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0.8.0 in progress
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Nikos M committed Jan 26, 2017
1 parent 0eebc65 commit 7538088
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83 changes: 55 additions & 28 deletions src/js/Abacus.js
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Original file line number Diff line number Diff line change
Expand Up @@ -666,27 +666,33 @@ function factorial( n, m )
factorial.mem1 = {};
factorial.mem2 = {};
factorial.mem3 = {};
function p_nkm( n, k, m )
function p_nkab( n, k, a, b )
{
// recursively compute the partition count using the recursive relation:
// http://en.wikipedia.org/wiki/Partition_(number_theory)#Partition_function
// http://www.programminglogic.com/integer-partition-algorithm/
// CLOSED FORM FORMULA FOR THE NUMBER OF RESTRICTED COMPOSITIONS (http://www.fmf.uni-lj.si/~jaklicg/papers/compositions_revision.pdf)
// compute number of integer partitions of n
// into exactly k parts having m as max value
// m + k-1 <= n <= k*m
// into exactly k parts having summands between a and b (inclusive)
// a + k-1 <= n <= k*b
var Arithmetic = Abacus.Arithmetic, add = Arithmetic.add,
key, p = Arithmetic.O;
if ( ((m === n) && (1 === k)) || ((k === n) && (1 === m)) ) return Arithmetic.I;
if ( (m+k > n+1) || (k*m < n) ) return p;
key = String(n)+','+String(k)+','+String(m);
if ( null == p_nkm.mem[key] )
if ( (0 > n) || (0 >= k) || (a > b) || (a+k > n+1) || (k*b < n) ) return p;
if ( ((b === n) && (1 === k)) || ((k === n) && (1 === b)) ) return Arithmetic.I;
//if ( a === b ) return k*a === n ? Arithmetic.I : p;
key = String(n)+','+String(k)+','+String(a)+','+String(b);
if ( null == p_nkab.mem[key] )
{
// compute it directly
p_nkm.mem[key] = operate(function(p, j){
return add(p, p_nkm(n-m, k-1, j));
}, p, null, stdMath.max(1, stdMath.ceil((n-m)/(k-1))), stdMath.min(m, n-m-k+2));
return p_nkm.mem[key];
//p_nkab(n-k*(a-1), k, 1, b-a+1);
n = n-k*(a-1); b = b-a+1;
p_nkab.mem[key] = operate(function(p, j){
return add(p, p_nkab(n-b, k-1, 1, j));
}, p, null, stdMath.max(1, stdMath.ceil((n-b)/(k-1))), stdMath.min(b, n-b-k+2), 1);
}
return p_nkab.mem[key];
}
p_nkm.mem = {};
p_nkab.mem = {};
function partitions( n, K /*exactly K parts or null*/, M /*max part is M or null*/ )
{
K = null == K ? null : K|0; M = null == M ? null : M|0;
Expand All @@ -699,35 +705,56 @@ function partitions( n, K /*exactly K parts or null*/, M /*max part is M or null
key = String(n)+'|'+String(K)+'|'+String(M);
if ( null == partitions.mem[key] )
{
for(k=k0; k<=k1; k++)for(m=m0?m0:n-k+1; m>=m1; m--) p = add(p, p_nkm(n, k, m));
partitions.mem[key] = p;
partitions.mem[key] = operate(function(p, k){
return add(p, operate(function(pk, m){
