1-bit and 2-bit Characters

This problem can be solved by checking the bits from left to right. A 0 represents a one-bit character, whereas a 1 represents a two-bit character. We need to find out if the last character in the list is a one-bit character or not.

Python solution:

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class Solution:
    def isOneBitCharacter(self, bits: List[int]) -> bool:
        # Initialize a pointer i to start from the beginning
        i = 0
        while i < len(bits) - 1:  # loop until the second last element
            if bits[i] == 0:  # one-bit character
                i += 1
            else:  # two-bit character
                i += 2
        # If the loop ends exactly at the last element (i.e., len(bits)-1), it means the last character is one-bit
        return i == len(bits) - 1

This solution works by scanning the bits list from the left. If it encounters a 0 (which is a one-bit character), it moves one step forward. If it encounters a 1 (which starts a two-bit character), it moves two steps forward. In the end, if i points to the last element, it means the last character is a one-bit character, and the function returns True. Otherwise, the function returns False.

Identifying Problem Isomorphism

“1-bit and 2-bit Characters” is approximately isomorphic to “Decode Ways”.

The “1-bit and 2-bit Characters” problem is about checking if the last character must be a 1-bit character given a binary array consisting of several 1-bit and 2-bit characters.

“Decode Ways” asks for the total number of ways that a given digit string can be decoded, where 1-26 corresponds to ‘A’-‘Z’.

The reasoning behind this isomorphism is that both problems essentially deal with interpreting an array or a string of digits based on whether they can be read in one or two digit units. Although the tasks are different - one asks to check if the last digit must be decoded as one digit, and the other asks to count the number of possible interpretations - they share the same core logic of interpreting a sequence of digits based on 1-bit or 2-bit units.

“Decode Ways” is more complex as it requires counting all possible interpretations, whereas “1-bit and 2-bit Characters” only requires a Boolean output determining the interpretation of the last digit. If there were multiple isomorphic problems, “1-bit and 2-bit Characters” would be the simpler one, followed by “Decode Ways”.

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class Solution:
    def isOneBitCharacter(self, bits: List[int]) -> bool:
        """
        :type bits: List[int]
        :rtype: bool
        """

        ret = True
        for bit in bits[-2::-1]:
            if bit: ret = not ret
            else: break
        return ret

Problem Classification

This problem belongs to the category of Array Manipulation and Bit Manipulation.

‘What’ Components:

  1. A binary array ‘bits’ ending with ‘0’.
  2. Two special characters represented by ‘0’ (one bit) and ‘10’ or ‘11’ (two bits).
  3. The task is to determine if the last character in the array must be a one-bit character.

This can be classified as a Decision Problem since we need to make a decision based on the data and return either ’true’ or ‘false’. It also involves Traversal, as we need to traverse the array to make the decision, and Pattern Recognition, as we need to identify patterns of bits representing characters.

In the problem, we are given a binary array that ends with a ‘0’. The array contains patterns representing two types of characters. The task is to identify these patterns and decide if the final character is a one-bit character. This problem is a mix of decision-making, array manipulation, and pattern recognition. The solution would likely involve traversing the array and identifying the patterns of ‘0’, ‘10’, and ‘11’ while ensuring that the last character is a one-bit character. Hence, the categorization as a decision, traversal, and pattern recognition problem.

Language Agnostic Coding Drills

  1. Dissection of Code and Identification of Distinct Concepts:

    • Concept 1: Function definition and return type declaration.
    • Concept 2: Python’s list slicing. It is used to reverse the list and to specify where to start and end the slicing.
    • Concept 3: Looping over a list in Python.
    • Concept 4: Conditional statements: using an if-else construct to apply logic based on the value of the bit.
    • Concept 5: The usage of a flag variable (ret) to store a temporary result. It is used to keep track of whether the last character is a one-bit character or not.
    • Concept 6: Logical negation (not operator): it’s used to flip the value of ret each time we encounter a ‘1’ while iterating.
    • Concept 7: Control flow statements: the break statement is used to terminate the loop as soon as we encounter a ‘0’.

  2. Ordering of Concepts Based on Difficulty:

    • Easy: Concept 1 (Function definition), Concept 3 (Looping over a list), Concept 4 (Conditional statements)
    • Medium: Concept 2 (List slicing), Concept 5 (Usage of a flag variable), Concept 7 (Control flow statements)
    • Hard: Concept 6 (Logical negation)

    The first three concepts are foundational to programming and Python. The medium concepts introduce more nuanced Python functionality and basic algorithmic techniques, while the logical negation concept can be confusing without a strong understanding of boolean logic.

  3. Problem-Solving Approach:

    The given problem can be solved by traversing the list in reverse, starting from the second last element (as the last element is always a ‘0’). As long as we encounter ‘1’s, we flip the ret variable. The moment we encounter a ‘0’, we break out of the loop. The value of ret at this point will be True if the last character is a one-bit character, and False otherwise.

    The various coding drills align with this strategy as follows:

    • Function definition (Concept 1) provides the framework to implement this solution.
    • Looping over the list (Concept 3) and List slicing (Concept 2) allow us to traverse the list in reverse.
    • The flag variable (Concept 5) stores the intermediate results of our computation.
    • The if-else construct (Concept 4) is used to implement the logic based on the value of the bit.
    • The not operator (Concept 6) is used to flip the value of ret.
    • The break statement (Concept 7) is used to exit the loop once we have enough information to decide the result.

Targeted Drills in Python

  1. Function Definition and Return Type Declaration: This is a simple drill to get familiar with defining a function in Python.
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def my_function():
    return "Hello, World!"
print(my_function())
  1. Python’s List Slicing: List slicing is a powerful feature in Python that allows us to access a subset of a list’s items.
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my_list = [1, 2, 3, 4, 5]
print(my_list[::-1])  # Reverses the list
  1. Looping Over a List in Python: This drill is about iterating over a list using a for loop.
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my_list = [1, 2, 3, 4, 5]
for item in my_list:
    print(item)
  1. Conditional Statements: Conditional statements let us execute certain pieces of code based on a condition.
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value = 5
if value > 0:
    print("Positive")
else:
    print("Non-positive")
  1. Usage of a Flag Variable: A flag variable is used to indicate whether a certain condition has been met.
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flag = False
for i in range(10):
    if i == 5:
        flag = True
        break
print("Flag:", flag)
  1. Logical Negation: Logical negation flips the truthiness of a value.
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value = True
print("Negated Value:", not value)
  1. Control Flow Statements: This drill is about using the break statement to terminate a loop prematurely.
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for i in range(10):
    print(i)
    if i == 5:
        break

Integration and Order:

All the drilled concepts come together to form the solution.

  1. We first define a function (Concept 1) where we initialize a flag variable to keep track of our status (Concept 5).
  2. We then use a for loop (Concept 3) to traverse the array from the second last element to the start, which is achieved by using Python’s list slicing (Concept 2).
  3. Inside the loop, we use conditional statements (Concept 4) to check if each bit is 1 or 0. If it’s 1, we use logical negation (Concept 6) to flip the flag variable. If it’s 0, we terminate the loop using a break statement (Concept 7).
  4. Finally, the function returns the flag variable, which now indicates whether the last character is a one-bit character or not.