feat:added Word Break problem in backtracking

Author: Akshat-Raii

Backtracking/WordBreak.js

@@ -0,0 +1,36 @@
+export class WordBreakSolution {
+  // Function to determine if the input string 's' can be segmented into words from the 'wordDict'
+  wordBreak(s, wordDict) {
+    const wordSet = new Set(wordDict) // Convert wordDict into a set for efficient lookups
+    const memo = Array(s.length).fill(null) // Initialize memoization array to store results of subproblems
+    return this.canBreak(0, s, wordSet, memo) // Start the recursive function from the 0th index
+  }
+
+  // Helper function to perform recursive backtracking with memoization
+  canBreak(start, s, wordSet, memo) {
+    if (start === s.length) {
+      return true // If we reach the end of the string, return true as we successfully segmented it
+    }
+
+    if (memo[start] !== null) {
+      return memo[start] // Return the cached result if already computed for this index
+    }
+
+    // Explore all possible substrings starting from 'start' index
+    for (let end = start + 1; end <= s.length; end++) {
+      const currentSubstring = s.slice(start, end) // Get the substring from 'start' to 'end'
+
+      // If the current substring is a valid word and the rest of the string can be broken, return true
+      if (
+        wordSet.has(currentSubstring) &&
+        this.canBreak(end, s, wordSet, memo)
+      ) {
+        memo[start] = true // Cache the result as true for this index
+        return true
+      }
+    }
+
+    memo[start] = false // Cache the result as false if no valid segmentation found
+    return false
+  }
+}

Backtracking/tests/WordBreak.test.js

@@ -0,0 +1,34 @@
+import { describe, it, expect } from 'vitest'
+import { WordBreakSolution } from '../WordBreak'
+
+describe('Word Break Algorithm', () => {
+  it('should return true for valid word segmentation', () => {
+    const solution = new WordBreakSolution()
+    const result = solution.wordBreak('leetcode', ['leet', 'code'])
+    expect(result).toBe(true)
+  })
+
+  it('should return false for invalid word segmentation', () => {
+    const solution = new WordBreakSolution()
+    const result = solution.wordBreak('applepenapple', ['apple', 'pen'])
+    expect(result).toBe(true)
+  })
+
+  it('should handle edge cases with empty strings', () => {
+    const solution = new WordBreakSolution()
+    const result = solution.wordBreak('', ['leet', 'code'])
+    expect(result).toBe(true)
+  })
+
+  it('should return false when no word break is possible', () => {
+    const solution = new WordBreakSolution()
+    const result = solution.wordBreak('catsandog', [
+      'cats',
+      'dog',
+      'sand',
+      'and',
+      'cat'
+    ])
+    expect(result).toBe(false)
+  })
+})