The challenge
For a given list [x1, x2, x3, ..., xn] compute the last (decimal) digit of x1 ^ (x2 ^ (x3 ^ (... ^ xn))).
Example:
last_digit({3, 4, 2}, 3) == 1
because 3 ^ (4 ^ 2) = 3 ^ 16 = 43046721.
Beware: powers grow incredibly fast. For example, 9 ^ (9 ^ 9) has more than 369 millions of digits. lastDigit has to deal with such numbers efficiently.
Corner cases: we assume that 0 ^ 0 = 1 and that lastDigit of an empty list equals to 1.
The solution in Golang
Option 1:
package solution
import "math"
func LastDigit(as []int) int {
var acc int = 1
for i := len(as) - 1; i >=0; i-- {
exp := acc % 4 + 4
if (acc < 4) { exp = acc }
base := as[i] % 20 + 20
if (as[i] < 20) { base = as[i] }
acc = int(math.Pow(float64(base), float64(exp)))
}
return acc % 10
}
Option 2:
package solution
import "math"
func LastDigit(as []int) (result int) {
if len(as) == 0 {
return 1
}
p := 1
for i := len(as) - 1; i >= 0; i-- {
result = low(as[i], 40)
result = int(math.Pow(float64(result), float64(p)))
p = low(result, 4)
}
return result % 10
}
func low(i int, base int) int {
if i > base {
i = i%base + base
}
return i
}
Option 3:
package solution
import "math/big"
func LastDigit(as []int) int {
if (len(as)==0) { return 1 }
r:=big.NewInt(1)
f:=big.NewInt(4)
for i:=len(as)-1; i>=0; i-- {
if r.Cmp(f) >=0 {
r = r.Mod(r,f)
r = r.Add(r,f)
}
r = r.Exp(big.NewInt(int64(as[i])),r,nil)
}
return int(r.Mod(r,big.NewInt(10)).Int64())
}
Test cases to validate our solution
package solution_test
import (
. "math/rand"
. "math"
. "github.com/onsi/ginkgo"
. "github.com/onsi/gomega"
)
var _ = Describe("Test Example", func() {
It("should handle basic cases", func() {
Expect(LastDigit( []int{} )).To(Equal(1))
Expect(LastDigit( []int{0,0} )).To(Equal(1)) // 0 ^ 0
Expect(LastDigit( []int{0,0,0} )).To(Equal(0)) // 0^(0 ^ 0) = 0^1 = 0
Expect(LastDigit( []int{1,2} )).To(Equal(1))
Expect(LastDigit( []int{3,4,5} )).To(Equal(1))
Expect(LastDigit( []int{4,3,6} )).To(Equal(4))
Expect(LastDigit( []int{7,6,21} )).To(Equal(1))
Expect(LastDigit( []int{12,30,21} )).To(Equal(6))
Expect(LastDigit( []int{2,0,1} )).To(Equal(1))
Expect(LastDigit( []int{2,2,2,0} )).To(Equal(4))
Expect(LastDigit( []int{937640,767456,981242} )).To(Equal(0))
Expect(LastDigit( []int{123232,694022,140249} )).To(Equal(6))
Expect(LastDigit( []int{499942,898102,846073} )).To(Equal(6))
})
It("should handle random cases", func() {
var r1 int = Intn(100)
var r2 int = Intn(10)
var pow int = int(Pow(float64(r1 % 10), float64(r2)))
Expect(LastDigit( []int{} )).To(Equal(1))
Expect(LastDigit( []int{r1} )).To(Equal(r1 % 10))
Expect(LastDigit( []int{r1, r2} )).To(Equal(pow % 10))
})
})
