Combinations and permutations: Difference between revisions

145 | big_permutation(133) #=> 1.6801459655817e+243

=={{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>