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//############################################################################
// Programmation IV - 2002 - Week 03
//############################################################################
object M0 {
class Rational(x: Int, y: Int) {
def numer = x;
def denom = y;
}
def addRational(r: Rational, s: Rational): Rational =
new Rational(
r.numer * s.denom + s.numer * r.denom,
r.denom * s.denom);
def makeString(r: Rational) =
r.numer + "/" + r.denom;
val x = new Rational(1, 2);
val y = new Rational(1, 3);
Console.println(x.numer);
Console.println(x.denom);
Console.println(makeString(x));
Console.println(makeString(addRational(x,y)));
Console.println;
}
//############################################################################
object M1 {
class Rational(x: Int, y: Int) {
def numer = x;
def denom = y;
def add(r: Rational) =
new Rational(
numer * r.denom + r.numer * denom,
denom * r.denom);
def mul(r: Rational) =
new Rational(
numer * r.numer,
denom * r.denom);
override def toString() = numer + "/" + denom;
}
val x = new Rational(1, 3);
val y = new Rational(5, 7);
val z = new Rational(3, 2);
Console.println(x);
Console.println(y);
Console.println(z);
Console.println(x.add(y).mul(z));
Console.println;
}
//############################################################################
object M2 {
class Rational(x: Int, y: Int) {
private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b);
private val g = gcd(x, y);
def numer = x / g;
def denom = y / g;
def add(r: Rational) =
new Rational(
numer * r.denom + r.numer * denom,
denom * r.denom);
def sub(r: Rational) =
new Rational(
numer * r.denom - r.numer * denom,
denom * r.denom);
def mul(r: Rational) =
new Rational(
numer * r.numer,
denom * r.denom);
def div(r: Rational) =
new Rational(
numer * r.denom,
denom * r.numer);
override def toString() = numer + "/" + denom;
}
val x = new Rational(1, 3);
val y = new Rational(5, 7);
val z = new Rational(3, 2);
Console.println(x);
Console.println(y);
Console.println(z);
Console.println(x.add(y).mul(z));
Console.println;
}
//############################################################################
object M3 {
class Rational(x: Int, y: Int) {
private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b);
def numer = x / gcd(x, y);
def denom = y / gcd(x, y);
def less(that: Rational) =
this.numer * that.denom < that.numer * this.denom;
def max(that: Rational) = if (this.less(that)) that else this;
override def toString() = numer + "/" + denom;
}
val x = new Rational(66, 42);
val y = new Rational(42, 66);
Console.println(x);
Console.println(y);
Console.println(x.max(y));
Console.println(y.max(x));
Console.println;
}
//############################################################################
object M4 {
class Rational(x: Int, y: Int) {
private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b);
private val g = gcd(x, y);
def numer = x / g;
def denom = y / g;
def + (r: Rational) =
new Rational(
numer * r.denom + r.numer * denom,
denom * r.denom);
def - (r: Rational) =
new Rational(
numer * r.denom - r.numer * denom,
denom * r.denom);
def * (r: Rational) =
new Rational(
numer * r.numer,
denom * r.denom);
def / (r: Rational) =
new Rational(
numer * r.denom,
denom * r.numer);
override def toString() = numer + "/" + denom;
}
val x = new Rational(1, 2);
val y = new Rational(1, 3);
Console.println(x * x + y * y);
Console.println;
}
//############################################################################
object M5 {
trait IntSet {
def incl(x: Int): IntSet;
def contains(x: Int): Boolean;
}
class Empty extends IntSet {
def contains(x: Int): Boolean = false;
def incl(x: Int): IntSet = new NonEmpty(x, new Empty, new Empty);
}
class NonEmpty(elem: Int, left: IntSet, right: IntSet) extends IntSet {
def contains(x: Int): Boolean =
if (x < elem) left contains x
else if (x > elem) right contains x
else true;
def incl(x: Int): IntSet =
if (x < elem) new NonEmpty(elem, left incl x, right)
else if (x > elem) new NonEmpty(elem, left, right incl x)
else this;
}
val x = new Empty incl 1 incl 2;
Console.println(x contains 0);
Console.println(x contains 1);
Console.println(x contains 2);
Console.println(x contains 3);
Console.println;
}
//############################################################################
object M6 {
trait Boolean {
def ifThenElse[a](t: => a)(e: => a): a;
def ! : Boolean = ifThenElse[Boolean](new False())(new True());
def && (x: => Boolean): Boolean = ifThenElse[Boolean](x)(new False());
def || (x: => Boolean): Boolean = ifThenElse[Boolean](new True())(x);
// !!! def == (x: Boolean): Boolean = ifThenElse[Boolean](x)(x.!);
// !!! def != (x: Boolean): Boolean = ifThenElse[Boolean](x.!)(x);
def < (x: Boolean): Boolean = ifThenElse[Boolean](new False())(x);
def > (x: Boolean): Boolean = ifThenElse[Boolean](x.!)(new False());
def <= (x: Boolean): Boolean = ifThenElse[Boolean](x)(new True());
def >= (x: Boolean): Boolean = ifThenElse[Boolean](new True())(x.!);
}
class True() extends Boolean { // !!! class -> object
