Merge pull request #410 from sir-gon/feature/sherlock_and_anagrams

Feature/sherlock and anagrams

Author: sir-gon

docs/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams-solution-notes.md

@@ -0,0 +1,30 @@
+# [Sherlock and Anagrams](https://www.hackerrank.com/challenges/sherlock-and-anagrams)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingMedium` `#DictionariesAndHashmaps` `#Strings`
+
+## About solution
+
+To answer the question of "how many pairs" of words can be anagrammed
+using fragments from adjacent letters of an initial word, two steps are needed:
+
+1) Obtain all possible fragment candidates to be anagrams,
+  from each of the possible fragments that can be generated
+  from adjacent letters of a word.
+
+2) For each list of candidate anagrams,
+  calculate all possible permutations and add them up.
+  The total gives the answer.
+
+The second part of this problem can be solved with the binomial coefficient formula:
+
+<https://en.wikipedia.org/wiki/Binomial_coefficient>
+
+But the entire cost of this formula falls on the "factorial" function.
+
+In javascript, the factorial quickly reaches results that return large numbers,
+in scientific notation, losing precision.
+This loss of precision can result in an erroneous result
+in the final calculation of permutations.
+
+To avoid this problem, it is necessary to introduce large number handling using BigInt.

src/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams.test.ts

@@ -2,51 +2,14 @@ import { describe, expect, it } from '@jest/globals';
 import { logger as console } from '../../../logger';
 
 import { sherlockAndAnagrams } from './sherlock_and_anagrams';
-
-const TEST_CASES = [
-  {
-    title: 'Sample Test Case 0',
-    tests: [
-      {
-        input: 'abba',
-        expected: 4
-      },
-      {
-        input: 'abcd',
-        expected: 0
-      }
-    ]
-  },
-  {
-    title: 'Sample Test Case 1',
-    tests: [
-      {
-        input: 'ifailuhkqq',
-        expected: 3
-      },
-      {
-        input: 'kkkk',
-        expected: 10
-      }
-    ]
-  },
-  {
-    title: 'Sample Test Case 1',
-    tests: [
-      {
-        input: 'cdcd',
-        expected: 5
-      }
-    ]
-  }
-];
+import TEST_CASES from './sherlock_and_anagrams.testcases.json';
 
 describe('sherlock_and_anagrams', () => {
   it('sherlockAndAnagrams test cases', () => {
-    expect.assertions(5);
+    expect.assertions(15);
 
     TEST_CASES.forEach((testSet) => {
-      testSet.tests.forEach((test) => {
+      testSet?.tests.forEach((test) => {
         const answer = sherlockAndAnagrams(test.input);
 
