I want to perform a big mod (%) operation like the example below:
083123456787654325500479087654 % 55
As you can see this number is bigger than Int64.max (9223372036854775807)
I tried to parse this "083123456787654325500479087654" from string into a Decimal but I can't perform mod operation with two Decimals.
Any suggestions?
You can define a custom mod operator between two decimals such as follow. I haven't the time to test for all scenarios. So I'm selecting the simplest case: modulo between 2 positive numbers. You can expand it to suit your situation:
func % (lhs: Decimal, rhs: Decimal) -> Decimal {
precondition(lhs > 0 && rhs > 0)
if lhs < rhs {
return lhs
} else if lhs == rhs {
return 0
}
var quotient = lhs / rhs
var rounded = Decimal()
NSDecimalRound(&rounded, "ient, 0, .down)
return lhs - (rounded * rhs)
}
let a = Decimal(string: "083123456787654325500479087654")!
print(a % 55)
The result is 49.
Related
This question already has answers here:
Modulus power of big numbers
(4 answers)
Closed 4 years ago.
I have to calculate power of two long integers in swift.
Swift gives an error of NaN (not a number) and fails to answer.
e.g
pow(2907,1177)
The main process id to calculate power and get remainder (a^b % n) where a= 2907, b= 1177, n= 1211
Any guidelines how to solve it?
You will have to use either 1. an external framework or 2. do it by yourself.
1. External Framework:
I think you can try : https://github.com/mkrd/Swift-Big-Integer
let a = BInt(2907)
let b = 1177
let n = BInt(1211)
let result = (a ** b) % n
print(result) // prints 331
Note: Cocoapods import failed so I just imported this file for it to work: https://github.com/mkrd/Swift-Big-Integer/tree/master/Sources
2. DIY:
Using the answer of Modulus power of big numbers
func powerMod(base: Int, exponent: Int, modulus: Int) -> Int {
guard base > 0 && exponent >= 0 && modulus > 0
else { return -1 }
var base = base
var exponent = exponent
var result = 1
while exponent > 0 {
if exponent % 2 == 1 {
result = (result * base) % modulus
}
base = (base * base) % modulus
exponent = exponent / 2
}
return result
}
let result = powerMod(base: 2907, exponent: 1177, modulus: 1211)
print(result) // prints 331
3. Bonus: Using the same as 2. but with custom ternary operator thanks to http://natecook.com/blog/2014/10/ternary-operators-in-swift/
precedencegroup ModularityLeft {
higherThan: ComparisonPrecedence
lowerThan: AdditionPrecedence
}
precedencegroup ModularityRight {
higherThan: ModularityLeft
lowerThan: AdditionPrecedence
}
infix operator *%* : ModularityLeft
infix operator %*% : ModularityRight
func %*%(exponent: Int, modulus: Int) -> (Int) -> Int {
return { base in
guard base > 0 && exponent >= 0 && modulus > 0
else { return -1 }
var base = base
var exponent = exponent
var result = 1
while exponent > 0 {
if exponent % 2 == 1 {
result = (result * base) % modulus
}
base = (base * base) % modulus
exponent = exponent / 2
}
return result
}
}
func *%*(lhs: Int, rhs: (Int) -> Int) -> Int {
return rhs(lhs)
}
And then you can just call:
let result = 2907 *%* 1177 %*% 1211
Additional information:
Just for information in binary 2907^1177 takes 13542bits...
https://www.wolframalpha.com/input/?i=2907%5E1177+in+binary
It takes a 4kb string to store it in base 10 : https://www.wolframalpha.com/input/?i=2907%5E1177
I have been working on a hacker rank problem where I have to print a number which is a factorial of 25. Here is the code I used.
func extraLongFactorials(n: Int) -> Void {
let factorialNumber = factorial(number: n)
var arrayForStorage: [Int] = []
var loop = factorialNumber
while (loop > 0) {
let digit = loop.truncatingRemainder(dividingBy: 10)
arrayForStorage.append(Int(digit))
loop /= 10
}
arrayForStorage = arrayForStorage.reversed()
var returnString = ""
for element in arrayForStorage {
returnString = "\(returnString)\(element)"
}
print(returnString)
}
func factorial(number: Int) -> Double {
if number == 0 || number == 1 {
return 1
} else if number == 2 {
return 2
} else {
return Double(number) * factorial(number: number - 1)
}
}
But when I try to print the factorial number it just prints 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000015511210043330982408266888 when it should print
15511210043330985984000000.
I think for a Double number truncatingRemainder(dividingBy: 10) method is not giving me the exact number of the remainder. Because when I tried to print the truncatingRemainder of 15511210043330985984000000 it is giving me as 8. Here is the code.
let number: Double = 15511210043330985984000000
print(number.truncatingRemainder(dividingBy: 10))
So finally I didn't find any solution for the problem of how to split the large number and add it into an array. Looking forward for the solution.
