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Combinations and permutations: Difference between revisions
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return(exp(lnfactorial(n)-lnfactorial(n-k)))
}</lang>
=={{header|Swift}}==
{{trans|Kotlin}}
Using AttaSwift's BigInt
<lang swift>import BigInt
func permutations(n: Int, k: Int) -> BigInt {
let l = n - k + 1
guard l <= n else {
return 1
}
return (l...n).reduce(BigInt(1), { $0 * BigInt($1) })
}
func combinations(n: Int, k: Int) -> BigInt {
let fact = {() -> BigInt in
guard k > 1 else {
return 1
}
return (2...k).map({ BigInt($0) }).reduce(1, *)
}()
return permutations(n: n, k: k) / fact
}
print("Sample of permutations from 1 to 12")
for i in 1...12 {
print("\(i) P \(i / 3) = \(permutations(n: i, k: i / 3))")
}
print("\nSample of combinations from 10 to 60")
for i in stride(from: 10, through: 60, by: 10) {
print("\(i) C \(i / 3) = \(combinations(n: i, k: i / 3))")
}
print("\nSample of permutations from 5 to 15,000")
for i in [5, 50, 500, 1000, 5000, 15000] {
let k = i / 3
let res = permutations(n: i, k: k).description
let extra = res.count > 40 ? "... (\(res.count - 40) more digits)" : ""
print("\(i) P \(k) = \(res.prefix(40))\(extra)")
}
print("\nSample of combinations from 100 to 1000")
for i in stride(from: 100, through: 1000, by: 100) {
let k = i / 3
let res = combinations(n: i, k: k).description
let extra = res.count > 40 ? "... (\(res.count - 40) more digits)" : ""
print("\(i) C \(k) = \(res.prefix(40))\(extra)")
}</lang>
{{out}}
<pre>Sample of permutations from 1 to 12
1 P 0 = 1
2 P 0 = 1
3 P 1 = 3
4 P 1 = 4
5 P 1 = 5
6 P 2 = 30
7 P 2 = 42
8 P 2 = 56
9 P 3 = 504
10 P 3 = 720
11 P 3 = 990
12 P 4 = 11880
Sample of combinations from 10 to 60
10 C 3 = 120
20 C 6 = 38760
30 C 10 = 30045015
40 C 13 = 12033222880
50 C 16 = 4923689695575
60 C 20 = 4191844505805495
Sample of permutations from 5 to 15,000
5 P 1 = 5
50 P 16 = 103017324974226408345600000
500 P 166 = 3534874921742942787609361826601762306844... (395 more digits)
1000 P 333 = 5969326288503415089039701765900784280998... (932 more digits)
5000 P 1666 = 6856745757255674275484536940248896062234... (5986 more digits)
15000 P 5000 = 9649853988727493922014858805931295980792... (20430 more digits)
Sample of combinations from 100 to 1000
100 C 33 = 294692427022540894366527900
200 C 66 = 7269752545169278341527066651192738976755... (14 more digits)
300 C 100 = 4158251463258564744783383526326405580280... (42 more digits)
400 C 133 = 1257948684182108702133348475651965004491... (70 more digits)
500 C 166 = 3926028386194422755220408345072331428197... (97 more digits)
600 C 200 = 2506017783221402805005616770513228835202... (125 more digits)
700 C 233 = 8103203563339599904740453644031138232944... (152 more digits)
800 C 266 = 2645623362683627034288829299556124255091... (180 more digits)
900 C 300 = 1743356373296446642960730765085718347630... (208 more digits)
1000 C 333 = 5776134553147651669777486323549601722339... (235 more digits)</pre>
=={{header|Tcl}}==
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