141,6 +205,21 @@ pub fn print_implicate(vars: &[(Variable, Output)]) -> String {
 	s
 }
 
+pub fn print_implicant(vars: &[(Variable, Output)]) -> String {
+	let mut s = String::new();
+	for i in 0..vars.len() {
+		let (var, out) = vars[i];
+		if out == Zero {
+			s += "~";
+		}
+		s += print_var(var);
+		if i != vars.len() - 1 {
+			s += " ";
+		}
+	}
+	s
+}
+
 fn print_var(var: Variable) -> &'static str {
 	match var {
 		A => "a",
@@ -149,3 +228,19 @@ fn print_var(var: Variable) -> &'static str {
 		_ => "?"
 	}
 }
+
+#[test]
+fn test_3var() {
+	let fun: FunctionSpec = vec![0, 0, 1, 0, 0, 1, 1, 1].into_iter().map(Into::into).collect();
+	let groups = find_groups(&fun, &mut [A, B, C], Zero);
+	assert_eq!(groups, vec![
+		vec![(A, Zero), (B, Zero)],
+		vec![(A, One), (C, Zero)],
+		vec![(B, Zero), (C, Zero)],
+	]);
+	let prime = find_prime(&fun, &mut [A, B, C], Zero, &groups);
+	assert_eq!(prime, vec![
+		vec![(A, Zero), (B, Zero)],
+		vec![(A, One), (C, Zero)],
+	]);
+}

src/main.rs

@@ -2,15 +2,26 @@ use kv::*;
 use kv::Output::*;
 
 fn main() {
-	let function = vec![0, 0, 1, 0, 0, 1, 1, 1].into_iter().map(Into::into).collect();
+	let function = vec![0, 0, 1, 1, 1, 1, 1, 0].into_iter().map(Into::into).collect();
-	let groups = find_groups(&function, &mut [A, B, C], Zero);
+	let groups = find_groups(&function, &[A, B, C], One);
 	println!("all:");
 	for x in &groups {
-		println!("{}", print_implicate(x));
+		println!("{}", print_implicant(x));
 	}
 	println!("prime:");
-	let prime = find_prime(&function, &mut [A, B, C], Zero, &groups);
+	let prime = find_prime(&function, &[A, B, C], One, &groups);
-	for x in prime {
+	for x in &prime {
-		println!("{}", print_implicate(&x));
+		println!("{}", print_implicant(x));
+	}
+	println!("solutions:");
+	let solutions = all_solutions(function, &[A, B, C], One, &prime, &groups);
+	for sol in solutions {
+		for x in &prime {
+			print!("{} | ", print_implicant(x));
+		}
+		for x in &sol {
+			print!("{} | ", print_implicant(x));
+		}
+		println!();
 	}
 }