Type Double stores a number as a mantissa and an exponent. The mantissa represents the significant figures of the number, and the exponent represents the magnitude of the number. A Double can only represent about 16 significant figures, and your number has 26 digits, so you can't accurately store 15511210043330985984000000 in a Double.
let number1: Double = 15511210043330985984000000
let number2: Double = 15511210043330985984012345
if number1 == number2 {
print("they are equal")
}
they are equal
You will need another approach to find large factorials like the one shown in this answer.
I'm looking to create a function that returns a solve for x math equation that can be preformed in ones head (Clearly thats a bit subjective but I'm not sure how else to phrase it).
Example problem: (x - 15)/10 = 6
Note: Only 1 x in the equation
I want to use the operations +, -, *, /, sqrt (Only applied to X -> sqrt(x))
I know that let mathExpression = NSExpression(format: question) converts strings into math equations but when solving for x I'm not sure how to go about doing this.
I previously asked Generating random doable math problems swift for non solving for x problems but I'm not sure how to convert that answer into solving for x
Edit: Goal is to generate an equation and have the user solve for the variable.
Since all you want is a string representing an equation and a value for x, you don't need to do any solving. Just start with x and transform it until you have a nice equation. Here's a sample: (copy and paste it into a Playground to try it out)
import UIKit
enum Operation: String {
case addition = "+"
case subtraction = "-"
case multiplication = "*"
case division = "/"
static func all() -> [Operation] {
return [.addition, .subtraction, .multiplication, .division]
}
static func random() -> Operation {
let all = Operation.all()
let selection = Int(arc4random_uniform(UInt32(all.count)))
return all[selection]
}
}
func addNewTerm(formula: String, result: Int) -> (formula: String, result: Int) {
// choose a random number and operation
let operation = Operation.random()
let number = chooseRandomNumberFor(operation: operation, on: result)
// apply to the left side
let newFormula = applyTermTo(formula: formula, number: number, operation: operation)
// apply to the right side
let newResult = applyTermTo(result: result, number: number, operation: operation)
return (newFormula, newResult)
}
func applyTermTo(formula: String, number:Int, operation:Operation) -> String {
return "\(formula) \(operation.rawValue) \(number)"
}
func applyTermTo(result: Int, number:Int, operation:Operation) -> Int {
switch(operation) {
case .addition: return result + number
case .subtraction: return result - number
case .multiplication: return result * number
case .division: return result / number
}
}
func chooseRandomNumberFor(operation: Operation, on number: Int) -> Int {
switch(operation) {
case .addition, .subtraction, .multiplication:
return Int(arc4random_uniform(10) + 1)
case .division:
// add code here to find integer factors
return 1
}
}
func generateFormula(_ numTerms:Int = 1) -> (String, Int) {
let x = Int(arc4random_uniform(10))
var leftSide = "x"
var result = x
for i in 1...numTerms {
(leftSide, result) = addNewTerm(formula: leftSide, result: result)
if i < numTerms {
leftSide = "(" + leftSide + ")"
}
}
let formula = "\(leftSide) = \(result)"
return (formula, x)
}
func printFormula(_ numTerms:Int = 1) {
let (formula, x) = generateFormula(numTerms)
print(formula, " x = ", x)
}
for i in 1...30 {
printFormula(Int(arc4random_uniform(3)) + 1)
}
There are some things missing. The sqrt() function will have to be implemented separately. And for division to be useful, you'll have to add in a system to find factors (since you presumably want the results to be integers). Depending on what sort of output you want, there's a lot more work to do, but this should get you started.
Here's sample output:
(x + 10) - 5 = 11 x = 6
((x + 6) + 6) - 1 = 20 x = 9
x - 2 = 5 x = 7
((x + 3) * 5) - 6 = 39 x = 6
(x / 1) + 6 = 11 x = 5
(x * 6) * 3 = 54 x = 3
x * 9 = 54 x = 6
((x / 1) - 6) + 8 = 11 x = 9
Okay, let’s assume from you saying “Note: Only 1 x in the equation” that what you want is a linear equation of the form y = 0 = β1*x + β0, where β0 and β1 are the slope and intercept coefficients, respectively.
The inverse of (or solution to) any linear equation is given by x = -β0/β1. So what you really need to do is generate random integers β0 and β1 to create your equation. But since it should be “solvable” in someone’s head, you probably want β0 to be divisible by β1, and furthermore, for β1 and β0/β1 to be less than or equal to 12, since this is the upper limit of the commonly known multiplication tables. In this case, just generate a random integer β1 ≤ 12, and β0 equal to β1 times some integer n, 0 ≤ n ≤ 12.
If you want to allow simple fractional solutions like 2/3, just multiply the denominator and the numerator into β0 and β1, respectively, taking care to prevent the numerator or denominator from getting too large (12 is again a good limit).
Since you probably want to make y non-zero, just generate a third random integer y between -12 and 12, and change your output equation to y = β1*x + β0 + y.
Since you mentioned √ could occur over the x variable only, that is pretty easy to add; the solution (to 0 = β1*sqrt(x) + β0) is just x = (β0/β1)**2.
Here is some very simple (and very problematic) code for generating random integers to get you started:
import func Glibc.srand
import func Glibc.rand
import func Glibc.time
srand(UInt32(time(nil)))
print(rand() % 12)
There are a great many answers on this website that deal with better ways to generate random integers.
