[pull] master from TheAlgorithms:master

Backtracking/KnightTour.js

@@ -2,12 +2,13 @@
 
 class OpenKnightTour {
   constructor(size) {
+    // Constructor to initialize the chessboard and size
     this.board = new Array(size).fill(0).map(() => new Array(size).fill(0))
     this.size = size
   }
 
   getMoves([i, j]) {
-    // helper function to get the valid moves of the knight from the current position
+    // Helper function to get the valid moves of the knight from the current position
     const moves = [
       [i + 2, j - 1],
       [i + 2, j + 1],
@@ -19,18 +20,19 @@ class OpenKnightTour {
       [i - 1, j + 2]
     ]
 
+    // Filter out moves that are within the board boundaries
     return moves.filter(
       ([y, x]) => y >= 0 && y < this.size && x >= 0 && x < this.size
     )
   }
 
   isComplete() {
-    // helper function to check if the board is complete
+    // Helper function to check if the board is complete
     return !this.board.map((row) => row.includes(0)).includes(true)
   }
 
   solve() {
-    // function to find the solution for the given board
+    // Function to find the solution for the given board
     for (let i = 0; i < this.size; i++) {
       for (let j = 0; j < this.size; j++) {
         if (this.solveHelper([i, j], 0)) return true
@@ -40,22 +42,23 @@ class OpenKnightTour {
   }
 
   solveHelper([i, j], curr) {
-    // helper function for the main computation
+    // Helper function for the main computation
     if (this.isComplete()) return true
 
+    // Iterate through possible moves and attempt to fill the board
     for (const [y, x] of this.getMoves([i, j])) {
       if (this.board[y][x] === 0) {
         this.board[y][x] = curr + 1
         if (this.solveHelper([y, x], curr + 1)) return true
-        // backtracking
+        // Backtracking: If the solution is not found, reset the cell to 0
         this.board[y][x] = 0
       }
     }
     return false
   }
 
   printBoard(output = (value) => console.log(value)) {
-    // utility function to display the board
+    // Utility function to display the board
     for (const row of this.board) {
       let string = ''
       for (const elem of row) {

Backtracking/MColoringProblem.js

@@ -0,0 +1,49 @@
+/**
+ * Colors a graph using up to m colors such that no two adjacent vertices share the same color.
+ * @param {number[][]} graph - Adjacency matrix of the graph, using 0 for no edge.
+ * @param {number} m - The number of colors to use.
+ * @returns {?Array.<number>} A valid M-coloring of the graph using colors 1 to m, or null if none exists.
+ * @see https://en.wikipedia.org/wiki/Graph_coloring
+ */
+function mColoring(graph, m) {
+  const colors = new Array(graph.length).fill(0);
+
+  // Check if it's safe to color a vertex with a given color.
+  function isSafe(vertex, color) {
+    for (let i = 0; i < graph.length; i++) {
+      if (graph[vertex][i] && colors[i] === color) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  // Use backtracking to try and color the graph.
+  function solveColoring(vertex = 0) {
+    if (vertex === graph.length) {
+      return true;
+    }
+
+    for (let color = 1; color <= m; color++) {
+      if (isSafe(vertex, color)) {
+        colors[vertex] = color;
+
+        if (solveColoring(vertex + 1)) {
+          return true;
+        }
+
+        // If no solution, backtrack.
+        colors[vertex] = 0;
+      }
+    }
+    return false;
+  }
+
+  // If coloring is possible, return the colors.
+  if (solveColoring()) {
+    return colors;
+  }
+  return null;
+}
+
+export { mColoring };

Backtracking/tests/MColoringProblem.test.js

@@ -0,0 +1,23 @@
+import { mColoring } from '../MColoringProblem';
+
+describe('MColoringProblem', () => {
+  it('should color a triangle with 3 colors', () => {
+    const graph = [
+      [0, 1, 1],
+      [1, 0, 1],
+      [1, 1, 0]
+    ];
+    const solution = mColoring(graph, 3);
+    expect(solution).not.toBeNull();
+  });
+
+  it('should not color a triangle with 2 colors', () => {
+    const graph = [
+      [0, 1, 1],
+      [1, 0, 1],
+      [1, 1, 0]
+    ];
+    const solution = mColoring(graph, 2);
+    expect(solution).toBeNull();
+  });
+});

