I am looking at the documentation of a big integer arithmetic in Go and trying to find a method suitable for calculation of a^n (something like pow(a, n) in python).
To my surprise among some straightforward functions like GCD, Binomial and not really straightforward as modinverse I can not find pow. Am I missing it or should I write my own?
func (z *Int) Exp(x, y, m *Int) *Int
Exp sets z = x^y mod |m| (i.e. the sign of m is ignored), and returns z. If y <= 0, the result is 1 mod |m|; if m == nil or m == 0, z = x^y. See Knuth, volume 2, section 4.6.3.
Because I almost finished my own implementation (Daniel's recommendation does not work, because you always have to provide a modulo there) I am adding it here in case someone would like to see how it might be implemented efficiently. Here is Go Playground and my function:
func powBig(a, n int) *big.Int{
tmp := big.NewInt(int64(a))
res := big.NewInt(1)
for n > 0 {
temp := new(big.Int)
if n % 2 == 1 {
temp.Mul(res, tmp)
res = temp
}
temp = new(big.Int)
temp.Mul(tmp, tmp)
tmp = temp
n /= 2
}
return res
}
Related
I keep getting the error "cannot use a (type int) as type float64 in argument to math.Pow, cannot use x (type int) as type float64 in argument to math.Pow,
invalid operation: math.Pow(a, x) % n (mismatched types float64 and int)"
func pPrime(n int) bool {
var nm1 int = n - 1
var x int = nm1/2
a := 1;
for a < n {
if (math.Pow(a, x)) % n == nm1 {
return true
}
}
return false
}
func powInt(x, y int) int {
return int(math.Pow(float64(x), float64(y)))
}
In case you have to reuse it and keep it a little more clean.
If your inputs are int and the output is always expected to be int, then you're dealing with 32-bit numbers. It's more efficient to write your own function to handle this multiplication rather than using math.Pow. math.Pow, as mentioned in the other answers, expects 64-bit values.
Here's a Benchmark comparison for 15^15 (which approaches the upper limits for 32-bit representation):
// IntPow calculates n to the mth power. Since the result is an int, it is assumed that m is a positive power
func IntPow(n, m int) int {
if m == 0 {
return 1
}
result := n
for i := 2; i <= m; i++ {
result *= n
}
return result
}
// MathPow calculates n to the mth power with the math.Pow() function
func MathPow(n, m int) int {
return int(math.Pow(float64(n), float64(m)))
}
The result:
go test -cpu=1 -bench=.
goos: darwin
goarch: amd64
pkg: pow
BenchmarkIntPow15 195415786 6.06 ns/op
BenchmarkMathPow15 40776524 27.8 ns/op
I believe the best solution is that you should write your own function similar to IntPow(m, n int) shown above. My benchmarks show that it runs more than 4x faster on a single CPU core compared to using math.Pow.
Since nobody mentioned an efficient way (logarithmic) to do Pow(x, n) for integers x and n is as follows if you want to implement it yourself:
// Assumption: n >= 0
func PowInts(x, n int) int {
if n == 0 { return 1 }
if n == 1 { return x }
y := PowInts(x, n/2)
if n % 2 == 0 { return y*y }
return x*y*y
}
If you want the exact exponentiation of integers, use (*big.Int).Exp. You're likely to overflow int64 pretty quickly with powers larger than two.
So I am new to Go and fairly inexperienced with programming in general so I hope I don't get downvoted again for asking stupid questions.
I am working my way through the project euler problems and at problem 25 "1000-digit Fibonacci number" I encountered what seems to be strange behavior. The following is the code I wrote that resulted in this behavior.
package main
import (
"fmt"
"math/big"
)
func main() {
index := 2
l := new(big.Int)
pl := big.NewInt(1)
i := big.NewInt(1)
for {
l = i
i.Add(i, pl)
pl = l
index++
if len(i.String()) == 1000 {
break
}
}
fmt.Println(i, "\nindex: ", index)
}
Naturally this did not generate the correct answer so in the process of determining why I discovered that I had inadvertently discovered a neat way to generate powers of 2. I made the following changes and this did generate the correct result.
package main
import (
"fmt"
"math/big"
)
func main() {
index := 2
l := new(big.Int)
pl := big.NewInt(1)
i := big.NewInt(1)
for {
l.Set(i)
i.Add(i, pl)
pl.Set(l)
index++
if len(i.String()) == 1000 {
break
}
}
fmt.Println(i, "\nindex: ", index)
}
My question is what is happening in the first example that causes each big Int variable to be set to the value of i and why this did not generate an error if this was not the correct way to assign a big Int var value? Is i = l, etc a legitimate big Int operation that is simply incorrect for this situation?
The lines
l = i
and
pl = l
aren't doing what you think they are.
l, pl, and i are pointers, and assigning them to each other copies the pointer value, not the big.Int value.
After executing l = i, l is now the same pointer value as i, pointing to the same big.Int. When you use l.Set(i), it sets l's big.Int value to i's big.Int value, but l and i still point to two separate values.
