Feature/recursive digit sum

docs/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive-digit-sum-solution-notes.md

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+# [Recursive Digit Sum](https://www.hackerrank.com/challenges/recursive-digit-sum)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingBasic`
+
+## Language Difficulties
+
+The first attempt solved most of the cases.
+The failed test cases reported a "Runtime error".
+Initially, it seemed pointless, since there are
+no edge cases in the calculations that could cause
+typical runtime errors like division by zero or
+performing operations on a null value.
+
+Unlocking a failed test case, and locally replicating the given input,
+found the real problem:
+
+```text
+ValueError: Exceeds the limit (4300) for integer string conversion
+```
+
+The input number is too high for some reason in Python.
+
+A [little reseach](https://stackoverflow.com/a/75162528/6366150) give some answers:
+
+### Problem fixes
+
+So, the problem arises from a limitation imposed in Python, which fixes
+the size of a number that will be transformed from a string to an integer.
+
+The limit can be increased via a parameter or programmatically.
+However, if the value is set as a hardcoded integer (in test cases),
+it will still fail at runtime.
+
+> [!IMPORTANT]
+>
+> The solution is then to enter the number (from the large test case)
+> as a string and then do the transformation at runtime,
+> including the parameter that arbitrarily extends the length of the number.
+
+## Sources
+
+- [Stackoverflow: ValueError: Exceeds the limit (4300) for integer string conversion](https://stackoverflow.com/a/75162528/6366150)
+- [CVE: CVE-2020-10735](https://cve.mitre.org/cgi-bin/cvename.cgi?name=CVE-2020-10735)
+- [Multiline String in Python - GeeksforGeeks](https://www.geeksforgeeks.org/multiline-string-in-python/)
+- [string splitterworld's simplest string tool](https://onlinestringtools.com/split-string)

docs/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive-digit-sum.md

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+# [Recursive Digit Sum](https://www.hackerrank.com/challenges/recursive-digit-sum)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingBasic`
+
+We define super digit of an integer `x` using the following rules:
+
+Given an integer, we need to find the super digit of the integer.
+
+- If `x` has only `1` digit, then its super digit is `x`.
+- Otherwise, the super digit of `x` is equal to the super digit of
+    the sum of the digits of `x`.
+
+For example, the super digit of `9875` will be calculated as:
+
+```text
+    super_digit(9875)       9+8+7+5 = 29
+    super_digit(29)         2 + 9   = 11
+    super_digit(11)         1 + 1   = 2
+    super_digit(2)                  = 2
+```
+
+## Example
+
+`n = 9875`
+
+`k = 4`
+
+The number `p` is created by concatenating the string `n` `k`
+times so the initial `p = 9875987598759875`.
+
+```text
+    superDigit(p) = superDigit(9875987598759875)
+                  9+8+7+5+9+8+7+5+9+8+7+5+9+8+7+5 = 116
+    superDigit(p) = superDigit(116)
+                  1+1+6 = 8
+    superDigit(p) = superDigit(8)
+```
+
+All of the digits of `p` sum to `116`. The digits of `116` sum to `8`.
+`8` is only one digit, so it is the super digit.
+
+## Function Description
+
+Complete the function superDigit in the editor below.
+It must return the calculated super digit as an integer.
+
+superDigit has the following parameter(s):
+
+- `string n`: a string representation of an integer
+- `int k`: the times to concatenate  to make
+
+## Returns
+
+- `int`: the super digit of  repeated  times
+
+## Input Format
+
+The first line contains two space separated integers, `n` and `k`.
+
+## Constraints
+
+- $ 1 \leq n \leq 10^100000 $
+- $ 1 \leq k \leq 10^5 $
+
+## Sample Input 0
+
+```text
+148 3
+```
+
+## Sample Output 0
+
+```text
+3
+```
+
+## Explanation 0
+
+Here `n = 148` and `k = 3`, so `p = 148148148`.
+
+```text
+super_digit(P) = super_digit(148148148)
+               = super_digit(1+4+8+1+4+8+1+4+8)
+               = super_digit(39)
+               = super_digit(3+9)
+               = super_digit(12)
+               = super_digit(1+2)
+               = super_digit(3)
+               = 3
+```
+
+## Sample Input 1
+
+```text
+9875 4
+```
+
+## Sample Output 1
+
+```text
+8
+```
+
+## Sample Input 2
+
+```text
+123 3
+```
+
+## Sample Output 2
+
+```text
+9
+```
+
+## Explanation 2
+
+Here `n = 123` and `k = 3`, so `p = 123123123`.
+
+```text
+super_digit(P) = super_digit(123123123)
+               = super_digit(1+2+3+1+2+3+1+2+3)
+               = super_digit(18)
+               = super_digit(1+8)
+               = super_digit(9)
+               = 9
+```