def ifThenElse[a](t: => a)(e: => a): a = t }
class False() extends Boolean { // !!! class -> object
def ifThenElse[a](t: => a)(e: => a): a = e }
}
//############################################################################
object M7 {
trait Nat {
def isZero(): Boolean;
def predecessor: Nat;
def successor: Nat;
def + (that: Nat): Nat;
def - (that: Nat): Nat;
}
}
//############################################################################
object M8 {
trait IntSet {
def incl(x: Int): IntSet;
def contains(x: Int): Boolean;
def map(f: Int => Int): IntSet;
def foreach(f: Int => Unit): Unit;
def intersect0(that: IntSet, accu: IntSet): IntSet;
def filter0(f: Int => Boolean, accu: IntSet): IntSet;
def intersect(that: IntSet): IntSet = intersect0(that, new Empty);
def intersect2(that: IntSet): IntSet = filter(x => that.contains(x));
def filter(f: Int => Boolean): IntSet = filter0(f, new Empty);
def print() = foreach(Console.println);
override def toString(): String = {
val buffer: StringBuilder = new StringBuilder();
buffer.append('[');
foreach(i => {
if (buffer.length > 1) {buffer.append(','); ()}; // !!! ; ()
buffer.append(i);
()});
buffer.append(']');
buffer.toString();
}
}
class Empty extends IntSet { // !!! class Empty() -> object Empty
def contains(x: Int): Boolean = false;
def incl(x: Int): IntSet = new NonEmpty(x, new Empty, new Empty);
def map(f: Int => Int): IntSet = this;
def foreach(f: Int => Unit): Unit = ();
def intersect0(that: IntSet, accu: IntSet): IntSet = accu;
def filter0(f: Int => Boolean, accu: IntSet): IntSet = accu;
}
class NonEmpty(elem: Int, left: IntSet, right: IntSet) extends IntSet {
def contains(x: Int): Boolean =
if (x < elem) left contains x
else if (x > elem) right contains x
else true;
def incl(x: Int): IntSet =
if (x < elem) new NonEmpty(elem, left incl x, right)
else if (x > elem) new NonEmpty(elem, left, right incl x)
else this;
def map(f: Int => Int): IntSet = {
val lset = left.map(f);
val rset = right.map(f);
new NonEmpty(f(elem), lset, rset)
}
def foreach(f: Int => Unit) {
left.foreach(f);
f(elem);
right.foreach(f);
}
def intersect0(that: IntSet, accu: IntSet): IntSet =
right.intersect0(that, left.intersect0(that,
if (that.contains(elem)) accu.incl(elem) else accu));
def filter0(f: Int => Boolean, accu: IntSet): IntSet =
right.filter0(f, left.filter0(f,
if (f(elem)) accu.incl(elem) else accu));
}
def test = {
val set0: IntSet = new Empty;
val set1: IntSet = new Empty incl 1;
val set2: IntSet = new Empty incl 1 incl 2;
val set3: IntSet = new Empty incl 1 incl 2 incl 3;
val set4: IntSet = new Empty incl 1 incl 2 incl 3 incl 4;
val setx: IntSet = set0 incl -10 incl 5 incl 21 incl -1 incl 0 incl 3;
val sety: IntSet = set0 incl 3 incl 7 incl -5 incl 0 incl-9 incl 8 incl-1;
Console.println("set0 = " + set0);
Console.println("set1 = " + (set1.toString()));
Console.println("set2 = " + set2);
Console.println("set3 = " + (set3.toString()));
Console.println("set4 = " + set4);
Console.println;
Console.println("set2 contains the following elements:");
set2.foreach(Console.println);
Console.println;
Console.println("set3 contains the following elements:");
set3 foreach Console.println;
Console.println;
Console.println("set4 contains the following elements:");
set4.print();
Console.println;
Console.println("2 <- set2: " + (set2 contains 2));
Console.println("3 <- set2: " + set2.contains(3));
Console.println;
Console.println("setx = " + setx);
Console.println("setx * 2 = " + (setx.map(x => 2 * x)));
Console.println;
Console.println("setx = " + setx);
Console.println("sety = " + sety);
Console.println("setx & sety = " + (setx.intersect(sety)));
Console.println("sety & setx = " + (sety.intersect(setx)));
Console.println("setx > 0 = " + (setx.filter(x => x > 0)));
Console.println("sety > 0 = " + (sety.filter(x => x > 0)));
Console.println("setx & sety = " + (setx.intersect2(sety)));
Console.println("sety & setx = " + (sety.intersect2(setx)));
Console.println;
}
}
//############################################################################
object M9 {
class Rational(x: Int, y: Int) {
private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b);
private val g = gcd(x, y);
def numer = x / g;
def denom = y / g;
def add(r: Rational) =
new Rational(
numer * r.denom + r.numer * denom,
denom * r.denom);
def sub(r: Rational) =
new Rational(
numer * r.denom - r.numer * denom,
denom * r.denom);
def mul(r: Rational) =
new Rational(
numer * r.numer,
denom * r.denom);
def equal(r: Rational) =
new Rational(
numer * r.denom,
denom * r.numer);
def asString = numer.toString().concat("/").concat(denom.toString());
override def toString() = asString;
}
def test = {
Console.println(new Rational(2,2).asString);
Console.println(new Rational(2,2).toString());
Console.println(new Rational(2,2));
Console.println;
}
}
//############################################################################
object Test {
def main(args: Array[String]) {
M0;
M1;
M2;
M3;
M4;
M5;
M6;
M7;
M8.test;
M9.test;
()
}
}
//############################################################################
|