I have implemented a simple function which returns the quotient and remainder when the divisor is the power of 10:
func getQuotientAndRemainder(num int64, digits uint) (int64, int64) {
divisor := int64(math.Pow(10, float64(digits)))
if num >= divisor {
return num / divisor, num % divisor
} else {
return 0, num
}
}
Just curious, except using directly / and % operators, is there any better algorithm to get the the quotient and remainder? Or only in the case when the divisor is the power of 10?
return num / divisor, num % divisor
The "algorithm" is sound and written in arguably the best way possible: expressively. If anything, this part of your code may be overly complicated:
int64(math.Pow(10, float64(digits)))
Converting to and from float64 is arguably sub-optimal. Also, 10 to the power of anything greater than 18 will overflow int64. I suggest you add a sanity check and replace the code with a multiplying loop and measure its performance.
But then: if performance is your concern, just implement it in assembly.
Obviously, you should run some Go benchmarks: Benchmarks, Package testing.
Your solution doesn't look very efficient. Try this:
package main
import "fmt"
func pow(base, exp int64) int64 {
p := int64(1)
for exp > 0 {
if exp&1 != 0 {
p *= base
}
exp >>= 1
base *= base
}
return p
}
func divPow(n, base, exp int64) (q int64, r int64) {
p := pow(base, exp)
q = n / p
r = n - q*p
return q, r
}
func main() {
fmt.Println(divPow(42, 10, 1))
fmt.Println(divPow(-42, 10, 1))
}
Output:
4 2
-4 -2
Benchmark:
BenchmarkDivPow 20000000 77.4 ns/op
BenchmarkGetQuotientAndRemainder 5000000 296 ns/op
I imported the math library in my program, and I was trying to find the minimum of three numbers in the following way:
v1[j+1] = math.Min(v1[j]+1, math.Min(v0[j+1]+1, v0[j]+cost))
where v1 is declared as:
t := "stackoverflow"
v1 := make([]int, len(t)+1)
However, when I run my program I get the following error:
./levenshtein_distance.go:36: cannot use int(v0[j + 1] + 1) (type int) as type float64 in argument to math.Min
I thought it was weird because I have another program where I write
fmt.Println(math.Min(2,3))
and that program outputs 2 without complaining.
so I ended up casting the values as float64, so that math.Min could work:
v1[j+1] = math.Min(float64(v1[j]+1), math.Min(float64(v0[j+1]+1), float64(v0[j]+cost)))
With this approach, I got the following error:
./levenshtein_distance.go:36: cannot use math.Min(int(v1[j] + 1), math.Min(int(v0[j + 1] + 1), int(v0[j] + cost))) (type float64) as type int in assignment
so to get rid of the problem, I just casted the result back to int
I thought this was extremely inefficient and hard to read:
v1[j+1] = int(math.Min(float64(v1[j]+1), math.Min(float64(v0[j+1]+1), float64(v0[j]+cost))))
I also wrote a small minInt function, but I think this should be unnecessary because the other programs that make use of math.Min work just fine when taking integers, so I concluded this has to be a problem of my program and not the library per se.
Is there anything that I'm doing terrible wrong?
Here's a program that you can use to reproduce the issues above, line 36 specifically:
package main
import (
"math"
)
func main() {
LevenshteinDistance("stackoverflow", "stackexchange")
}
func LevenshteinDistance(s string, t string) int {
if s == t {
return 0
}
if len(s) == 0 {
return len(t)
}
if len(t) == 0 {
return len(s)
}
v0 := make([]int, len(t)+1)
v1 := make([]int, len(t)+1)
for i := 0; i < len(v0); i++ {
v0[i] = i
}
for i := 0; i < len(s); i++ {
v1[0] = i + 1
for j := 0; j < len(t); j++ {
cost := 0
if s[i] != t[j] {
cost = 1
}
v1[j+1] = int(math.Min(float64(v1[j]+1), math.Min(float64(v0[j+1]+1), float64(v0[j]+cost))))
}
for j := 0; j < len(v0); j++ {
v0[j] = v1[j]
}
}
return v1[len(t)]
}
Until Go 1.18 a one-off function was the standard way; for example, the stdlib's sort.go does it near the top of the file:
func min(a, b int) int {
if a < b {
return a
}
return b
}
You might still want or need to use this approach so your code works on Go versions below 1.18!
Starting with Go 1.18, you can write a generic min function which is just as efficient at run time as the hand-coded single-type version, but works with any type with < and > operators:
func min[T constraints.Ordered](a, b T) T {
if a < b {
return a
}
return b
}
func main() {
fmt.Println(min(1, 2))
fmt.Println(min(1.5, 2.5))
fmt.Println(min("Hello", "世界"))
}
There's been discussion of updating the stdlib to add generic versions of existing functions, but if that happens it won't be until a later version.
math.Min(2, 3) happened to work because numeric constants in Go are untyped. Beware of treating float64s as a universal number type in general, though, since integers above 2^53 will get rounded if converted to float64.