return add(pk, p_nkab(n, k, 1, m));
}, p, null, m1, m0?m0:n-k+1, 1));
}, p, null, k0, k1, 1);
}
return partitions.mem[key];
}
partitions.mem = {};
function c_nkab( n, k, a, b )
{
// recursively compute the composition count using the recursive relation:
// CLOSED FORM FORMULA FOR THE NUMBER OF RESTRICTED COMPOSITIONS (http://www.fmf.uni-lj.si/~jaklicg/papers/compositions_revision.pdf)
// compute number of integer compositions of n
// into exactly k parts having summands between a and b (inclusive)
var Arithmetic = Abacus.Arithmetic, add = Arithmetic.add,
key, c = Arithmetic.O;
if ( (0 > n) || (0 >= k) || (a > b) || (a+k > n+1) || (k*b < n) ) return c;
if ( a === b ) return k*a === n ? Arithmetic.I : c;
if ( n === b ) return factorial(n-k*a+k-1, k-1);
if ( a+1 === b ) return factorial(k, n-k*a);
key = String(n)+','+String(k)+','+String(a)+','+String(b);
if ( null == c_nkab.mem[key] )
{
// compute it directly
c_nkab.mem[key] = operate(function(c, i){
return add(c, c_nkab(i, k-1, a, b));
}, c, null, n-b, n-a, 1);
}
return c_nkab.mem[key];
}
c_nkab.mem = {};
function compositions( n, K /*exactly K parts or null*/, M /*max part is M or null*/ )
{
K = null == K ? null : K|0; M = null == M ? null : M|0;
var mul = Abacus.Arithmetic.mul, key, k, c = Abacus.Arithmetic.O;
var key, c = Abacus.Arithmetic.O, add = Abacus.Arithmetic.add;
if ( (0 > n) || (K && M && ((K+M > n+1) || (K*M < n))) || (M && M > n) || (K && K > n) ) return c;
key = String(n)+'|'+String(K)+'|'+String(M);
if ( null == compositions.mem[key] )
{
if ( /*K &&*/ M )
{
//k = stdMath.floor(n/M)||1;
//compositions.mem[key] = mul(factorial(stdMath.min(M,n-M)-1, K-1-k),K-1);
// TODO
compositions.mem[key] = c;
}
if ( K && M )
compositions.mem[key] = c_nkab(n, K, 1, M);
else if ( K )
{
compositions.mem[key] = factorial(n-1, K-1);
}
compositions.mem[key] = c_nkab(n, K, 1, n);
else if ( M )
compositions.mem[key] = operate(function(c, k){
return add(c, c_nkab(n, k, 1, M));
}, c, null, stdMath.ceil(n/M), n, 1);
else
{
compositions.mem[key] = pow2(n-1);
}
compositions.mem[key] = 1 <= n ? pow2(n-1) : Arithmetic.I;
}
return compositions.mem[key];
}
Expand Down
12 changes: 6 additions & 6 deletions test/restricted_compositions.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@ Abacus.Compositions (VERSION = 0.8.0)
---
o = Abacus.Partition(7,{type:"composition","max=":4})
o.total()
0
32
o.next()
[ 1, 1, 1, 4 ]
o.hasNext()
Expand All @@ -20,11 +20,11 @@ o.order("lex,reflected")
o.order("lex,reversed")
[ 4, 1, 1, 1 ]
o.random()
[ 4, 1, 1, 1 ]
[ 4, 1, 2 ]
o.dispose()
o = Abacus.Partition(8,{type:"composition","max=":4})
o.total()
0
64
o.next()
[ 1, 1, 1, 5 ]
o.hasNext()
Expand All @@ -42,7 +42,7 @@ o.order("lex,reflected")