I am making fuction that calculate factorial in swift. like this
func factorial(factorialNumber: UInt64) -> UInt64 {
if factorialNumber == 0 {
return 1
} else {
return factorialNumber * factorial(factorialNumber - 1)
}
}
let x = factorial(20)
this fuction can calculate untill 20.
I think factorial(21) value bigger than UINT64_MAX.
then How to calculate the 21! (21 factorial) in swift?
func factorial(_ n: Int) -> Double {
return (1...n).map(Double.init).reduce(1.0, *)
}
(1...n): We create an array of all the numbers that are involved in the operation (i.e: [1, 2, 3, ...]).
map(Double.init): We change from Int to Double because we can represent bigger numbers with Doubles than with Ints (https://en.wikipedia.org/wiki/Double-precision_floating-point_format). So, we now have the array of all the numbers that are involved in the operation as Doubles (i.e: [1.0, 2.0, 3.0, ...]).
reduce(1.0, *): We start multiplying 1.0 with the first element in the array (1.0*1.0 = 1.0), then the result of that with the next one (1.0*2.0 = 2.0), then the result of that with the next one (2.0*3.0 = 6.0), and so on.
Step 2 is to avoid the overflow issue.
Step 3 is to save us from explicitly defining a variable for keeping track of the partial results.
Unsigned 64 bit integer has a maximum value of 18,446,744,073,709,551,615. While 21! = 51,090,942,171,709,440,000. For this kind of case, you need a Big Integer type. I found a question about Big Integer in Swift. There's a library for Big Integer in that link.
BigInteger equivalent in Swift?
Did you think about using a double perhaps? Or NSDecimalNumber?
Also calling the same function recursively is really bad performance wise.
How about using a loop:
let value = number.intValue - 1
var product = NSDecimalNumber(value: number.intValue)
for i in (1...value).reversed() {
product = product.multiplying(by: NSDecimalNumber(value: i))
}
Here's a function that accepts any type that conforms to the Numeric protocol, which are all builtin number types.
func factorial<N: Numeric>(_ x: N) -> N {
x == 0 ? 1 : x * factorial(x - 1)
}
First we need to declare temp variable of type double so it can hold size of number.
Then we create a function that takes a parameter of type double.
Then we check, if the number equal 0 we can return or do nothing. We have an if condition so we can break the recursion of the function. Finally we return temp, which holds the factorial of given number.
var temp:Double = 1.0
func factorial(x:Double) -> Double{
if(x==0){
//do nothing
}else{
factorial(x: x-1)
temp *= x
}
return temp
}
factorial(x: 21.0)
I make function calculate factorial like this:
func factorialNumber( namber : Int ) -> Int {
var x = 1
for i in 1...namber {
x *= i
}
return x
}
print ( factorialNumber (namber : 5 ))
If you are willing to give up precision you can use a Double to roughly calculate factorials up to 170:
func factorial(_ n: Int) -> Double {
if n == 0 {
return 1
}
var a: Double = 1
for i in 1...n {
a *= Double(i)
}
return a
}
If not, use a big integer library.
func factoruial(_ num:Int) -> Int{
if num == 0 || num == 1{
return 1
}else{
return(num*factoruial(num - 1))
}
}
Using recursion to solve this problem:
func factorial(_ n: UInt) -> UInt {
return n < 2 ? 1 : n*factorial(n - 1)
}
func factorial(a: Int) -> Int {
return a == 1 ? a : a * factorial(a: a - 1)
}
print(factorial(a : 5))
print(factorial(a: 9))
any of you knows how can I check if the division remainder is integer or zero?
if ( integer ( 3/2))
You should use the modulo operator like this
// a,b are ints
if ( a % b == 0) {
// remainder 0
} else
{
// b does not divide a evenly
}
It sounds like what you are looking for is the modulo operator %, which will give you the remainder of an operation.
3 % 2 // yields 1
3 % 1 // yields 0
3 % 4 // yields 1
However, if you want to actually perform the division first, you may need something a bit more complex, such as the following:
//Perform the division, then take the remainder modulo 1, which will
//yield any decimal values, which then you can compare to 0 to determine if it is
//an integer
if((a / b) % 1 > 0))
{
//All non-integer values go here
}
else
{
//All integer values go here
}
Walkthrough
(3 / 2) // yields 1.5
1.5 % 1 // yields 0.5
0.5 > 0 // true
swift 3:
if a.truncatingRemainder(dividingBy: b) == 0 {
//All integer values go here
}else{
//All non-integer values go here
}
You can use the below code to know which type of instance it is.
var val = 3/2
var integerType = Mirror(reflecting: val)
if integerType.subjectType == Int.self {
print("Yes, the value is an integer")
}else{
print("No, the value is not an integer")
}
let me know if the above was useful.
Swift 5
if numberOne.isMultiple(of: numberTwo) { ... }
Swift 4 or less
if numberOne % numberTwo == 0 { ... }
Swift 2.0
print(Int(Float(9) % Float(4))) // result 1