1bit and 2bit Characters
This problem can be solved by checking the bits from left to right. A 0 represents a onebit character, whereas a 1 represents a twobit character. We need to find out if the last character in the list is a onebit character or not.
Python solution:


This solution works by scanning the bits
list from the left. If it encounters a 0
(which is a onebit character), it moves one step forward. If it encounters a 1
(which starts a twobit character), it moves two steps forward. In the end, if i
points to the last element, it means the last character is a onebit character, and the function returns True
. Otherwise, the function returns False
.
Identifying Problem Isomorphism
“1bit and 2bit Characters” is approximately isomorphic to “Decode Ways”.
The “1bit and 2bit Characters” problem is about checking if the last character must be a 1bit character given a binary array consisting of several 1bit and 2bit characters.
“Decode Ways” asks for the total number of ways that a given digit string can be decoded, where 126 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 1bit or 2bit units.
“Decode Ways” is more complex as it requires counting all possible interpretations, whereas “1bit and 2bit Characters” only requires a Boolean output determining the interpretation of the last digit. If there were multiple isomorphic problems, “1bit and 2bit Characters” would be the simpler one, followed by “Decode Ways”.


Problem Classification
This problem belongs to the category of Array Manipulation and Bit Manipulation.
‘What’ Components:
 A binary array ‘bits’ ending with ‘0’.
 Two special characters represented by ‘0’ (one bit) and ‘10’ or ‘11’ (two bits).
 The task is to determine if the last character in the array must be a onebit 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 onebit character. This problem is a mix of decisionmaking, 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 onebit character. Hence, the categorization as a decision, traversal, and pattern recognition problem.
Language Agnostic Coding Drills
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 ifelse 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 onebit character or not.  Concept 6: Logical negation (
not
operator): it’s used to flip the value ofret
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’.
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.
ProblemSolving 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 ofret
at this point will beTrue
if the last character is a onebit character, andFalse
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 ifelse 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 ofret
.  The
break
statement (Concept 7) is used to exit the loop once we have enough information to decide the result.
Targeted Drills in Python
 Function Definition and Return Type Declaration: This is a simple drill to get familiar with defining a function in Python.


 Python’s List Slicing: List slicing is a powerful feature in Python that allows us to access a subset of a list’s items.


 Looping Over a List in Python: This drill is about iterating over a list using a for loop.


 Conditional Statements: Conditional statements let us execute certain pieces of code based on a condition.


 Usage of a Flag Variable: A flag variable is used to indicate whether a certain condition has been met.


 Logical Negation: Logical negation flips the truthiness of a value.


 Control Flow Statements: This drill is about using the
break
statement to terminate a loop prematurely.


Integration and Order:
All the drilled concepts come together to form the solution.
 We first define a function (Concept 1) where we initialize a flag variable to keep track of our status (Concept 5).
 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).
 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).
 Finally, the function returns the flag variable, which now indicates whether the last character is a onebit character or not.