combinatorics.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
@testset "binomial" begin
@test binomial(5,-1) == 0
@test binomial(5,10) == 0
@test binomial(5,3) == 10
@test binomial(2,1) == 2
@test binomial(1,2) == 0
@test binomial(-2,1) == -2 # let's agree
@test binomial(2,-1) == 0
#Issue 6154
@test binomial(Int32(34), Int32(15)) == binomial(BigInt(34), BigInt(15)) == 1855967520
@test binomial(Int64(67), Int64(29)) == binomial(BigInt(67), BigInt(29)) == 7886597962249166160
@test binomial(Int128(131), Int128(62)) == binomial(BigInt(131), BigInt(62)) == 157311720980559117816198361912717812000
@test_throws InexactError binomial(Int64(67), Int64(30))
end
@testset "permutations" begin
p = shuffle([1:1000;])
@test isperm(p)
@test all(invperm(invperm(p)) .== p)
@test isperm(()) == true
@test isperm((1,)) == true
@test isperm((2,)) == false
@test isperm((1,2)) == true
@test isperm((2,1)) == true
@test isperm((2,2)) == false
@test isperm((1,3)) == false
@test invperm(()) == ()
@test invperm((1,)) == (1,)
@test invperm((1,2)) == (1,2)
@test invperm((2,1)) == (2,1)
@test_throws ArgumentError invperm((1,3))
push!(p, 1)
@test !isperm(p)
a = randcycle(10)
@test invpermute!(permute!([1:10;], a),a) == [1:10;]
# PR 12785
let ai = 2:-1:1
@test invpermute!(permute!([1, 2], ai), ai) == [1, 2]
end
end
@testset "factorial" begin
@test factorial(7) == 5040
@test factorial(Int8(7)) == 5040
@test factorial(UInt8(7)) == 5040
@test factorial(Int16(7)) == 5040
@test factorial(UInt16(7)) == 5040
@test factorial(Int32(7)) == 5040
@test factorial(UInt32(7)) == 5040
@test factorial(Int64(7)) == 5040
@test factorial(UInt64(7)) == 5040
@test factorial(Int128(7)) == 5040
@test factorial(UInt128(7)) == 5040
@test factorial(0) == 1
@test_throws DomainError factorial(-1)
@test factorial(Int64(20)) == 2432902008176640000
# issue #6579
@test_throws OverflowError factorial(Int64(21))
@test typeof(factorial(Int8(2))) == typeof(factorial(Int8(1)))
if Int === Int32
@test factorial(Int32(12)) === Int32(479001600)
@test_throws OverflowError factorial(Int32(13))
end
_fact_table64 =
Int64[1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,
87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,
121645100408832000,2432902008176640000]
_fact_table128 =
UInt128[0x00000000000000000000000000000001, 0x00000000000000000000000000000002,
0x00000000000000000000000000000006, 0x00000000000000000000000000000018,
0x00000000000000000000000000000078, 0x000000000000000000000000000002d0,
0x000000000000000000000000000013b0, 0x00000000000000000000000000009d80,
0x00000000000000000000000000058980, 0x00000000000000000000000000375f00,
0x00000000000000000000000002611500, 0x0000000000000000000000001c8cfc00,
0x0000000000000000000000017328cc00, 0x0000000000000000000000144c3b2800,
0x00000000000000000000013077775800, 0x00000000000000000000130777758000,
0x00000000000000000001437eeecd8000, 0x00000000000000000016beecca730000,
0x000000000000000001b02b9306890000, 0x000000000000000021c3677c82b40000,
0x0000000000000002c5077d36b8c40000, 0x000000000000003ceea4c2b3e0d80000,
0x000000000000057970cd7e2933680000, 0x00000000000083629343d3dcd1c00000,
0x00000000000cd4a0619fb0907bc00000, 0x00000000014d9849ea37eeac91800000,
0x00000000232f0fcbb3e62c3358800000, 0x00000003d925ba47ad2cd59dae000000,
0x0000006f99461a1e9e1432dcb6000000, 0x00000d13f6370f96865df5dd54000000,
0x0001956ad0aae33a4560c5cd2c000000, 0x0032ad5a155c6748ac18b9a580000000,
0x0688589cc0e9505e2f2fee5580000000, 0xde1bc4d19efcac82445da75b00000000]
for expected in Any[_fact_table64, _fact_table128]
for (n, factn) in enumerate(expected)
@test factorial(oftype(factn, n)) === factn
end
end
end