September 2017 Update
This commit is contained in:
Ingy döt Net
parent
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commit
ba8067c3b7
14570 changed files with 153136 additions and 63871 deletions
10
Task/Catalan-numbers/ALGOL-W/catalan-numbers.alg
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10
Task/Catalan-numbers/ALGOL-W/catalan-numbers.alg
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@ -0,0 +1,10 @@
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begin
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% print the catalan numbers up to C15 %
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integer Cprev;
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Cprev := 1; % C0 %
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write( s_w := 0, i_w := 3, 0, ": ", i_w := 9, Cprev );
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for n := 1 until 15 do begin
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Cprev := round( ( ( ( 4 * n ) - 2 ) / ( n + 1 ) ) * Cprev );
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write( s_w := 0, i_w := 3, n, ": ", i_w := 9, Cprev );
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end for_n
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end.
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17
Task/Catalan-numbers/BASIC/catalan-numbers-2.basic
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17
Task/Catalan-numbers/BASIC/catalan-numbers-2.basic
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@ -0,0 +1,17 @@
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10 FOR N=0 TO 14
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20 LET X=N
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30 GOSUB 130
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40 LET A=FX
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50 LET X=N+1
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60 GOSUB 130
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70 LET B=FX
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80 LET X=2*N
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90 GOSUB 130
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100 PRINT N,FX/(B*A)
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110 NEXT N
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120 STOP
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130 LET FX=1
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140 FOR I=1 TO X
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150 LET FX=FX*I
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160 NEXT I
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170 RETURN
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@ -1,16 +0,0 @@
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// Generate Catalan Numbers
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//
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// Nigel Galloway: June 9th., 2012
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//
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#include <iostream>
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int main() {
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const int N = 15;
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int t[N+2] = {0,1};
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for(int i = 1; i<=N; i++){
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for(int j = i; j>1; j--) t[j] = t[j] + t[j-1];
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t[i+1] = t[i];
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for(int j = i+1; j>1; j--) t[j] = t[j] + t[j-1];
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std::cout << t[i+1] - t[i] << " ";
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}
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return 0;
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}
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@ -1,19 +0,0 @@
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class
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CATALAN_NUMBERS
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feature
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cat_num(n:INTEGER): DOUBLE
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require
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n_not_negative:n>= 0
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local
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s,t: DOUBLE
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do
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if n=0 then
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Result:= 1.0
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else
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t:= 4*n.to_double-2
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s:= n.to_double+1
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Result:= t/s*cat_num(n-1)
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end
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end
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end
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@ -1,24 +0,0 @@
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class
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APPLICATION
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inherit
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ARGUMENTS
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create
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make
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feature {NONE} -- Initialization
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make
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local
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s: STRING
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do
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create cat
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from
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i:=0
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until
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i>14
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loop
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io.put_double (cat.cat_num (i))
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io.put_string ("%N")
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i:= i+1
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end
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end
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cat: CATALAN_NUMBERS
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end
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23
Task/Catalan-numbers/Groovy/catalan-numbers.groovy
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23
Task/Catalan-numbers/Groovy/catalan-numbers.groovy
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@ -0,0 +1,23 @@
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class Catalan
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{
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public static void main(String[] args)
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{
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BigInteger N = 15;
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BigInteger k,n,num,den;
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BigInteger catalan;
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print(1);
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for(n=2;n<=N;n++)
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{
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num = 1;
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den = 1;
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for(k=2;k<=n;k++)
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{
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num = num*(n+k);
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den = den*k;
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catalan = num/den;
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}
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println(catalan);
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}
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}
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}
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@ -1,29 +0,0 @@
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<html><head><title>Catalan</title></head>
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<body><pre id='x'></pre><script type="application/javascript">
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function disp(x) {
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var e = document.createTextNode(x + '\n');
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document.getElementById('x').appendChild(e);
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}
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var fc = [], c2 = [], c3 = [];
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function fact(n) { return fc[n] ? fc[n] : fc[n] = (n ? n * fact(n - 1) : 1); }
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function cata1(n) { return Math.floor(fact(2 * n) / fact(n + 1) / fact(n) + .5); }
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function cata2(n) {
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if (n == 0) return 1;
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if (!c2[n]) {
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var s = 0;
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for (var i = 0; i < n; i++) s += cata2(i) * cata2(n - i - 1);
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c2[n] = s;
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}
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return c2[n];
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}
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function cata3(n) {
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if (n == 0) return 1;
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return c3[n] ? c3[n] : c3[n] = (4 * n - 2) * cata3(n - 1) / (n + 1);
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}
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disp(" meth1 meth2 meth3");
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for (var i = 0; i <= 15; i++)
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disp(i + '\t' + cata1(i) + '\t' + cata2(i) + '\t' + cata3(i));
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</script></body></html>
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@ -1,17 +0,0 @@
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meth1 meth2 meth3
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0 1 1 1
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1 1 1 1
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2 2 2 2
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3 5 5 5
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4 14 14 14
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5 42 42 42
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6 132 132 132
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7 429 429 429
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8 1430 1430 1430
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9 4862 4862 4862
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10 16796 16796 16796
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11 58786 58786 58786
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12 208012 208012 208012
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13 742900 742900 742900
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14 2674440 2674440 2674440
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15 9694845 9694845 9694845
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@ -1,33 +1,31 @@
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import net.openhft.koloboke.collect.map.hash.HashIntDoubleMaps.*
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abstract class Catalan {
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abstract operator fun invoke(n: Int) : Double
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protected val m = newUpdatableMapOf(0 , 1.0)
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protected val m = mutableMapOf(0 to 1.0)
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}
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object CatalanI : Catalan() {
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override fun invoke(n: Int): Double {
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if (n !in m)
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m[n] = Math.round(fact(2 * n) / (fact(n + 1) * fact(n))).toDouble()
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return m[n]
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return m[n]!!