src/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive_digit_sum.bruteforce-test.js

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+import { describe, expect, it } from '@jest/globals';
+import { logger as console } from '../../../logger.js';
+
+import { superDigit } from './recursive_digit_sum.js';
+import TEST_CASES from './recursive_digit_sum.bruteforce.testcases.json';
+
+describe('recursive_digit_sum bruteforce', () => {
+  it('superDigit test cases', () => {
+    expect.assertions(3);
+
+    TEST_CASES.forEach((test) => {
+      const answer = superDigit(test.n, test.k);
+
+      console.debug(`superDigit(${test.n}) solution found: ${answer}`);
+
+      expect(answer).toStrictEqual(test.expected);
+    });
+  });
+});

src/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive_digit_sum.bruteforce.testcases.json

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+[
+  {
+    "expected": 7,
+    "k": 100000,
+    "n": "2365978831649490136475575038877779575813226775851820912370812124502641538947920808397703549713678494683928497712437176140282589350277653479225520602813456433277417366680426198633681891184348757007292907409160353745221125354212095528784124728447770959861439390350308313917365021363541712618686942946773324003146008424205688630371656757561012224744901800726911246423272186301595490993253791386102270201965996662707215300748516732223935858816466886068592299708740453558018878677753623653080545592459765998008028026982510689469213738241205802446029154833458048894002646934119082621498341445221491190955459548371083839625590505228681017724678315572531551988758568150699821635779156685637531274097856486075649357610713833072735231599919848220063026429718137766286716343385059699133211699189933339174843625266398503099203416124466032711453854413933737536836406105991857744766344461162222670876732729171585512468615558499979720269427922798431312270483732004392503905160233457811525428432787732543799783309593536386190295516419339222642886780012683583264436427241020490358960438948951090123073035203797984302163150042110707217274102457735317367100133807782064391421012191958312396649052833396257876824943425814834615313474161638240747120342368147351931074481983318414461554116111216672594256301273113776892080967125790153125125885441941114178586071406149630777323200516190208241341822285244325578953416388462284725673478766919050744786263188733438572307443267700831425575113213359873223948072988922668251652320316884761627830570057061821492039968369341602081382603302965910382997241199808824091331180464950187035576778206683245316006405529597170652549163351875206280564448346510252775085876212617353369513619186390565654064068546863018765466029315754619416429621887091818939474391383675337791979997519954871635692656223852981330368145996344325688247632566665645262588764650823901065646663460851602833982853795901687202035893967893724362979886948663369428689585509715442019662325024294581705265808022570365351645495802686891955348084550615538750809287498241260408673517746608582833123696027380353038348218786331710334697053069152326732702246704177127367642287975998486114018970510842276024855162228267767755948030029723573646908844109049374244456580474922058250964260437721278380069311972455077102266167098465788845261016395772392904280411167763443571285141388567074805986331207454652671618663858701085276806486000014124900483188940484497173286284987124699515039831183902383877120136788492339903316093693938833730548247174799553092402671083313285813003903363625219370039413610850308966558948057932583576771492037811460439359542902624599661588624295232252616245186844975995180218889230403968087888108494214819234992007182241562844376961711438491105585390645332161544542326095869642445733823661806228697208277656426326128938546125761166960351482948539114133280810916317873360419836067625116114001377672929333638768292095236809153349426894896869446197395671771932928211109385884940274160388152027885130001908095515987519207099973668415699818805100890690896126345099249836616348702742776559368591004254298734292430313132506862931339852599450961120591169865484036943294045257801193102728400887526383477970523720630900867795111210451854194391002244150921934506879640791680297603712618076174694948300699937409787596860516266369711284028834238022724596540529491965656156574337073988564171171562036245389632730259264953520190321920347601255396137920500496074443380910841069973360586715775083998842187392360751892748665579312212647821816086677544702037289983388842777905728540745718314922321086695691823249801139552886748181144717500999021690749662561227798159566905725946118195067702032931332172088385727012140744362147720922176656204772910422189621466379287662792372374145383317294646977085291873933547226857758530880168793511465268400187943977613894365634645591604177130794105552582447385631392788652188052953414781129655671439788151513996304231024358843023105354157338564270003904673736178109502550650713167258319522545824056524791781105181639237127875356417268878249642171688744070159985867211941494396566216365392991627962886902198712613982017603237174682825814797983967054038269833008728407345912699623004623467287738296110774212005294050799218227654983820235796069236099706911525806244933683548619651925300435846989868138976944006822652462513903624200398184640627878400159480147462063679751851193719499676402496701528971830054482832320057097082360875809145428036636600549270698504540758319126452884313155162288201445118708935758033035083555929081756050975974040793712887964439001525986626643925845343840647344753344394209812309532147589135665638895095150172324875219965305745649692175878476631167339609984047545458299489650202318886162798841051758853022389219423402386031324398337411422060786064174337895040820526914615325075313448800789763344707190242881920892579588963376086146960633381215378914452523108903834607764477580583821712879080194987840450703336371649758616364805184545636558639909806705757141231728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4",
+    "title": "Sample Test case 7"
+  }
+]

