#/usr/bin/env julia function factorial( n::Integer )::Integer if n == 0 error("put zero in factorial") end return reduce(*, 1:n) end factorial(arr) = Integer(factorial( length(arr) - 1)) #basic permutation P(n,r) function permut( n, p::Integer = 0 )::Integer nLength = length(n) pLength = length(p) if nLength <= 0 || pLength > nLength error("illegal input") end return Integer( factorial(nLength) / factorial(pLength - p) ) end #n/(k1!*k2!*k3!) ..... function divide_by_fact(n)::Integer nLength = length(n) if nLength <= 0 error("illegal input") end nSet = Set(n) nBag = Dict( key => 0 for key in nSet ) for each = n nBag[each] += 1 end step01 = factorial(nLength) step02 = reduce(*, map(factorial,values(filter((k,v)-> v != 1, nBag)))) return Integer( step01 / step02 ) end """ NOT NEEDED #basic circular permutation function count(n)::Integer nLength = length(n) if nLength <= 0 error("illegal input") end return Integer(factorial( nLength - 1)) end """ ans1 = Integer(factorial(10) / factorial(5)) ans2 = permut(1:7) ans3 = divide_by_fact("MASSASAUGA") ans4 = factorial(1:6) ans5 = ( factorial(["A","B","C","D","E","F"]) - ( factorial(["AB","C","D","E","F"]) * factorial(2) + factorial(["AF","B","C","D","E"]) * factorial(2) ) + factorial(["DAF", "B", "C", "E"]) * factorial(2)) println(""" counting arrangement by factorial EX: 10!/5! = ? $(ans1) counting permutation EX: P( 7 , 2 ) P(7, 2) = $(ans2) EX: counting the arrangement of MASSASAUGA 10! / 4! * 3! = $(ans3) EX: There are 6 people at a party sitting at a round table with 6 seats: How many ways can the 6 people be seated? we have $(ans4) to sit Ex: There are 6 people at a party sitting at a round table with 6 seats: A, B, C, D, E and F. A CANNOT sit next to either D or F. How many ways can the 6 people be seated? need use Inclusion-exclusion principle we have $(ans5) way to sit """)