feat: implement Booth's algorithm for lexicographically minimal rotation of a string.

String/BoothsAlgorithm.js

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+/**
+ * Booth's Algorithm finds the lexicographically minimal rotation of a string.
+ * Time Complexity: O(n) - Linear time where n is the length of input string
+ * Space Complexity: O(n) - Linear space for failure function array
+ * For More Visit - https://en.wikipedia.org/wiki/Booth%27s_multiplication_algorithm
+ * @example
+ * Input: "baca"
+ * All possible rotations:
+ * - "baca"
+ * - "acab"
+ * - "caba"
+ * - "abac"
+ * Output: "abac" (lexicographically smallest)
+ * 
+ * How it works:
+ * 1. Doubles the input string to handle all rotations
+ * 2. Uses failure function (similar to KMP) to find minimal rotation
+ * 3. Maintains a pointer to the start of minimal rotation found so far
+
+ * @param {string} str - Input string to find minimal rotation
+ * @returns {string} - Lexicographically minimal rotation of the input string
+ * @throws {Error} - If input is not a string or is empty
+ */
+export function findMinimalRotation(str) {
+  if (typeof str !== 'string') {
+    throw new Error('Input must be a string')
+  }
+
+  if (str.length === 0) {
+    throw new Error('Input string cannot be empty')
+  }
+
+  // Double the string for rotation comparison
+  // This allows us to check all rotations by just sliding a window
+  const s = str + str
+  const n = s.length
+
+  // Initialize failure function array
+  const f = new Array(n).fill(-1)
+  let k = 0 // Starting position of minimal rotation
+
+  //Algorithm's implementation
+  // Iterate through the doubled string
+  // j is the current position we're examining
+  for (let j = 1; j < n; j++) {
+    // i is the length of the matched prefix in the current candidate
+    // Get the failure function value for the previous position
+    let i = f[j - k - 1]
+    // This loop handles the case when we need to update our current minimal rotation
+    // It compares characters and finds if there's a better (lexicographically smaller) rotation
+    while (i !== -1 && s[j] !== s[k + i + 1]) {
+      // If we find a smaller character, we've found a better rotation
+      // Update k to the new starting position
+      if (s[j] < s[k + i + 1]) {
+        // j-i-1 gives us the starting position of the new minimal rotation
+        k = j - i - 1
+      }
+      // Update i using the failure function to try shorter prefixes
+      i = f[i]
+    }
+
+    // This block updates the failure function and handles new character comparisons
+    if (i === -1 && s[j] !== s[k + i + 1]) {
+      // If current character is smaller, update the minimal rotation start
+      if (s[j] < s[k + i + 1]) {
+        k = j
+      }
+      //If no match found,mark failure function accordingly
+      f[j - k] = -1
+    } else {
+      //If match found, extend the matched length
+      f[j - k] = i + 1
+    }
+  }
+  // After finding k (the starting position of minimal rotation):
+  // 1. slice(k): Take substring from position k to end
+  // 2. slice(0, k): Take substring from start to position k
+  // 3. Concatenate them to get the minimal rotation
+  return str.slice(k) + str.slice(0, k)
+}

String/test/BoothsAlgorithm.test.js

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+import { findMinimalRotation } from '../BoothsAlgorithm'
+
+describe('BoothsAlgorithm', () => {
+  it('should throw an error if input is not a string', () => {
+    expect(() => findMinimalRotation(null)).toThrow('Input must be a string')
+    expect(() => findMinimalRotation(undefined)).toThrow(
+      'Input must be a string'
+    )
+    expect(() => findMinimalRotation(123)).toThrow('Input must be a string')
+    expect(() => findMinimalRotation([])).toThrow('Input must be a string')
+  })
+
+  it('should throw an error if input string is empty', () => {
+    expect(() => findMinimalRotation('')).toThrow(
+      'Input string cannot be empty'
+    )
+  })
+
+  it('should find minimal rotation for simple strings', () => {
+    expect(findMinimalRotation('abc')).toBe('abc')
+    expect(findMinimalRotation('bca')).toBe('abc')
+    expect(findMinimalRotation('cab')).toBe('abc')
+  })
+
+  it('should handle strings with repeated characters', () => {
+    expect(findMinimalRotation('aaaa')).toBe('aaaa')
+    expect(findMinimalRotation('aaab')).toBe('aaab')
+    expect(findMinimalRotation('baaa')).toBe('aaab')
+  })
+
+  it('should handle strings with special characters', () => {
+    expect(findMinimalRotation('12#$')).toBe('#$12')
+    expect(findMinimalRotation('@abc')).toBe('@abc')
+    expect(findMinimalRotation('xyz!')).toBe('!xyz')
+  })
+
+  it('should handle longer strings', () => {
+    expect(findMinimalRotation('algorithm')).toBe('algorithm')
+    expect(findMinimalRotation('rithmalgo')).toBe('algorithm')
+    expect(findMinimalRotation('gorithmal')).toBe('algorithm')
+  })
+
+  it('should be case sensitive', () => {
+    expect(findMinimalRotation('AbC')).toBe('AbC')
+    expect(findMinimalRotation('BcA')).toBe('ABc')
+    expect(findMinimalRotation('CAb')).toBe('AbC')
+  })
+
+  it('should handle palindromes', () => {
+    expect(findMinimalRotation('radar')).toBe('adarr')
+    expect(findMinimalRotation('level')).toBe('ellev')
+  })
+})