Create look_and_say_sequence.py

maths/look_and_say_sequence.py

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+"""
+Look-and-Say Sequence
+=====================
+The Look-and-Say sequence is a sequence of integers where each term is
+generated by reading the digits of the previous term aloud.
+
+Starting from "1":
+  1 -> "one 1"           -> 11
+  11 -> "two 1s"         -> 21
+  21 -> "one 2, one 1"   -> 1211
+  1211 -> "one 1, one 2, two 1s" -> 111221
+  ...
+
+Reference: https://en.wikipedia.org/wiki/Look-and-say_sequence
+
+Examples:
+>>> list(look_and_say_sequence(1))
+['1']
+>>> list(look_and_say_sequence(5))
+['1', '11', '21', '1211', '111221']
+>>> next_term('1')
+'11'
+>>> next_term('111221')
+'312211'
+>>> next_term('')
+Traceback (most recent call last):
+    ...
+ValueError: Input term must be a non-empty string of digits.
+"""
+
+from itertools import groupby
+
+
+def next_term(term: str) -> str:
+    """
+    Generate the next term in the Look-and-Say sequence.
+
+    Each group of consecutive identical digits is replaced by
+    the count of digits followed by the digit itself.
+
+    Args:
+        term: A non-empty string of digits representing the current term.
+
+    Returns:
+        The next term in the sequence as a string.
+
+    Raises:
+        ValueError: If the input term is empty.
+
+    Examples:
+        >>> next_term('1')
+        '11'
+        >>> next_term('11')
+        '21'
+        >>> next_term('21')
+        '1211'
+        >>> next_term('1211')
+        '111221'
+        >>> next_term('111221')
+        '312211'
+    """
+    if not term:
+        raise ValueError("Input term must be a non-empty string of digits.")
+    return "".join(str(len(list(group))) + digit for digit, group in groupby(term))
+
+
+def look_and_say_sequence(num_terms: int, start: str = "1"):
+    """
+    Generate the Look-and-Say sequence up to num_terms terms.
+
+    Args:
+        num_terms: The number of terms to generate (must be >= 1).
+        start: The starting term (default is "1").
+
+    Yields:
+        Each term of the sequence as a string.
+
+    Raises:
+        ValueError: If num_terms is less than 1.
+
+    Examples:
+        >>> list(look_and_say_sequence(1))
+        ['1']
+        >>> list(look_and_say_sequence(5))
+        ['1', '11', '21', '1211', '111221']
+        >>> list(look_and_say_sequence(6))
+        ['1', '11', '21', '1211', '111221', '312211']
+        >>> list(look_and_say_sequence(0))
+        Traceback (most recent call last):
+            ...
+        ValueError: num_terms must be a positive integer.
+    """
+    if num_terms < 1:
+        raise ValueError("num_terms must be a positive integer.")
+    term = start
+    for _ in range(num_terms):
+        yield term
+        term = next_term(term)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print("Look-and-Say Sequence (first 8 terms):")
+    for i, term in enumerate(look_and_say_sequence(8), start=1):
+        print(f"  Term {i}: {term}")