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/*
* Number Splitting
* Problem 719
*
* We define an $S$-number to be a natural number, $n$, that is a perfect square and its
* square root can be obtained by splitting the decimal representation of $n$ into 2 or more
* numbers then adding the numbers.
* For example, 81 is an $S$-number because $\sqrt{81} = 8+1$.
* 6724 is an $S$-number: $\sqrt{6724} = 6+72+4$.
* 8281 is an $S$-number: $\sqrt{8281} = 8+2+81 = 82+8+1$.
* 9801 is an $S$-number: $\sqrt{9801}=98+0+1$.
* Further we define $T(N)$ to be the sum of all $S$ numbers $n\le N$. You are given
* $T(10^4) = 41333$.
* Find $T(10^{12})$
*/
package main
import (
"fmt"
"math"
)
type digitSum struct {
sum int
current int
currentPow10 int
}
func digitsSums(digits []int) []digitSum {
if len(digits) == 0 {
panic("len(digits) == 0")
} else if len(digits) == 1 {
return []digitSum{
{sum: digits[0], current: 0, currentPow10: 0},
}
}
subSums := digitsSums(digits[:len(digits) - 1])
currentDigit := digits[len(digits) - 1]
addSums := make([]digitSum, 0, len(subSums) * 2)
for _, s := range subSums {
digitAdd := s
digitAdd.sum += digitAdd.current
digitAdd.current = currentDigit
digitAdd.currentPow10 = 0
addSums = append(addSums, digitAdd)
concatAdd := s
concatAdd.currentPow10++
concatAdd.current += int(math.Pow10(concatAdd.currentPow10)) * currentDigit
addSums = append(addSums, concatAdd)
}
return addSums
}
func numberDigitsSummations(n int) []int {
digits := make([]int, 0)
for n > 0 {
digits = append(digits, n % 10)
n /= 10
}
sums := digitsSums(digits)
intSums := make([]int, len(sums))
for i, ds := range sums {
intSums[i] = ds.sum + ds.current
}
return intSums
}
const MAX_NUM int = 1e12
func main() {
maxNumSqrt := int(math.Ceil(math.Sqrt(float64(MAX_NUM))))
fmt.Println("max sqrt:", maxNumSqrt)
total := 0
for nRoot := 2; nRoot <= maxNumSqrt; nRoot++ {
if nRoot % 1_000 == 0 {
fmt.Printf("> %d%%\r", int(100 * float64(nRoot) / float64(maxNumSqrt)))
}
n := nRoot * nRoot
sums := numberDigitsSummations(n)
for _, s := range sums {
if s * s == n {
total += n
fmt.Println(n, " ")
break
}
}
}
fmt.Println(total)
}
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