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//############################################################################
// Programmation IV - 2002 - Week 05
//############################################################################
object M0 {
def partition[a](xs: List[a], pred: a => Boolean): Tuple2[List[a], List[a]] = {
if (xs.isEmpty)
(List(),List())
else {
val tailPartition = partition(xs.tail, pred);
if (pred(xs.head))
(xs.head :: tailPartition._1, tailPartition._2)
else
(tailPartition._1, xs.head :: tailPartition._2)
}
}
def quicksort[a] (less : (a,a) => Boolean) (xs : List[a]) : List[a] = {
if (xs.isEmpty)
xs
else {
val pivot = xs.head;
val sub = partition(xs.tail, { elem : a => less(elem, pivot) });
quicksort(less)(sub._1) ::: List(pivot) ::: quicksort(less)(sub._2)
}
}
def test = {
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 0)));
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 5)));
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 9)));
Console.println;
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 0)));
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 5)));
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 9)));
Console.println;
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 0)));
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 5)));
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 9)));
Console.println;
Console.println(quicksort[Int]((x,y) => x < y)(List(7,2,1,5,4,3,8,6)));
Console.println;
}
}
//############################################################################
object M1 {
def partition[a](xs: List[a], pred: a => Boolean): Tuple2[List[a], List[a]] = {
xs.foldRight[Tuple2[List[a], List[a]]]((List(), List())) {
(x, p) => if (pred (x)) (x :: p._1, p._2) else (p._1, x :: p._2)
}
}
def quicksort[a] (less : (a,a) => Boolean) (xs : List[a]) : List[a] = {
if (xs.isEmpty)
xs
else {
val pivot = xs.head;
val sub = partition(xs.tail, (elem : a) => less(elem, pivot));
quicksort(less)(sub._1) ::: List(pivot) ::: quicksort(less)(sub._2)
}
}
def test = {
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 0)));
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 5)));
Console.println(partition[Int](List(1,2,3,4,5,6,7,8), (x => x < 9)));
Console.println;
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 0)));
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 5)));
Console.println(partition[Int](List(8,7,6,5,4,3,2,1), (x => x < 9)));
Console.println;
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 0)));
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 5)));
Console.println(partition[Int](List(7,2,1,5,4,3,8,6), (x => x < 9)));
Console.println;
Console.println(quicksort[Int]((x,y) => x < y)(List(7,2,1,5,4,3,8,6)));
Console.println;
}
}
//############################################################################
object M2 {
def powerset[a] (s: List[a]): List[List[a]] = {
if (s.isEmpty)
List(List())
else {
val x = s.head;
val withoutX = powerset(s.tail);
withoutX ::: withoutX.map { s1 : List[a] => x::s1 }
}
}
def test = {
Console.println(powerset(List()));
Console.println(powerset(List(1)));
Console.println(powerset(List(1,2)));
Console.println(powerset(List(1,2,3)));
Console.println(powerset(List(1,2,3,4)));
Console.println;
}
}
//############################################################################
object M3 {
def abs(x: Int) = if (x < 0) 0 - x else x;
def range(lo: Int, hi: Int): List[Int] =
if (lo > hi) List()
else lo :: range(lo + 1, hi);
type Placement = List[(Int, Int)];
def queens(n: Int): List[Placement] = {
def placeQueens(row: Int): List[Placement] = {
if (row == 0)
List(List())
else {
def isSafe(column: Int, placement: Placement): Boolean =
placement forall {
pos => (pos._2 != column &&
abs(pos._2 - column) != row - pos._1)
}
def adjoinRow(placement: Placement): List[Placement] =
range(1, n)
.filter (column => isSafe(column, placement))
.map (column => (row, column) :: placement);
placeQueens(row - 1) flatMap adjoinRow
}
}
placeQueens(n)
}
def test: Unit = {
Console.println("queens(1) = " + queens(1));
Console.println("queens(2) = " + queens(2));
Console.println("queens(3) = " + queens(3));
Console.println("queens(4) = " + queens(4));
Console.println;
}
}
//############################################################################
object M4 {
def abs(x: Int) = if (x < 0) 0 - x else x;
def range(lo: Int, hi: Int): List[Int] =
if (lo > hi) List()
else lo :: range(lo + 1, hi);
type Placement = List[Int];
def queens(n: Int): List[Placement] = {
val columns = range(1, n);
def placeQueens(row: Int): List[Placement] = {
if (row == 0)
List(List())
else {
def isSafe(col: Int, p: Placement, delta: Int): Boolean =
(p.isEmpty ||
(col != p.head &&
abs(col - p.head) != delta &&
isSafe(col, p.tail, delta + 1)));
for (
placement <- placeQueens(row - 1);
col <- columns;
if isSafe(col, placement, 1)
) yield {
col :: placement
}
}
}
placeQueens(n);
}
def test: Unit = {
Console.println("queens(1) = " + queens(1));
Console.println("queens(2) = " + queens(2));
Console.println("queens(3) = " + queens(3));
Console.println("queens(4) = " + queens(4));
Console.println;
}
}
//############################################################################
object Test {
def main(args: Array[String]): Unit = {
M0.test;
M1.test;
M2.test;
M3.test;
M4.test;
()
}
}
//############################################################################
|