src/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive_digit_sum.js

@@ -0,0 +1,31 @@
+/**
+ * @link Problem definition [[docs/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive-digit-sum.md]]
+ */
+
+const RADIX = 10;
+
+export function superDigitCompute(n) {
+  if (n.length === 1) {
+    return parseInt(n, RADIX);
+  }
+
+  let partial = 0;
+  for (const digit of n) {
+    partial += parseInt(digit, RADIX);
+  }
+
+  return superDigitCompute(`${partial}`);
+}
+
+export function superDigit(n, k) {
+  const accumulator = `${superDigitCompute(n)}`;
+
+  let result = '';
+  for (let i = 0; i < k; i++) {
+    result = `${result}${accumulator}`;
+  }
+
+  return superDigitCompute(result);
+}
+
+export default { superDigit };

src/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive_digit_sum.test.js

@@ -0,0 +1,19 @@
+import { describe, expect, it } from '@jest/globals';
+import { logger as console } from '../../../logger.js';
+
+import { superDigit } from './recursive_digit_sum.js';
+import TEST_CASES from './recursive_digit_sum.testcases.json';
+
+describe('recursive_digit_sum', () => {
+  it('superDigit test cases', () => {
+    expect.assertions(4);
+
+    TEST_CASES.forEach((test) => {
+      const answer = superDigit(test.n, test.k);
+
+      console.debug(`superDigit(${test.n}) solution found: ${answer}`);
+
+      expect(answer).toStrictEqual(test.expected);
+    });
+  });
+});

src/hackerrank/interview_preparation_kit/recursion_and_backtracking/recursive_digit_sum.testcases.json

@@ -0,0 +1,26 @@
+[
+  {
+    "title": "Sample Test case 0",
+    "n": "148",
+    "k": 3,
+    "expected": 3
+  },
+  {
+    "title": "Sample Test case 10",
+    "n": "9875",
+    "k": 4,
+    "expected": 8
+  },
+  {
+    "title": "Sample Test case 11",
+    "n": "123",
+    "k": 3,
+    "expected": 9
+  },
+  {
+    "title": "Sample Test case 10",
+    "n": "9875",
+    "k": 4,
+    "expected": 8
+  }
+]