June 2018 Update

Task/Pascals-triangle/00DESCRIPTION

@@ -1,4 +1,4 @@
-[[wp:Pascal's triangle|Pascal's triangle]]   is an arithmetic and geometric figure first imagined by   [[wp:Blaise Pascal|Blaise Pascal]].
+[[wp:Pascal's triangle|Pascal's triangle]] is an arithmetic and geometric figure often associated with the name of [[wp:Blaise Pascal|Blaise Pascal]], but also studied centuries earlier in India, Persia, China and elsewhere.
 
 Its first few rows look like this:
      1

Task/Pascals-triangle/Commodore-BASIC/pascals-triangle-1.commodore

@@ -0,0 +1,24 @@
+10 INPUT "HOW MANY";N
+20 IF N<1 THEN END
+30 DIM C(N)
+40 DIM D(N)
+50 LET C(1)=1
+60 LET D(1)=1
+70 FOR J=1 TO N
+80 FOR I=1 TO N-J+1
+90 PRINT "  ";
+100 NEXT I
+110 FOR I=1 TO J
+120 PRINT C(I)" ";
+130 NEXT I
+140 PRINT
+150 IF J=N THEN END
+160 C(J+1)=1
+170 D(J+1)=1
+180 FOR I=1 TO J-1
+190 D(I+1)=C(I)+C(I+1)
+200 NEXT I
+210 FOR I=1 TO J
+220 C(I)=D(I)
+230 NEXT I
+240 NEXT J

Task/Pascals-triangle/Commodore-BASIC/pascals-triangle-2.commodore

@@ -0,0 +1,12 @@
+RUN
+HOW MANY? 8
+                   1
+                 1   1
+               1   2   1
+             1   3   3   1
+           1   4   6   4   1
+         1   5   10   10   5   1
+       1   6   15   20   15   6   1
+     1   7   21   35   35   21   7   1
+   1   8   28   56   70   56   28   8    1
+READY.

Task/Pascals-triangle/Modula-2/pascals-triangle.mod2

@@ -0,0 +1,33 @@
+MODULE Pascal;
+FROM FormatString IMPORT FormatString;
+FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
+
+PROCEDURE PrintLine(n : INTEGER);
+VAR
+    buf : ARRAY[0..63] OF CHAR;
+    m,j : INTEGER;
+BEGIN
+    IF n<1 THEN RETURN END;
+    m := 1;
+    WriteString("1 ");
+    FOR j:=1 TO n-1 DO
+        m := m * (n - j) DIV j;
+        FormatString("%i ", buf, m);
+        WriteString(buf)
+    END;
+    WriteLn
+END PrintLine;
+
+PROCEDURE Print(n : INTEGER);
+VAR i : INTEGER;
+BEGIN
+    FOR i:=1 TO n DO
+        PrintLine(i)
+    END
+END Print;
+
+BEGIN
+    Print(10);
+
+    ReadChar
+END Pascal.

Task/Pascals-triangle/Perl/pascals-triangle-4.pl

@@ -0,0 +1,34 @@
+#!/usr/bin/perl
+use strict;
+use warnings;
+
+{
+  my @tartaglia ;
+  sub tartaglia {
+      my ($x,$y) = @_;
+      if ($x == 0 or $y == 0)  { $tartaglia[$x][$y]=1 ; return 1};
+      my $ret ;
+      foreach my $yps (0..$y){
+        $ret += ( $tartaglia[$x-1][$yps] || tartaglia($x-1,$yps) );
+      }
+      $tartaglia[$x][$y] = $ret;
+      return $ret;
+  }
+}
+sub tartaglia_row {
+    my $y = shift;
+    my $x = 0;
+    my @row;
+    $row[0] = &tartaglia($x,$y+1);
+    foreach my $pos (0..$y-1) {push @row, tartaglia(++$x,--$y)}
+    return @row;
+}
+
+
+for (0..5) {print join ' ', tartaglia_row($_),"\n"}
+print "\n\n";
+
+
+print tartaglia(3,3),"\n";
+my @third = tartaglia_row(5);
+print "@third\n";

Task/Pascals-triangle/Ruby/pascals-triangle-1.rb

@@ -3,7 +3,7 @@ def pascal(n)
   yield ar = [1]
   (n-1).times do
     ar.unshift(0).push(0) # tack a zero on both ends
-    yield ar = ar.each_cons(2).map{|a, b| a + b }
+    yield ar = ar.each_cons(2).map(&:sum)
   end
 end
 

