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September 28, 2011 12:27
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// *** S-99: Ninety-Nine Scala Problems *** | |
// http://aperiodic.net/phil/scala/s-99/ | |
type B = Boolean | |
// P46: Truth tables for logical expressions. | |
// Define functions and, or, nand, nor, xor, impl, | |
// and equ (for logical equivalence) which return true or false | |
// according to the result of their respective operations; | |
// e.g. and(A, B) is true if and only if both A and B are true. | |
object P46 { | |
def not(a: B) = a match { | |
case true => false | |
case false => true | |
} | |
def and(a: B, b: B) = (a, b) match { | |
case (true, true) => true | |
case _ => false | |
} | |
def or(a: B, b: B) = (a, b) match { | |
case (true, _) => true | |
case (_, true) => true | |
case _ => false | |
} | |
def equ(a: B, b: B) = or(and(a, b), and(not(a), not(b))) | |
def xor(a: B, b: B) = not(equ(a, b)) | |
def nor(a: B, b: B) = not(or(a, b)) | |
def nand(a: B, b: B) = not(and(a, b)) | |
def impl(a: B, b: B) = or(not(a), b) | |
def table2(f: (B, B) => B): String = { | |
val header = "A B result\n" | |
val values = { for( a <- List(true, false); b <- List(true, false)) | |
yield "%-5s %-5s %-5s".format(a, b, f(a, b)) | |
}.mkString("\n") | |
header + values + "\n" | |
} | |
def test { | |
println(and(true, true)) | |
println(and(true, true)==true) | |
println(xor(true, true)) | |
println(xor(true, true)==false) | |
val actual = table2((a: B, b: B) => and(a, or(a, b))) | |
val expected = """A B result | |
true true true | |
true false true | |
false true false | |
false false false | |
""" | |
print(actual) | |
print(expected) | |
} | |
} | |
object P47 { | |
class P47B(a: B) { | |
import P46._ | |
def and(b: B) = P46.and(a: B, b: B) | |
def or(b: B) = P46.or(a: B, b: B) | |
def equ(b: B) = P46.equ(a: B, b: B) | |
def xor(b: B) = P46.xor(a: B, b: B) | |
def nor(b: B) = P46.nor(a: B, b: B) | |
def nand(b: B) = P46.nand(a: B, b: B) | |
def impl(b: B) = P46.impl(a: B, b: B) | |
} | |
implicit def toP47B(a: B) = new P47B(a) | |
def test { | |
import P46._ | |
print(table2((a: B, b: B) => a and (a or not(b)))) | |
} | |
} | |
object P49 { | |
def gray(n: Int): List[String] = { | |
def _gray(m:Int): List[List[Int]] = { | |
List(0,1) flatMap { | |
case i if m == 1 => List(List(i)) | |
case i => _gray(m-1) map { l => i :: l } | |
} | |
} | |
_gray(n) map { case list => list.mkString("") } | |
} | |
def test { | |
println(gray(1)) | |
println(gray(2)) | |
println(gray(3)) | |
} | |
} | |
object P50 { | |
abstract class Tree[A] { | |
val freq: Int | |
def toCode: List[(A, String)] = toCodePrefixed("") | |
def toCodePrefixed(prefix: String): List[(A, String)] | |
} | |
case class InternalNode[A](left: Tree[A], right: Tree[A]) extends Tree[A] { | |
val freq: Int = left.freq + right.freq | |
def toCodePrefixed(prefix: String): List[(A, String)] = | |
left.toCodePrefixed(prefix + "0") ::: right.toCodePrefixed(prefix + "1") | |
} | |
case class LeafNode[A](element: A, freq: Int) extends Tree[A] { | |
def toCodePrefixed(prefix: String): List[(A, String)] = List((element, prefix)) | |
} | |
def huffman[A](ls: List[(A, Int)]): List[(A, String)] = { | |
import collection.immutable.Queue | |
def dequeueSmallest(q1: Queue[Tree[A]], q2: Queue[Tree[A]]) = { | |
// This ordering chooses q1 in case of ties, which helps minimize tree | |
// depth. | |
if (q2.isEmpty) (q1.front, q1.dequeue._2, q2) | |
else if (q1.isEmpty || q2.front.freq < q1.front.freq) (q2.front, q1, q2.dequeue._2) | |
else (q1.front, q1.dequeue._2, q2) | |
} | |
def huffmanR(q1: Queue[Tree[A]], q2: Queue[Tree[A]]): List[(A, String)] = { | |
if (q1.length + q2.length == 1) (if (q1.isEmpty) q2.front else q1.front).toCode | |
else { | |
val (v1, q3, q4) = dequeueSmallest(q1, q2) | |
val (v2, q5, q6) = dequeueSmallest(q3, q4) | |
huffmanR(q5, q6.enqueue(InternalNode(v1, v2))) | |
} | |
} | |
huffmanR( | |
Queue.empty.enqueue(ls sortWith { _._2 < _._2 } map { e => LeafNode(e._1, e._2) }), | |
Queue.empty | |
) | |
} | |
def test { | |
val f = huffman( | |
List( | |
("a", 45), | |
("b", 13), | |
("c", 12), | |
("d", 16), | |
("e", 9), | |
("f", 5) | |
) | |
) | |
println(f) | |
// List((a,0), (b,101), (c,100), (d,111), (e,1101), (f,1100)) | |
} | |
} | |
P46.test | |
P47.test | |
P49.test | |
P50.test | |
// vim: set ts=4 sw=4 et: |
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