o.order("lex,reversed")
[ 5, 1, 1, 1 ]
o.random()
[ 2, 4, 2 ]
[ 3, 4, 1 ]
o.dispose()
o = Abacus.Partition(7,{type:"composition","parts=":4})
o.total()
Expand Down Expand Up @@ -140,7 +140,7 @@ o.order("lex,reversed")
[ 1, 1, 2, 3 ]
[ 1, 1, 1, 4 ]
o.random()
[ 3, 1, 2, 1 ]
[ 3, 2, 1, 1 ]
o.dispose()
o = Abacus.Partition(8,{type:"composition","parts=":4})
o.total()
Expand Down Expand Up @@ -298,5 +298,5 @@ o.order("lex,reversed")
[ 1, 1, 2, 4 ]
[ 1, 1, 1, 5 ]
o.random()
[ 1, 1, 5, 1 ]
[ 2, 1, 4, 1 ]
o.dispose()
20 changes: 10 additions & 10 deletions test/restricted_partitions.txt
View file
Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@ o.order("lex,reversed")
[ 4, 2, 1 ]
[ 4, 1, 1, 1 ]
o.random()
[ 4, 3 ]
[ 4, 1, 1, 1 ]
o.dispose()
o = Abacus.Partition(8,{"max=":4})
o.total()
Expand Down Expand Up @@ -54,7 +54,7 @@ o.order("lex,reversed")
[ 4, 2, 1, 1 ]
[ 4, 1, 1, 1, 1 ]
o.random()
[ 4, 2, 2 ]
[ 4, 3, 1 ]
o.dispose()
o = Abacus.Partition(11,{"max=":5})
o.total()
Expand Down Expand Up @@ -106,7 +106,7 @@ o.order("lex,reversed")
[ 5, 2, 1, 1, 1, 1 ]
[ 5, 1, 1, 1, 1, 1, 1 ]
o.random()
[ 5, 2, 2, 1, 1 ]
[ 5, 4, 2 ]
o.dispose()
o = Abacus.Partition(12,{"max=":4})
o.total()
Expand Down Expand Up @@ -178,7 +178,7 @@ o.order("lex,reversed")
[ 4, 2, 1, 1, 1, 1, 1, 1 ]
[ 4, 1, 1, 1, 1, 1, 1, 1, 1 ]
o.random()
[ 4, 2, 2, 1, 1, 1, 1 ]
[ 4, 3, 2, 1, 1, 1 ]
o.dispose()
o = Abacus.Partition(17,{"max=":4})
o.total()
Expand Down Expand Up @@ -346,7 +346,7 @@ o.order("lex,reversed")
[ 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
o.random()
[ 4, 3, 3, 2, 2, 1, 1, 1 ]
[ 4, 3, 3, 3, 1, 1, 1, 1 ]
o.dispose()
o = Abacus.Partition(7,{"parts=":4})
o.total()
Expand All @@ -369,7 +369,7 @@ o.order("lex,reversed")
[ 3, 2, 1, 1 ]
[ 4, 1, 1, 1 ]
o.random()
[ 3, 2, 1, 1 ]
[ 4, 1, 1, 1 ]
o.dispose()
o = Abacus.Partition(8,{"parts=":4})
o.total()
Expand Down Expand Up @@ -400,7 +400,7 @@ o.order("lex,reversed")
[ 4, 2, 1, 1 ]
[ 5, 1, 1, 1 ]
o.random()
[ 3, 3, 1, 1 ]
[ 3, 2, 2, 1 ]
o.dispose()
o = Abacus.Partition(11,{"parts=":5})
o.total()
Expand Down Expand Up @@ -452,7 +452,7 @@ o.order("lex,reversed")
[ 6, 2, 1, 1, 1 ]
[ 7, 1, 1, 1, 1 ]
o.random()
[ 4, 4, 1, 1, 1 ]
[ 4, 3, 2, 1, 1 ]
o.dispose()
o = Abacus.Partition(12,{"parts=":4})
o.total()
Expand Down Expand Up @@ -523,7 +523,7 @@ o.order("lex,reversed")
[ 8, 2, 1, 1 ]
[ 9, 1, 1, 1 ]
o.random()
[ 6, 3, 2, 1 ]
[ 9, 1, 1, 1 ]
o.dispose()
o = Abacus.Partition(20,{"parts=":4})
o.total()
Expand Down Expand Up @@ -790,7 +790,7 @@ o.order("lex,reversed")
[ 16, 2, 1, 1 ]
[ 17, 1, 1, 1 ]
o.random()
[ 15, 3, 1, 1 ]
[ 9, 5, 4, 2 ]
o.dispose()
o = Abacus.Partition(12,{"parts=":4,"max=":4})
o.total()
Expand Down

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