         console.debug(

src/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams.testcases.json

@@ -0,0 +1,92 @@
+[
+  {
+    "title": "Sample Test Case 0",
+    "tests": [
+      {
+        "input": "abba",
+        "expected": 4
+      },
+      {
+        "input": "abcd",
+        "expected": 0
+      }
+    ]
+  },
+  {
+    "title": "Sample Test Case 1",
+    "tests": [
+      {
+        "input": "ifailuhkqq",
+        "expected": 3
+      },
+      {
+        "input": "kkkk",
+        "expected": 10
+      }
+    ]
+  },
+  {
+    "title": "Sample Test Case 1",
+    "tests": [
+      {
+        "input": "cdcd",
+        "expected": 5
+      }
+    ]
+  },
+  {
+    "title": "Test case 3",
+    "tests": [
+      {
+        "input":
+          "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+        "expected": 166650
+      },
+      {
+        "input":
+          "bbcaadacaacbdddcdbddaddabcccdaaadcadcbddadababdaaabcccdcdaacadcababbabbdbacabbdcbbbbbddacdbbcdddbaaa",
+        "expected": 4832
+      },
+      {
+        "input":
+          "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+        "expected": 166650
+      },
+      {
+        "input":
+          "cacccbbcaaccbaacbbbcaaaababcacbbababbaacabccccaaaacbcababcbaaaaaacbacbccabcabbaaacabccbabccabbabcbba",
+        "expected": 13022
+      },
+      {
+        "input":
+          "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+        "expected": 166650
+      },
+      {
+        "input":
+          "bbcbacaabacacaaacbbcaabccacbaaaabbcaaaaaaaccaccabcacabbbbabbbbacaaccbabbccccaacccccabcabaacaabbcbaca",
+        "expected": 9644
+      },
+      {
+        "input":
+          "cbaacdbaadbabbdbbaabddbdabbbccbdaccdbbdacdcabdbacbcadbbbbacbdabddcaccbbacbcadcdcabaabdbaacdccbbabbbc",
+        "expected": 6346
+      },
+      {
+        "input":
+          "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+        "expected": 166650
+      },
+      {
+        "input":
+          "babacaccaaabaaaaaaaccaaaccaaccabcbbbabccbbabababccaabcccacccaaabaccbccccbaacbcaacbcaaaaaaabacbcbbbcc",
+        "expected": 8640
+      },
+      {
+        "input":
+          "bcbabbaccacbacaacbbaccbcbccbaaaabbbcaccaacaccbabcbabccacbaabbaaaabbbcbbbbbaababacacbcaabbcbcbcabbaba",
+        "expected": 11577
+      }
+    ]
+  }
+]

src/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams.ts

@@ -1,12 +1,13 @@
 /**
  * @link Problem definition [[docs/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams.md]]
+ * @see Solution Notes: [[docs/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/sherlock_and_anagrams-solution-notes.md]]
  */
 
-function factorial(n: number): number {
-  if (n == 0) {
-    return 1;
-  }
-  return n * factorial(n - 1);
+import { logger as console } from '../../../logger';
+
+function extraLongFactorials(n: number): bigint {
+  const rs = [...Array(n)].reduce((a, b, i) => a * BigInt(i + 1), 1n);
+  return rs;
 }
 
 export function sherlockAndAnagrams(s: string): number {
@@ -16,6 +17,9 @@ export function sherlockAndAnagrams(s: string): number {
   for (let i = 0; i < size; i++) {
     for (let j = 0; j < size - i; j++) {
       const substr = s.substring(i, size - j);
+      console.debug(
+        `i: ${i}, size: ${size}, size - j: ${size - j} | substr: ${substr}`
+      );
 
       // Add substrings to a candidate list.
       // two strings are anagrams if sorted strings are the same.
@@ -32,7 +36,8 @@ export function sherlockAndAnagrams(s: string): number {
     }
   }
 
-  let count = 0;
+  let total: bigint = BigInt(0);
+  let q_candidates = 0;
   // Final Anagram list
   for (const word of Object.keys(candidates)) {
     const quantity_of_anagrams = candidates[word].length;
@@ -42,15 +47,23 @@ export function sherlockAndAnagrams(s: string): number {
       delete candidates[word];
     } else {
       // Binomial coefficient: https://en.wikipedia.org/wiki/Binomial_coefficient
-      count += Math.floor(
-        factorial(quantity_of_anagrams) /
-          (factorial(k) * factorial(quantity_of_anagrams - k))
-      );
+      q_candidates += quantity_of_anagrams;
+
+      const count =
+        extraLongFactorials(quantity_of_anagrams) /
+        (extraLongFactorials(k) *
+          extraLongFactorials(quantity_of_anagrams - k));
+      total += count;
+
+      console.debug(`'Partial anagrams of ${word}: ${count}`);
     }
   }
-  console.debug(`filtered candidates: ${count}`);
+  console.debug(
+    `'sherlockAndAnagrams(${s}) Filtered # candidates: ${q_candidates}`
+  );
+  console.debug(`'sherlockAndAnagrams(${s}) # anagrams: ${total}`);
 
-  return count;
+  return Number(total);
 }
 
 export default { sherlockAndAnagrams };