Data commit

Task/Combinations-and-permutations/Sidef/combinations-and-permutations.sidef

@@ -0,0 +1,45 @@
+func P(n, k) { n! / ((n-k)!) }
+func C(n, k) { binomial(n, k) }
+
+class Logarithm(value) {
+    method to_s {
+        var e = int(value/10.log)
+        "%.8fE%+d" % (exp(value - e*10.log), e)
+    }
+}
+
+func lstirling(n) {
+    n < 10 ? (lstirling(n+1) - log(n+1))
+           : (0.5*log(2*Num.pi*n) + n*log(n/Num.e + 1/(12*Num.e*n)))
+}
+
+func P_approx(n, k) {
+    Logarithm((lstirling(n) - lstirling(n -k)))
+}
+
+func C_approx(n, k) {
+    Logarithm((lstirling(n) - lstirling(n -k) - lstirling(k)))
+}
+
+say "=> Exact results:"
+for n (1..12) {
+    var p = n//3
+    say "P(#{n}, #{p}) = #{P(n, p)}"
+}
+
+for n (10..60 `by` 10) {
+    var p = n//3
+    say "C(#{n}, #{p}) = #{C(n, p)}"
+}
+
+say '';
+say "=> Floating point approximations:"
+for n ([5, 50, 500, 1000, 5000, 15000]) {
+    var p = n//3
+    say "P(#{n}, #{p}) = #{P_approx(n, p)}"
+}
+
+for n (100..1000 `by` 100) {
+    var p = n//3
+    say "C(#{n}, #{p}) = #{C_approx(n, p)}"
+}