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Combinations and permutations: Difference between revisions
→{{header|Julia}}: A new entry for Julia
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Line 524:
60 | big_combination(53) #=> 386206920.0000046
145 | big_permutation(133) #=> 1.
170 | big_permutation(133) #=> 5.272846415658284e+263
=={{header|Julia}}==
Infix operators are interpreted by Julia's parser, and (to my knowledge) it isn't possible to define arbitrary characters as such operators. However one can define Unicode "Symbol, Math" characters as infix operators. This solution uses ⊞ for combinations and ⊠ for permutations. An alternative to using the <tt>FloatingPoint</tt> versions of these operators for large numbers would be to use arbitrary precision integers, <tt>BigInt</tt>.
'''Functions'''
<lang Julia>
function Base.binomial{T<:FloatingPoint}(n::T, k::T)
exp(lfact(n) - lfact(n - k) - lfact(k))
end
function Base.factorial{T<:FloatingPoint}(n::T, k::T)
exp(lfact(n) - lfact(k))
end
⊞{T<:Real}(n::T, k::T) = binomial(n, k)
⊠{T<:Real}(n::T, k::T) = factorial(n, n-k)
</lang>
'''Main'''
<lang Julia>
function picknk{T<:Integer}(lo::T, hi::T)
n = rand(lo:hi)
k = rand(1:n)
return (n, k)
end
nsamp = 10
print("Tests of the combinations (⊞) and permutations (⊠) operators for ")
println("integer values.")
println()
lo, hi = 1, 12
print(nsamp, " samples of n ⊠ k with n in [", lo, ", ", hi, "] ")
println("and k in [1, n].")
for i in 1:nsamp
(n, k) = picknk(lo, hi)
println(@sprintf " %2d ⊠ %2d = %18d" n k n ⊠ k)
end
lo, hi = 10, 60
println()
print(nsamp, " samples of n ⊞ k with n in [", lo, ", ", hi, "] ")
println("and k in [1, n].")
for i in 1:nsamp
(n, k) = picknk(lo, hi)
println(@sprintf " %2d ⊞ %2d = %18d" n k n ⊞ k)
end
println()
print("Tests of the combinations (⊞) and permutations (⊠) operators for ")
println("(big) float values.")
println()
lo, hi = 5, 15000
print(nsamp, " samples of n ⊠ k with n in [", lo, ", ", hi, "] ")
println("and k in [1, n].")
for i in 1:nsamp
(n, k) = picknk(lo, hi)
n = BigFloat(n)
k = BigFloat(k)
println(@sprintf " %7.1f ⊠ %7.1f = %10.6e" n k n ⊠ k)
end
lo, hi = 100, 1000
println()
print(nsamp, " samples of n ⊞ k with n in [", lo, ", ", hi, "] ")
println("and k in [1, n].")
for i in 1:nsamp
(n, k) = picknk(lo, hi)
n = BigFloat(n)
k = BigFloat(k)
println(@sprintf " %7.1f ⊞ %7.1f = %10.6e" n k n ⊞ k)
end
</lang>
{{out}}
<pre>
Tests of the combinations (⊞) and permutations (⊠) operators for integer values.
10 samples of n ⊠ k with n in [1, 12] and k in [1, n].
4 ⊠ 2 = 12
9 ⊠ 2 = 72
2 ⊠ 1 = 2
8 ⊠ 2 = 56
7 ⊠ 5 = 2520
4 ⊠ 2 = 12
9 ⊠ 8 = 362880
11 ⊠ 6 = 332640
1 ⊠ 1 = 1
8 ⊠ 5 = 6720
10 samples of n ⊞ k with n in [10, 60] and k in [1, n].
58 ⊞ 26 = 22150361247847371
22 ⊞ 21 = 22
32 ⊞ 30 = 496
11 ⊞ 4 = 330
32 ⊞ 29 = 4960
16 ⊞ 7 = 11440
31 ⊞ 25 = 736281
13 ⊞ 13 = 1
43 ⊞ 28 = 151532656696
49 ⊞ 37 = 92263734836
Tests of the combinations (⊞) and permutations (⊠) operators for (big) float values.
10 samples of n ⊠ k with n in [5, 15000] and k in [1, n].
8375.0 ⊠ 5578.0 = 2.200496e+20792
1556.0 ⊠ 592.0 = 1.313059e+1833
1234.0 ⊠ 910.0 = 2.231762e+2606
12531.0 ⊠ 9361.0 = 2.339542e+36188
12418.0 ⊠ 6119.0 = 1.049662e+24251
9435.0 ⊠ 8960.0 = 4.273644e+32339
9430.0 ⊠ 5385.0 = 1.471741e+20551
9876.0 ⊠ 5386.0 = 9.073417e+20712
941.0 ⊠ 911.0 = 8.689430e+2358
8145.0 ⊠ 4357.0 = 1.368129e+16407
10 samples of n ⊞ k with n in [100, 1000] and k in [1, n].
757.0 ⊞ 237.0 = 6.813837e+202
457.0 ⊞ 413.0 = 4.816707e+61
493.0 ⊞ 372.0 = 8.607443e+117
206.0 ⊞ 26.0 = 6.911828e+32
432.0 ⊞ 300.0 = 1.248351e+114
650.0 ⊞ 469.0 = 3.284854e+165
203.0 ⊞ 115.0 = 1.198089e+59
583.0 ⊞ 429.0 = 5.700279e+144
329.0 ⊞ 34.0 = 2.225630e+46
464.0 ⊞ 178.0 = 5.615925e+132
</pre>
=={{header|Mathematica}}==
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