The problem
The prime quantity sequence begins with: 2,3,5,7,11,13,17,19.... Discover that 2 is in place one.
3 occupies place two, which is a prime-numbered place. Equally, 5, 11 and 17 additionally occupy prime-numbered positions. We will name primes similar to 3,5,11,17 dominant primes as a result of they occupy prime-numbered positions within the prime quantity sequence. Let’s name this listA.
As you’ll be able to see from listA, for the prime vary vary(0,10), there are solely two dominant primes (3 and 5) and the sum of those primes is: 3 + 5 = 8.
Equally, as proven in listA, within the vary (6,20), the dominant primes on this vary are 11 and 17, with a sum of 28.
Given a vary (a,b), what’s the sum of dominant primes inside that vary? Observe that a <= vary <= b and b won’t exceed 500000.
The answer in Golang
Possibility 1:
package deal resolution
func Remedy(a, b int) int {
sum := 0
sv := make([]bool, b+1)
pos := 1
if a <= 3 && b >= 3 {
sum += 3
}
for i := 3; i <= b; i += 2 {
if sv[i] == false {
pos++
if i >= a && pospercent2 == 1 && sv[pos] == false {
sum += i
}
for j := i + i; j <= b; j += i {
sv[j] = true
}
}
}
return sum
}
Possibility 2:
package deal resolution
func Remedy(a, b int) (sum int) {
primes := make([]int, 0, 5000)
primes = append(primes, 2, 3, 5, 7)
prime := func(n int) int {
for n > len(primes) {
subsequent := primes[len(primes) - 1] + 1
for i := 0; primes[i]*primes[i] <= subsequent; i++ {
if nextpercentprimes[i] == 0 { subsequent += 1 ; i = -1 }
}
primes = append(primes, subsequent)
}
return primes[n-1]
}
for i := 1 ;; i++ {
dominantPrime := prime(prime(i))
if dominantPrime > b { break }
if dominantPrime < a { proceed }
sum += dominantPrime
}
return
}
Possibility 3:
package deal resolution
func isPrime(n int) bool {
for i := 2; i*i < n+i; i++ {
if npercenti == 0 {
return false
}
}
return n > 1
}
func Remedy(a, b int) int {
c, pos := 0, 0
for i := 0; i <= b; i++ {
if isPrime(i) {
pos++
if i >= a && isPrime(pos) {
c += i
}
}
}
return c
}
Take a look at circumstances to validate our resolution
package deal solution_test
import (
. "github.com/onsi/ginkgo"
. "github.com/onsi/gomega"
)
func dotest(s, g, exp int) {
var ans = Remedy(s,g)
Anticipate(ans).To(Equal(exp))
}
var _ = Describe("Instance checks", func() {
It("It ought to work for primary checks", func() {
dotest(0,10, 8)
dotest(2,200, 1080)
dotest(1000,100000,52114889)
dotest(4000,500000,972664400)
})
})