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}
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private fun fact(n: Int): Double {
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if (n in facts)
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return facts[n]
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var f = n * fact(n -1)
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return facts[n]!!
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val f = n * fact(n -1)
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facts[n] = f
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return f
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}
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private val facts = newUpdatableMapOf(0 , 1.0, 1 , 1.0, 2 , 2.0)
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private val facts = mutableMapOf(0 to 1.0, 1 to 1.0, 2 to 2.0)
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}
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object CatalanR1 : Catalan() {
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override fun invoke(n: Int): Double {
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if (n in m)
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return m[n]
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return m[n]!!
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var sum = 0.0
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for (i in 0..n - 1)
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@ -42,7 +40,7 @@ object CatalanR2 : Catalan() {
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override fun invoke(n: Int): Double {
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if (n !in m)
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m[n] = Math.round(2.0 * (2 * (n - 1) + 1) / (n + 1) * invoke(n - 1)).toDouble()
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return m[n]
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return m[n]!!
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}
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}
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@ -1,3 +1,3 @@
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function n = catalanNumbers(n)
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n = prod(n+1:2*n)/prod(1:n+1);
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n = arrayfun(@(n)prod(n+1:2*n)/prod(1:n+1), n);
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end
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12
Task/Catalan-numbers/OCaml/catalan-numbers.ocaml
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12
Task/Catalan-numbers/OCaml/catalan-numbers.ocaml
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@ -0,0 +1,12 @@
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let catalan : int ref = ref 0 in
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Printf.printf "%d ," 1 ;
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for i = 2 to 9 do
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let nm : int ref = ref 1 in
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let den : int ref = ref 1 in
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for k = 2 to i do
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nm := (!nm)*(i+k);
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den := (!den)*k;
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catalan := (!nm)/(!den) ;
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done;
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print_int (!catalan); print_string "," ;
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done;;
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81
Task/Catalan-numbers/OoRexx/catalan-numbers.rexx
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81
Task/Catalan-numbers/OoRexx/catalan-numbers.rexx
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loop i = 0 to 15
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say "catI("i") =" .catalan~catI(i)
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say "catR1("i") =" .catalan~catR1(i)
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say "catR2("i") =" .catalan~catR2(i)
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end
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-- This is implemented as static members on a class object
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-- so that the code is able to keep state information between calls. This
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-- memoization will speed up things like factorial calls by remembering previous
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-- results.
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::class catalan
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-- initialize the class object
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::method init class
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expose facts catI catR1 catR2
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facts = .table~new
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catI = .table~new
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catR1 = .table~new
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catR2 = .table~new
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-- seed a few items
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facts[0] = 1
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facts[1] = 1
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facts[2] = 2
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catI[0] = 1
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catR1[0] = 1
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catR2[0] = 1
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-- private factorial method
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::method fact private class
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expose facts
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use arg n
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-- see if we've calculated this before
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if facts~hasIndex(n) then return facts[n]
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numeric digits 120
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fact = 1
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loop i = 2 to n
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fact *= i
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end
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-- save this result
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facts[n] = fact
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return fact
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::method catI class
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expose catI
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use arg n
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numeric digits 20
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res = catI[n]
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if res == .nil then do
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-- dividing by 1 removes insignificant trailing 0s
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res = (self~fact(2 * n)/(self~fact(n + 1) * self~fact(n))) / 1
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catI[n] = res
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end
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return res
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::method catR1 class
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expose catR1
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use arg n
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numeric digits 20
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if catR1~hasIndex(n) then return catR1[n]
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sum = 0
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loop i = 0 to n - 1
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sum += self~catR1(i) * self~catR1(n - 1 - i)
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end
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-- remove insignificant trailing 0s
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sum = sum / 1
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catR1[n] = sum
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return sum
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::method catR2 class
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expose catR2
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use arg n
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numeric digits 20
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res = catR2[n]
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if res == .nil then do
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res = ((2 * (2 * n - 1) * self~catR2(n - 1)) / (n + 1))
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catR2[n] = res
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end
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return res
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@ -1 +1 @@
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.say for Catalan[^15];
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.say for Catalan[^16];
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@ -10,7 +10,7 @@ call hdr 2 ; do j=LO to HI; say ' Catalan' right(j, w)": " Cat2(
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call hdr 3 ; do j=LO to HI; say ' Catalan' right(j, w)": " Cat3(j) ; end
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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!: arg z; if !.z\==. then return !.z; !=1; do k=2 for z; !=!*k; end; !.z=!; return !
