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CountDownProblem.java
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317 lines (276 loc) · 8.99 KB
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import java.util.ArrayList;
import java.util.List;
import java.util.OptionalInt;
import java.util.Set;
import java.util.stream.Stream;
/*
* This program is Java port of the Haskell example at
* https://www.cs.nott.ac.uk/~pszgmh/pgp-countdown.hs
*
* The problem and the solution approaches are explained
* in Prof. Graham Hutton's youtube video at
* https://youtu.be/CiXDS3bBBUo?list=PLF1Z-APd9zK7usPMx3LGMZEHrECUGodd3
*
* This Java program requires JDK 21+
*/
class CountDownProblem {
// data Op = Add | Sub | Mul | Div
enum Op {
Add, Sub, Mul, Div;
// instance show Op
@Override
public String toString() {
return switch (this) {
case Add -> "+";
case Sub -> "-";
case Mul -> "*";
case Div -> "/";
};
}
}
// cache enum value array
static final Op[] operators = Op.values();
// valid' :: Op -> Int -> Int -> Bool
static boolean isValid(Op op, int x, int y) {
return switch (op) {
case Add -> x <= y;
case Sub -> x > y;
case Mul -> x != 1 && y != 1 && x <= y;
case Div -> y != 1 && x % y == 0;
};
}
// apply :: Op -> Int -> Int -> Int
static int apply(Op op, int x, int y) {
return switch (op) {
case Add -> x + y;
case Sub -> x - y;
case Mul -> x * y;
case Div -> x / y;
};
}
// data Expr = Val Int | App Op Expr Expr
sealed interface Expr {
// brak helper for instance Show Expr
static String brak(Expr expr) {
return switch (expr) {
// brak (Val n) = show n
case Val(var n) -> Integer.toString(n);
// brak e = "(" ++ show e ++ ")"
default -> "(" + toStr(expr) + ")";
};
}
// instance Show Expr
static String toStr(Expr expr) {
return switch (expr) {
// show (Val n) = show n
case Val(var n) -> Integer.toString(n);
// show (App o l r) = brak l ++ show o ++ brak r
// where
// brak (Val n) = show n
// brak e = "(" ++ show e ++ ")"
case App(var op, var l, var r) -> brak(l) + op + brak(r);
};
}
}
record Val(int v) implements Expr {
// instance Show Expr
@Override
public String toString() {
return Expr.toStr(this);
}
}
record App(Op op, Expr l, Expr r) implements Expr {
// instance Show Expr
@Override
public String toString() {
return Expr.toStr(this);
}
}
// eval :: Expr -> [Int]
// Using OptionalInt instead of List<Integer>
static OptionalInt eval(Expr expr) {
return switch (expr) {
// eval (Val n) = [n | n > 0]
case Val(var n) -> n > 0 ? OptionalInt.of(n) : OptionalInt.empty();
// eval (App o l r) = [apply o x y | x <- eval l,
// y <- eval r,
// valid o x y]
case App(var op, var l, var r) -> {
var x = eval(l);
var y = eval(r);
yield (x.isPresent() && y.isPresent() &&
isValid(op, x.getAsInt(), y.getAsInt())) ?
OptionalInt.of(apply(op, x.getAsInt(), y.getAsInt())) :
OptionalInt.empty();
}
};
}
// type Result = (Expr,Int)
record Result(Expr expr, int value) {
@Override
public String toString() {
return expr.toString() + " = " + value;
}
}
// combine'' :: Result -> Result -> [Result]
static List<Result> combine(Result lx, Result ry) {
// (l,x), (r,y) pattern
var l = lx.expr();
var x = lx.value();
var r = ry.expr();
var y = ry.value();
// combine'' (l,x) (r,y) = [(App o l r, apply o x y) | o <- ops, valid' o x y]
return Stream.of(operators).
filter(op -> isValid(op, x, y)).
map(op -> new Result(new App(op, l, r), apply(op, x, y))).