Bit-Manipulation/BinaryCountSetBits.js

@@ -16,7 +16,7 @@ function BinaryCountSetBits(a) {
 
   let count = 0
   while (a) {
-    a &= (a - 1)
+    a &= a - 1
     count++
   }
 

DIRECTORY.md

@@ -3,6 +3,7 @@
   * [generateParentheses](Backtracking/generateParentheses.js)
   * [GeneratePermutations](Backtracking/GeneratePermutations.js)
   * [KnightTour](Backtracking/KnightTour.js)
+  * [MColoringProblem](Backtracking/MColoringProblem.js)
   * [NQueens](Backtracking/NQueens.js)
   * [RatInAMaze](Backtracking/RatInAMaze.js)
   * [Sudoku](Backtracking/Sudoku.js)
@@ -166,6 +167,7 @@
   * [Area](Maths/Area.js)
   * [ArithmeticGeometricMean](Maths/ArithmeticGeometricMean.js)
   * [ArmstrongNumber](Maths/ArmstrongNumber.js)
+  * [AutomorphicNumber](Maths/AutomorphicNumber.js)
   * [AverageMean](Maths/AverageMean.js)
   * [AverageMedian](Maths/AverageMedian.js)
   * [BinaryConvert](Maths/BinaryConvert.js)

Maths/AutomorphicNumber.js

@@ -35,6 +35,6 @@ export const isAutomorphic = (n) => {
     n = Math.floor(n / 10)
     n_sq = Math.floor(n_sq / 10)
   }
-  
+
   return true
 }

Maths/test/AutomorphicNumber.test.js

@@ -9,19 +9,19 @@ describe('AutomorphicNumber', () => {
   })
 
   test.each([
-    { n: -3 , expected: false },
-    { n: -25 , expected: false },
+    { n: -3, expected: false },
+    { n: -25, expected: false }
   ])('should return false when n is negetive', ({ n, expected }) => {
     expect(isAutomorphic(n)).toBe(false)
   })
 
   test.each([
-    { n: 7 , expected: false },
-    { n: 83 , expected: false },
-    { n: 0 , expected: true },
-    { n: 1 , expected: true },
-    { n: 376 , expected: true },
-    { n: 90625 , expected: true },
+    { n: 7, expected: false },
+    { n: 83, expected: false },
+    { n: 0, expected: true },
+    { n: 1, expected: true },
+    { n: 376, expected: true },
+    { n: 90625, expected: true }
   ])('should return $expected when n is $n', ({ n, expected }) => {
     expect(isAutomorphic(n)).toBe(expected)
   })

Project-Euler/Problem006.js

@@ -1,8 +1,8 @@
 // https://projecteuler.net/problem=6
 
 export const squareDifference = (num = 100) => {
-  let sumOfSquares = (num)*(num+1)*(2*num+1)/6
-  let sums = (num*(num+1))/2
-  
+  let sumOfSquares = (num * (num + 1) * (2 * num + 1)) / 6
+  let sums = (num * (num + 1)) / 2
+
   return sums ** 2 - sumOfSquares // difference of square of the total sum and sum of squares
 }

Project-Euler/test/Problem004.test.js

@@ -0,0 +1,11 @@
+import { largestPalindromic } from '../Problem004.js'
+
+describe('Largest Palindromic Number', () => {
+  test('if digit is 2', () => {
+    expect(largestPalindromic(2)).toBe(9009)
+  })
+  // Project Euler Condition Check
+  test('if digit is 3', () => {
+    expect(largestPalindromic(3)).toBe(906609)
+  })
+})

Recursive/test/BinaryEquivalent.test.js

@@ -1,29 +1,29 @@
-import { binaryEquivalent } from "../BinaryEquivalent";
+import { binaryEquivalent } from '../BinaryEquivalent'
 
 const tests = [
-    {
-        test: 2,
-        expectedValue: "10"
-    },
-    {       
-        test: 0,
-        expectedValue: "0"
-    },
-    {
-        test: 543,
-        expectedValue: "1000011111"
-    },
-    {
-        test: 4697621023,
-        expectedValue: "100011000000000000000001000011111"
-    }
+  {
+    test: 2,
+    expectedValue: '10'
+  },
+  {
+    test: 0,
+    expectedValue: '0'
+  },
+  {
+    test: 543,
+    expectedValue: '1000011111'
+  },
+  {
+    test: 4697621023,
+    expectedValue: '100011000000000000000001000011111'
+  }
 ]
 
-describe("Binary Equivalent", () => {
-    test.each(tests)(
-        "of $test should be $expectedValue",
-        ({test, expectedValue}) => {
-            expect(binaryEquivalent(test)).toBe(expectedValue);
-        }
-    )
+describe('Binary Equivalent', () => {
+  test.each(tests)(
+    'of $test should be $expectedValue',
+    ({ test, expectedValue }) => {
+      expect(binaryEquivalent(test)).toBe(expectedValue)
+    }
+  )
 })

Search/InterpolationSearch.js

@@ -36,4 +36,4 @@ export function interpolationSearch(arr, key) {
   }
 
   return -1
-}
+}