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!: arg z; if !.z\==. then return !.z; !=1; do k=2 to z; !=!*k; end; !.z=!; return !
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Cat1A: procedure expose !.; parse arg n; return comb(n+n, n) % (n+1)
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Cat1B: procedure expose !.; parse arg n; return !(n+n) % ((n+1) * !(n)**2)
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Cat3: procedure expose c.; arg n; if c.n==. then c.n=(4*n-2)*cat3(n-1)%(n+1); return c.n
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@ -18,6 +18,6 @@ comb: procedure; parse arg x,y; return pFact(x-y+1, x) % pFact(2,
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hdr: !.=.; c.=.; c.0=1; say; say center('Catalan numbers, method' arg(1),79,'─'); return
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pFact: procedure; !=1; do k=arg(1) to arg(2); !=!*k; end; return !
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Cat2: procedure expose c.; parse arg n; $=0; if c.n\==. then return c.n
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do k=0 to n-1; $=$ + cat2(k) * cat2(n-k-1); end
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Cat2: procedure expose c.; parse arg n; $=0; if c.n\==. then return c.n
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do k=0 for n; $=$ + Cat2(k) * Cat2(n-k-1); end
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c.n=$; return $ /*use a memoization technique.*/
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@ -1,3 +1,3 @@
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func c(n) is cached {
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n == 0 ? 1 : (c(n-1) * (4 * n - 2) / (n + 1));
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n == 0 ? 1 : (c(n-1) * (4 * n - 2) / (n + 1))
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}
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@ -1,3 +1,3 @@
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15.times { |i|
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say "#{i-1}\t#{c(i-1)}";
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say "#{i}\t#{c(i)}"
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}
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30
Task/Catalan-numbers/Smart-BASIC/catalan-numbers.smart
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30
Task/Catalan-numbers/Smart-BASIC/catalan-numbers.smart
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PRINT "Recursive:"!PRINT
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FOR n = 0 TO 15
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PRINT n,"#######":catrec(n)
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NEXT n
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PRINT!PRINT
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PRINT "Non-recursive:"!PRINT
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FOR n = 0 TO 15
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PRINT n,"#######":catnonrec(n)
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NEXT n
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END
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DEF catrec(x)
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IF x = 0 THEN
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temp = 1
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ELSE
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n = x
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temp = ((2*((2*n)-1))/(n+1))*catrec(n-1)
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END IF
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catrec = temp
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END DEF
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DEF catnonrec(x)
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temp = 1
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FOR n = 1 TO x
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temp = (2*((2*n)-1))/(n+1)*temp
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NEXT n
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catnonrec = temp
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END DEF
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11
Task/Catalan-numbers/XLISP/catalan-numbers.xlisp
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11
Task/Catalan-numbers/XLISP/catalan-numbers.xlisp
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(defun catalan (n)
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(if (= n 0)
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1
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(* (/ (* 2 (- (* 2 n) 1)) (+ n 1)) (catalan (- n 1))) ) )
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(defun range (x y)
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(cons x
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(if (< x y)
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(range (+ x 1) y) ) ) )
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(print (mapcar catalan (range 0 14)))
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9
Task/Catalan-numbers/Zkl/catalan-numbers-1.zkl
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9
Task/Catalan-numbers/Zkl/catalan-numbers-1.zkl
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@ -0,0 +1,9 @@
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var BN=Import("zklBigNum");
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fcn catalan(n){
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BN(2*n).factorial() / BN(n+1).factorial() / BN(n).factorial();
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}
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foreach n in (16){
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println("%2d --> %,d".fmt(n, catalan(n)));
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}
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println("%2d --> %,d".fmt(100, catalan(100)));
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1
Task/Catalan-numbers/Zkl/catalan-numbers-2.zkl
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1
Task/Catalan-numbers/Zkl/catalan-numbers-2.zkl
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@ -0,0 +1 @@
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fcn catalan(n){ (1).reduce(n,fcn(p,n){ 2*(2*n-1)*p/(n+1) },1) }
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