Add Word Break algorithm (#11687)

* Add Word Break algorithm

* Add Word Break algorithm

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backtracking/word_break.py

@@ -0,0 +1,71 @@
+"""
+Word Break Problem is a well-known problem in computer science.
+Given a string and a dictionary of words, the task is to determine if
+the string can be segmented into a sequence of one or more dictionary words.
+
+Wikipedia: https://en.wikipedia.org/wiki/Word_break_problem
+"""
+
+
+def backtrack(input_string: str, word_dict: set[str], start: int) -> bool:
+    """
+    Helper function that uses backtracking to determine if a valid
+    word segmentation is possible starting from index 'start'.
+
+    Parameters:
+    input_string (str): The input string to be segmented.
+    word_dict (set[str]): A set of valid dictionary words.
+    start (int): The starting index of the substring to be checked.
+
+    Returns:
+    bool: True if a valid segmentation is possible, otherwise False.
+
+    Example:
+    >>> backtrack("leetcode", {"leet", "code"}, 0)
+    True
+
+    >>> backtrack("applepenapple", {"apple", "pen"}, 0)
+    True
+
+    >>> backtrack("catsandog", {"cats", "dog", "sand", "and", "cat"}, 0)
+    False
+    """
+
+    # Base case: if the starting index has reached the end of the string
+    if start == len(input_string):
+        return True
+
+    # Try every possible substring from 'start' to 'end'
+    for end in range(start + 1, len(input_string) + 1):
+        if input_string[start:end] in word_dict and backtrack(
+            input_string, word_dict, end
+        ):
+            return True
+
+    return False
+
+
+def word_break(input_string: str, word_dict: set[str]) -> bool:
+    """
+    Determines if the input string can be segmented into a sequence of
+    valid dictionary words using backtracking.
+
+    Parameters:
+    input_string (str): The input string to segment.
+    word_dict (set[str]): The set of valid words.
+
+    Returns:
+    bool: True if the string can be segmented into valid words, otherwise False.
+
+    Example:
+    >>> word_break("leetcode", {"leet", "code"})
+    True
+
+    >>> word_break("applepenapple", {"apple", "pen"})
+    True
+
+    >>> word_break("catsandog", {"cats", "dog", "sand", "and", "cat"})
+    False
+    """
+
+    return backtrack(input_string, word_dict, 0)