toList();
}
// results' :: [Int] -> [Result]
static List<Result> results(List<Integer> ns) {
// results' [] = []
if (ns.isEmpty()) {
return List.of();
}
// results' [n] = [(Val n,n) | n > 0]
if (ns.size() == 1) {
var n = head(ns);
return n > 0 ? List.of(new Result(new Val(n), n)) : List.of();
}
// results' ns = [res | (ls,rs) <- split ns,
// lx <- results' ls,
// ry <- results' rs,
// res <- combine'' lx ry]
var res = new ArrayList<Result>();
// all possible non-empty splits of the input list
// split :: [a] -> [([a],[a])] equivalent for-loop
for (int i = 1; i < ns.size(); i++) {
var ls = ns.subList(0, i);
var rs = ns.subList(i, ns.size());
var lxs = results(ls);
var rys = results(rs);
for (Result lx : lxs) {
for (Result ry : rys) {
res.addAll(combine(lx, ry));
}
}
return res;
}
// List utilities
// : operator
static <T> List<T> cons(T head, List<T> tail) {
final var tailLen = tail.size();
return switch (tailLen) {
case 0 -> List.of(head);
case 1 -> List.of(head, tail.get(0));
case 2 -> List.of(head, tail.get(0), tail.get(1));
case 3 -> List.of(head, tail.get(0), tail.get(1), tail.get(2));
default -> {
var res = new ArrayList<T>(1 + tailLen);
res.add(head);
res.addAll(tail);
yield res;
}
};
}
static <T> T head(List<T> list) {
return list.get(0);
}
static <T> List<T> tail(List<T> list) {
final var len = list.size();
return len == 1 ? List.of() : list.subList(1, len);
}
// subs :: [a] -> [[a]]
static List<List<Integer>> subs(List<Integer> ns) {
// subs [] = [[]]
if (ns.isEmpty()) {
return List.of(List.of());
}
// subs (x:xs)
var x = head(ns);
var xs = tail(ns);
// where yss = sub(xs)
var yss = subs(xs);
// yss ++ map (x:) yss
var res = new ArrayList<List<Integer>>();
res.addAll(yss);
yss.stream().
map(l -> cons(x, l)).
forEach(res::add);
return res;
}
// interleave :: a -> [a] -> [[a]]
// Using Stream<List<Integer> instead of List<List<Integer>>
static Stream<List<Integer>> interleave(int x, List<Integer> ns) {
// interleave x [] = [[x]]
if (ns.isEmpty()) {
return Stream.of(List.of(x));
}
// interleave x (y:ys)
var y = head(ns);
var ys = tail(ns);
// outer : translated as Stream.concat
// (x:y:ys) : map (y:) (interleave x ys)
return Stream.concat(
// x:y:ys == x:ns
Stream.of(cons(x, ns)),
// map (y:) (interleave x ys)
interleave(x, ys).map(l -> cons(y, l))
);
}
// perms :: [a] -> [[a]]
// Using Stream<List<Integer> instead of List<List<Integer>>
static Stream<List<Integer>> perms(List<Integer> ns) {
// perms [] = [[]]
if (ns.isEmpty()) {
return Stream.of(List.of());
}
// perms (x:xs)
var x = head(ns);
var xs = tail(ns);
// concat (map ...) is translated as flatMap
// concat (map (interleave x) (perms xs))
return perms(xs).flatMap(l -> interleave(x, l));
}
// choices :: [a] -> [[a]]
// Using Stream<List<Integer> instead of List<List<Integer>>
static Stream<List<Integer>> choices(List<Integer> ns) {
// concat . map is translated as flatMap
// choices = concat . map perms . subs
return subs(ns).stream().flatMap(CountDownProblem::perms);
}
// solutions'' :: [Int] -> Int -> [Expr]
// Using Stream<Expr> instead of List<Expr>
static Stream<Expr> solutions(List<Integer> ns, int n) {
// solutions'' ns n = [e | ns' <- choices ns, (e,m) <- results' ns', m == n]
return choices(ns).
flatMap(choice -> results(choice).stream()).
filter(res -> res.value() == n).
map(Result::expr);
}
/*
* usage example:
*
* java CountDownProblem.java 1,3,7,10,25,50 765
*/
public static void main(String[] args) {
if (args.length != 2) {
System.err.println("usage: java CountDownProblem.java <comma-separated-values> <target>");
System.exit(1);
}
int target = Integer.parseInt(args[1]);
List<Integer> numbers = Stream.of(args[0].split(",")).map(Integer::parseInt).toList();
// uniqueness check
try {
Set.of(numbers.toArray());
} catch (IllegalArgumentException iae) {
System.err.println(iae);
System.exit(2);
}
var start = System.currentTimeMillis();
solutions(numbers, target).forEach(e -> {
System.out.println(e);
});
System.out.println("Time taken (ms): " + (System.currentTimeMillis() - start));
}
}