Task/Pascals-triangle/Rust/pascals-triangle.rust

@@ -0,0 +1,15 @@
+fn pascal_triangle(n: u64)
+{
+
+  for i in 0..n {
+    let mut c = 1;
+    for _j in 1..2*(n-1-i)+1 {
+      print!(" ");
+    }
+    for k in 0..i+1 {
+      print!("{:2} ", c);
+      c = c * (i-k)/(k+1);
+    }
+    println!();
+  }
+}

Task/Pascals-triangle/Scala/pascals-triangle-1.scala

@@ -1,5 +1,5 @@
-def tri(row:Int):List[Int] = { row match {
-  case 1 => List(1)
-  case n:Int => List(1) ::: ((tri(n-1) zip tri(n-1).tail) map {case (a,b) => a+b}) ::: List(1)
-  }
-}
+  def tri(row: Int): List[Int] =
+    row match {
+      case 1 => List(1)
+      case n: Int => 1 +: ((tri(n - 1) zip tri(n - 1).tail) map { case (a, b) => a + b }) :+ 1
+    }

Task/Pascals-triangle/Scala/pascals-triangle-2.scala

@@ -1,2 +1,3 @@
-def prettytri(n:Int) = (1 to n) foreach {i=>print(" "*(n-i)); tri(i) map (c=>print(c+" ")); println}
-prettytri(5)
+def prettyTri(n:Int) = (1 to n) foreach {i => print(" "*(n-i)); tri(i) map (c => print(c + " ")); println}
+
+prettyTri(5)

Task/Pascals-triangle/Scala/pascals-triangle-3.scala

@@ -0,0 +1,10 @@
+object Blaise extends App {
+  def pascalTriangle(): Stream[Vector[Int]] =
+    Vector(1) #:: Stream.iterate(Vector(1, 1))(1 +: _.sliding(2).map(_.sum).toVector :+ 1)
+
+  val output = pascalTriangle().take(15).map(_.mkString(" "))
+  val longest = output.last.length
+
+  println("Pascal's Triangle")
+  output.foreach(line => println(s"${" " * ((longest - line.length) / 2)}$line"))
+}

Task/Pascals-triangle/Stata/pascals-triangle-1.stata

@@ -0,0 +1,26 @@
+function pascal1(n) {
+	return(comb(J(1,n,0::n-1),J(n,1,0..n-1)))
+}
+
+function pascal2(n) {
+	a = I(n)
+	a[.,1] = J(n,1,1)
+	for (i=3; i<=n; i++) {
+		a[i,2..i-1] = a[i-1,2..i-1]+a[i-1,1..i-2]
+	}
+	return(a)
+}
+
+function pascal3(n) {
+	a = J(n,n,0)
+	for (i=1; i<n; i++) {
+		a[i+1,i] = i
+	}
+	s = p = I(n)
+	k = 1
+	for (i=0; i<n; i++) {
+		p = p*a/k++
+		s = s+p
+	}
+	return(s)
+}

Task/Pascals-triangle/Stata/pascals-triangle-2.stata

@@ -0,0 +1,16 @@
+function print_pascal_triangle(n) {
+	a = pascal1(n)
+	for (i=1; i<=n; i++) {
+		for (j=1; j<=i; j++) {
+			printf("%10.0f",a[i,j])
+		}
+		printf("\n")
+	}
+}
+
+print_pascal_triangle(5)
+         1
+         1         1
+         1         2         1
+         1         3         3         1
+         1         4         6         4         1

Task/Pascals-triangle/ZX-Spectrum-Basic/pascals-triangle-1.zx

@@ -0,0 +1,24 @@
+ 10 INPUT "How many rows? ";n
+ 15 IF n<1 THEN GO TO 210
+ 20 DIM c(n)
+ 25 DIM d(n)
+ 30 LET c(1)=1
+ 35 LET d(1)=1
+ 40 FOR r=1 TO n
+ 50 FOR i=1 TO (n-r)
+ 60 PRINT " ";
+ 70 NEXT i
+ 80 FOR i=1 TO r
+ 90 PRINT c(i);" ";
+100 NEXT i
+110 PRINT
+120 IF r>=n THEN GO TO 140
+130 LET d(r+1)=1
+140 FOR i=2 TO r
+150 LET d(i)=c(i-1)+c(i)
+160 NEXT i
+165 IF r>=n THEN GO TO 200
+170 FOR i=1 TO r+1
+180 LET c(i)=d(i)
+190 NEXT i
+200 NEXT r

Task/Pascals-triangle/ZX-Spectrum-Basic/pascals-triangle-2.zx

@@ -0,0 +1 @@
+RUN