Binary Number with Alternating Bits

Here is a Python solution.

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class Solution:
    def hasAlternatingBits(self, n: int) -> bool:
        n = bin(n)[2:] # convert the integer to binary representation (string format)
        for i in range(len(n) - 1):
            if n[i] == n[i + 1]: # check if there are consecutive same bits
                return False
        return True

This code first transforms the input integer n to its binary representation. The bin() function returns a string which starts with ‘0b’, so we use [2:] to slice off the first two characters.

Then, we iterate over the string. For each bit, we compare it with the next one. If we find any pair of adjacent bits that are the same, we immediately return False, indicating that n does not have alternating bits. If we finish the loop without finding any such pair, we return True.

This solution uses string manipulation and loop iteration, which are basic programming constructs. It directly implements the problem statement.

In this problem, we’re doing a “Neighbor Comparison”. That is, we’re going through each bit in the binary representation of the number and checking if it’s the same as the next one. If it is, we immediately know that the number doesn’t have alternating bits and we can return False.

Another high level construct at play here is “Binary Conversion”. Before we can compare neighboring bits, we first need to convert the integer into its binary representation. This is done using the built-in bin() function.

So, in this problem, the high level constructs are:

  1. Binary Conversion: to get a string representing the binary form of the number.
  2. Neighbor Comparison: to check if any two adjacent bits in the binary string are the same.

Identifying Problem Isomorphism

“Binary Number with Alternating Bits” can be approximately mapped to “Palindrome Number”.

In “Binary Number with Alternating Bits”, you’re required to check if a given number in binary representation does not have any adjacent bits that are the same. This involves a degree of checking the number’s binary structure and examining its pattern.

“Palindrome Number” also involves examining the pattern of a number - in this case, whether it reads the same backward as forward. Both problems involve a process of deconstructing the number and examining its pattern.

“Binary Number with Alternating Bits” is more complex due to the binary representation involved, whereas “Palindrome Number” only requires the basic understanding of a palindrome and number manipulation.

Before tackling the “Binary Number with Alternating Bits” problem, understand binary representation of numbers and bitwise operations. Here are some simpler problems to understand these necessary concepts:

  1. “Number of 1 Bits” (LeetCode 191): Understand how to manipulate and count bits in a number.

  2. “Reverse Bits” (LeetCode 190): Get comfortable with reversing binary representation.

  3. “Single Number” (LeetCode 136): A problem to understand the bitwise XOR operation.

  4. “Power of Two” (LeetCode 231): Understand how binary representation works in the case of numbers which are powers of two.

  5. “Power of Four” (LeetCode 342): Similar to the previous problem but requires an extra step of understanding.

  6. “Counting Bits” (LeetCode 338): A problem to understand bit manipulation and dynamic programming.

  7. “Sum of Two Integers” (LeetCode 371): Understand how binary addition works.

  8. “Missing Number” (LeetCode 268): A problem that uses bitwise manipulation to find a missing number.

  9. “Binary Watch” (LeetCode 401): This problem can help you understand how to relate real-world scenarios with binary numbers.

  10. “Convert a Number to Hexadecimal” (LeetCode 405): This problem can help you understand binary to hexadecimal conversion.

These cover fundamental operations and concepts around binary numbers and bitwise operations.

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class Solution:
    def hasAlternatingBits(self, n: int) -> bool:
        bits = bin(n)
        return "00" not in bits and "11" not in bits

Problem Classification

The problem falls into the domain of Bit Manipulation in Computer Science. Bit manipulation involves directly working with the smallest unit of data in a machine, the binary digit or ‘bit’.

Problem Components:

Inputs:

  1. A positive integer

Outputs:

  1. A Boolean value (True or False), indicating whether the integer has alternating bits.

This is a decision problem where you’re asked to decide whether a given condition is true or false. It’s also a validation problem where you need to validate whether the given integer has alternating bits or not. The problem is essentially about binary representation and manipulation of integers.

The problem can be categorized as a bit manipulation problem because it requires analysis and manipulation of the binary representation of an integer. We need to check each pair of adjacent bits in the binary representation to see if they are always different, which is a classic bit manipulation task. Furthermore, it’s a decision problem since the output is a boolean value, and it is a validation problem as we are validating the condition of alternating bits.

Clarification Questions

What are the clarification questions we can ask about this problem?

Identifying Problem Isomorphism

Language Agnostic Coding Drills

  1. Dissection of Code into Distinct Concepts:

a. Data Type Conversion: Conversion of an integer to its binary representation using the built-in bin function.

b. String Manipulation: Checking if a particular substring is present in a given string using the in keyword.

c. Logical Operators: Use of the and logical operator to combine two conditions.

d. Return Statements: The function returns the result of a logical expression.

  1. List of Coding Concepts (Drills) in Increasing Difficulty:

a. Data Type Conversion: This is a relatively simple concept that involves changing the data type of a value. Python provides built-in functions for data type conversions.

b. Return Statements: Return statements are used in functions to send the results back to the caller. This concept is also simple and fundamental to the structure of functions.

c. String Manipulation: Checking for the presence of a substring in a string can be done using the in keyword in Python. This requires an understanding of strings and the operations that can be performed on them.

d. Logical Operators: Logical operators are used to combine multiple conditions. An understanding of boolean logic is needed to effectively use these operators. This concept might be slightly more complex than the previous ones.

  1. Problem-Solving Approach:

a. Step 1 (Data Type Conversion): Convert the given integer into binary representation. The bin function is used to accomplish this. This binary string now needs to be checked to see if it has alternating bits.

b. Step 2 (String Manipulation): Check if the binary string contains “00” or “11”. These substrings would indicate that the integer does not have alternating bits. We use the in keyword in Python to check for the presence of these substrings.

c. Step 3 (Logical Operators): We want to make sure that neither “00” nor “11” are present in the binary string. Therefore, we use the logical and operator to combine these two conditions. If neither condition is true, it means that the integer does have alternating bits.

d. Step 4 (Return Statements): Return the result of the logical expression from the function. If the expression is true, then the integer has alternating bits, and if it’s false, then the integer doesn’t have alternating bits.

The correct application and integration of these concepts result in a function that successfully determines whether a given integer has alternating bits.

Targeted Drills in Python

Sure, let’s create separate Python-based drills for each identified coding concept:

  1. Data Type Conversion: Python provides several built-in functions to convert between different data types. In our case, we’re interested in converting an integer to a binary string.
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def convert_to_binary(n):
    return bin(n)
  1. Return Statements: A function in Python can send back a result using a return statement. The return statement immediately ends the function’s execution and sends the result back to the caller.
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def square(n):
    return n ** 2
  1. String Manipulation: In Python, you can check if a substring exists within a larger string using the in keyword.
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def check_substring(s, sub):
    return sub in s
  1. Logical Operators: Python’s logical operators and, or, not are used to combine, invert or test boolean values.
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def check_conditions(condition1, condition2):
    return condition1 and condition2

Problem-specific Concept: The problem-specific concept for this problem is checking for alternating bits in a binary representation, which is a combination of the general concepts we discussed above.

The Python drill for this concept would involve converting the number to its binary representation and checking if it contains consecutive 0’s or 1’s.

Assembling the Drills:

To assemble these drills into the final solution, you would:

  1. Convert the given integer to its binary representation.
  2. Check if the binary string contains ‘00’ or ‘11’.
  3. Use logical and to combine the conditions and return the result.