From 8b3efe814dc92a38943647ad7d7e2eeae6722418 Mon Sep 17 00:00:00 2001
From: Charles Cabergs <me@cacharle.xyz>
Date: Tue, 11 Oct 2022 17:49:44 +0200
Subject: problem 719 in go

---
 go/719-number_splitting.go | 92 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 go/719-number_splitting.go

diff --git a/go/719-number_splitting.go b/go/719-number_splitting.go
new file mode 100644
index 0000000..4f2ac4b
--- /dev/null
+++ b/go/719-number_splitting.go
@@ -0,0 +1,92 @@
+/*
+* 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)
+}
-- 
cgit