Evaluate binomial coefficients: Difference between revisions

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 =={{header|Seed7}}==
+The infix operator [http://seed7.sourceforge.net/libraries/integer.htm#%28in_integer%29!%28in_integer%29 !] computes the binomial coefficient.
+E.g.: <tt>5 ! 3</tt> evaluates to 10. The binomial coefficient operator works also for negative values of n.
+E.g.: <tt>(-6) ! 10</tt> evaluates to 3003.
 <lang seed7>$ include "seed7_05.s7i";
-const func integer: binomial (in integer: n, in var integer: k) is func
+const proc: main is func
-  result
-    var integer: binomial is 0;
   local
-    var integer: l is 0;
+    var integer: n is 0;
+    var integer: k is 0;
   begin
-    if n >= k then
+    for n range 0 to 66 do
-      if k > n - k then
+      for k range 0 to n do
-        k := n - k;  # Optimization
+         write(n ! k <& " ");
-      end if;
+      end for;
-      binomial := 1;
+      writeln;
-      l := 0;
+    end for;
-      while l < k do
-        binomial *:= n - l;
-        incr(l);
-        binomial := binomial div l;
-      end while;
-    end if;
-  end func;
-const proc: main is func
-  begin
-    writeln("binomial coefficient of (5, 3) is " <& binomial(5, 3));
   end func;</lang>
 {{Out}}
 <pre>
-binomial coefficient of (5, 3) is 10
+1
+2 1
+3 3 1
+4 6 4 1
+5 10 10 5 1
+6 15 20 15 6 1
+7 21 35 35 21 7 1
+8 28 56 70 56 28 8 1
+9 36 84 126 126 84 36 9 1
+10 45 120 210 252 210 120 45 10 1
+11 55 165 330 462 462 330 165 55 11 1
+12 66 220 495 792 924 792 495 220 66 12 1
+13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
+14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
+15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1
+16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1
+17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1
+18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816 153 18 1
+19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876 969 171 19 1
+20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1
+...
 </pre>
+The library [http://seed7.sourceforge.net/libraries/bigint.htm bigint.s7i] contains a definition of the binomial coefficient operator
+[http://seed7.sourceforge.net/libraries/bigint.htm#%28in_bigInteger%29!%28in_var_bigInteger%29 !]
+for the type [http://seed7.sourceforge.net/manual/types.htm#bigInteger bigInteger]:
+<lang seed7>const func bigInteger: (in bigInteger: n) ! (in var bigInteger: k) is func
+  result
+    var bigInteger: binom is 0_;
+  local
+    var bigInteger: numerator is 0_;
+    var bigInteger: denominator is 0_;
+  begin
+    if n >= 0_ and k > n >> 1 then
+      k := n - k;
+    end if;
+    if k < 0_ then
+      binom := 0_;
+    elsif k = 0_ then
+      binom := 1_;
+    else
+      binom := n;
+      numerator := pred(n);
+      denominator := 2_;
+      while denominator <= k do
+        binom *:= numerator;
+        binom := binom div denominator;
+        decr(numerator);
+        incr(denominator);
+      end while;
+    end if;
+  end func;
+</lang>
+Original source [http://seed7.sourceforge.net/algorith/math.htm#binomial_coefficient].
 =={{header|Tcl}}==