There is no built-in min or max function for integers, but it’s simple to write your own. Thanks to support for variadic functions we can even compare more integers with just one call:
func MinOf(vars ...int) int {
min := vars[0]
for _, i := range vars {
if min > i {
min = i
}
}
return min
}
Usage:
MinOf(3, 9, 6, 2)
Similarly here is the max function:
func MaxOf(vars ...int) int {
max := vars[0]
for _, i := range vars {
if max < i {
max = i
}
}
return max
}
For example,
package main
import "fmt"
func min(x, y int) int {
if x < y {
return x
}
return y
}
func main() {
t := "stackoverflow"
v0 := make([]int, len(t)+1)
v1 := make([]int, len(t)+1)
cost := 1
j := 0
v1[j+1] = min(v1[j]+1, min(v0[j+1]+1, v0[j]+cost))
fmt.Println(v1[j+1])
}
Output:
1
Though the question is quite old, maybe my package imath can be helpful for someone who does not like reinventing a bicycle. There are few functions, finding minimal of two integers: ix.Min (for int), i8.Min (for int8), ux.Min (for uint) and so on. The package can be obtained with go get, imported in your project by URL and functions referred as typeabbreviation.FuncName, for example:
package main
import (
"fmt"
"<Full URL>/go-imath/ix"
)
func main() {
a, b := 45, -42
fmt.Println(ix.Min(a, b)) // Output: -42
}
As the accepted answer states, with the introduction of generics in go 1.18 it's now possible to write a generic function that provides min/max for different numeric types (there is not one built into the language). And with variadic arguments we can support comparing 2 elements or a longer list of elements.
func Min[T constraints.Ordered](args ...T) T {
min := args[0]
for _, x := range args {
if x < min {
min = x
}
}
return min
}
func Max[T constraints.Ordered](args ...T) T {
max := args[0]
for _, x := range args {
if x > max {
max = x
}
}
return max
}
example calls:
Max(1, 2) // 2
Max(4, 5, 3, 1, 2) // 5
Could use https://github.com/pkg/math:
import (
"fmt"
"github.com/pkg/math"
)
func main() {
a, b := 45, -42
fmt.Println(math.Min(a, b)) // Output: -42
}
Since the issue has already been resolved, I would like to add a few words. Always remember that the math package in Golang operates on float64. You can use type conversion to cast int into a float64. Keep in mind to account for type ranges. For example, you cannot fit a float64 into an int16 if the number exceeds the limit for int16 which is 32767. Last but not least, if you convert a float into an int in Golang, the decimal points get truncated without any rounding.
If you want the minimum of a set of N integers you can use (assuming N > 0):
import "sort"
func min(set []int) int {
sort.Slice(set, func(i, j int) bool {
return set[i] < set[j]
})
return set[0]
}
Where the second argument to min function is your less function, that is, the function that decides when an element i of the passed slice is less than an element j
Check it out here in Go Playground: https://go.dev/play/p/lyQYlkwKrsA
As the question states, I'm having trouble finding where is the issue within the following algorithm. It is the aux function for mergesort, i.e. the one used for combining sorted arrays.
func Merge(toSort *[]int, p, q, r int) {
arr := *toSort
L := arr[p:q]
R := arr[q:r+1]
fmt.Println(L)
fmt.Println(R)
i := 0
j := 0
for index := p; index <= r; index++ {
if i >= len(L) {
arr[index] = R[j]
j += 1
continue
} else if j >= len(R) {
arr[index] = L[i]
i += 1
continue
}
if L[i] > R[j] {
fmt.Println("right smaller")
arr[index] = R[j]
j += 1
continue
}
if L[i] <= R[j] {
fmt.Println("left smaller")
arr[index] = L[i]
i += 1
continue
}
}
}
For arr := []int{1,7,14,15,44,65,79,2,3,6,55,70} it gives as output [1 2 2 2 2 2 2 2 3 6 55 70].
Golang Play link
The JavaScript equivalent for this function works as expected, but I don't know why it isn't working in Go
Thank you
Golang slices are passed by reference. So you don't need to pass a pointer into the function in the first place, but you do need to take explicit copies of L and R or else merge into a different slice entirely. You are currently writing into the same underlying memory from which you are getting your values.
Code like L := arr[p:q] does not create a copy. I suppose you are overwriting your L and R parts during the assignments to arr. Have a look at http://blog.golang.org/slices to understand how slices work. (E.g. you'll basically never write stuff like toSort *[]int as []int is almost kinda pointer)
This seems to work: http://play.golang.org/p/vPo2ZKXtI9
You don't need all the indexes: slices are already views into an array. Here's a complete example using purely slice manipulation:
package main
import "fmt"
// Merge takes two sorted, increasing slices of ints and
// returns a slice combining them into a single sorted, increasing
// slice.
func Merge(a, b []int) []int {
res := make([]int, 0, len(a)+len(b))
for len(a) > 0 || len(b) > 0 {
if len(b) == 0 || len(a) > 0 && a[0] <= b[0] {
res = append(res, a[0])
a = a[1:]
} else {
res = append(res, b[0])
b = b[1:]
}
}
return res
}
func main() {
a := []int{1, 2, 5, 6, 3, 4, 7, 9}
fmt.Println(Merge(a[:4], a[4:]))
}