Base 7

To convert a number to base 7, we’ll use the divmod() function which returns a pair of numbers (a tuple) representing the quotient and remainder.

Here’s the python code:

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class Solution:
    def convertToBase7(self, num: int) -> str:
        # if num is 0, return "0"
        if num == 0:
            return "0"

        # check if num is negative
        is_negative = num < 0

        # make num positive if it's negative
        if is_negative:
            num = -num

        result = ''

        # convert num to base 7
        while num > 0:
            num, remainder = divmod(num, 7)
            result = str(remainder) + result

        # add "-" prefix if num was negative
        if is_negative:
            result = "-" + result

        return result

In this code, the while loop keeps dividing the number by 7 and prepending the remainder to the result string until the number becomes 0. If the original number was negative, a “-” is prepended to the result.

“Base 7” asks you to convert a given integer to base 7. Before trying to solve it, you might want to familiarize yourself with some problems that involve basic arithmetic operations, number systems and conversions. Here are some problems that can be a good warm-up:

  1. “Reverse Integer” (LeetCode 7): This problem will help you understand how to handle digits of a number, which is useful for the Base 7 problem.

  2. “Palindrome Number” (LeetCode 9): Similar to Reverse Integer, this problem gives you practice in dealing with digits of a number.

  3. “Add Binary” (LeetCode 67): This problem asks you to add two binary strings, which is a similar concept to Base 7, but with a simpler base.

  4. “Add Digits” (LeetCode 258): This problem can give you practice on how to manipulate the digits of a number.

  5. “Number Complement” (LeetCode 476): This problem asks you to find the complement of a number in binary form, which can help you understand how different number systems work.

  6. “Add Strings” (LeetCode 415): This problem asks you to perform arithmetic without using integer-to-string conversions, which is a good practice for understanding number manipulation at a more fundamental level.

  7. “Binary Number with Alternating Bits” (LeetCode 693): This problem helps you understand binary representation better, which is a simpler case of Base 7.

  8. “Base 2” (LeetCode 1017): This problem is about converting a number to base -2. It’s more complex than the Base 7 problem, but working on it will surely help you understand the Base 7 problem better.

  9. “Hexspeak” (LeetCode 1271): This problem is about converting a decimal number to hexadecimal, which can help you understand the concept of different number bases.

  10. “Complement of Base 10 Integer” (LeetCode 1009): This problem gives you more practice on number manipulation and conversion to binary, which is helpful for understanding the Base 7 problem.

These cover number systems and conversions, which will be useful when tackling the “Base 7” problem.

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class Solution:
    def convertToBase7(self, num: int) -> str:
        if not num:
            return "0"
        l = []
        x = num
        if num < 0:
            num =- num
        while num > 0:
            r = num%7
            l.append(str(r))
            num //= 7
        return "".join(l[::-1]) if x>=0 else "-"+ "".join(l[::-1])

Problem Classification

This falls into the domain of Number Theory and String Manipulation.

  1. ‘What’ Components:

    • An integer number (num) is provided as input.
    • The task is to convert this integer into its base 7 representation.
    • The output must be a string representing the base 7 number.

  2. Classification:

    • Problem Type: Conversion problem.
    • Sub-category: Base conversion.

The problem involves converting an integer from base 10 to base 7, which is a common task in Number Theory and Computer Science. It requires understanding of base conversion and arithmetic operations.

Furthermore, since the output should be a string, it also involves String Manipulation, which means turning the numerical result into a string.

This problem can be seen as an application of the ‘division-remainder’ method (repeatedly dividing the number by 7 and noting the remainder) to convert between numerical bases, which is a fundamental concept in Computer Science and Discrete Mathematics. This categorization is based on the specific mathematical concept and the programming skills (arithmetic operations, loops, base conversion, and string manipulation) required to solve the problem.

Clarification Questions

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

Identifying Problem Isomorphism

Can you help me with finding the isomorphism for this problem?

Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?

Language Agnostic Coding Drills

  1. Identification of Coding Concepts:

    • Condition checking: This is the ability to control the flow of code execution based on certain conditions (e.g., if, else).
    • Arithmetic operations: This includes basic mathematical operations like addition, subtraction, multiplication, division, and modulus.
    • Loops: In this code, a while loop is used to repeatedly perform an operation until a certain condition is met.
    • List manipulation: This involves creating an empty list, appending items to it, and reversing it.
    • String manipulation: This includes converting integers to strings, and using the join() method to convert a list of strings to a single string.
    • Negation operation: This involves changing the sign of a number.

  2. Order of Increasing Difficulty:

    • Condition checking: This is a fundamental concept in any programming language and is relatively easy to grasp.
    • Arithmetic operations: These are also fundamental concepts but understanding the modulus operation may be slightly more complex for beginners.
    • List manipulation: While creating and appending to a list is fairly simple, reversing a list might pose a slight challenge for beginners.
    • Loops: Understanding how loops work can be tricky for beginners, especially when loops involve complex conditions or operations.
    • String manipulation: Converting other data types to strings, and understanding the join() method requires a solid understanding of data types and string methods.
    • Negation operation: While it’s a simple operation, understanding where and how to apply it correctly can be challenging.

  3. Problem-Solving Approach:

    • First, check if the given number is zero. If it is, return “0” as a string.
    • Next, handle the case where the number is negative. If it is, convert it to a positive number for the base conversion process, and remember that it was negative.
    • Then, start the process of converting the number to base 7. This involves using a loop that continues until the number is greater than 0. In each iteration of the loop, calculate the remainder when the number is divided by 7, append it to a list, and then update the number by doing integer division by 7.
    • Once the number has been completely converted to base 7, reverse the list (since the digits were calculated in the opposite order), convert it to a string, and return it. If the original number was negative, prepend a “-” to the string.
    • Each of these steps corresponds to a coding concept or drill, and together they form the complete solution to the problem.

Targeted Drills in Python

  1. Python-based coding drills:

    • Condition checking:
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      x = 5
if x < 10:
    print("x is less than 10")
else:
    print("x is greater than or equal to 10")
    • Arithmetic operations:
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      a = 10
b = 3
print("Addition:", a + b)
print("Subtraction:", a - b)
print("Multiplication:", a * b)
print("Division:", a / b)
print("Modulus:", a % b)
    • Loops:
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      i = 0
while i < 5:
    print(i)
    i += 1
    • List manipulation:
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      myList = []
myList.append(1)
myList.append(2)
print(myList)
myList.reverse()
print(myList)
    • String manipulation:
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      myList = ["Hello", "World"]
myString = " ".join(myList)
print(myString)
    • Negation operation:
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      x = 10
x = -x
print(x)

  2. Problem-specific concept:

    • Base conversion: Converting a number from one base to another is a key concept for this problem. The modulus operation is used to find the remainder when the number is divided by the base, and integer division updates the number. This process is repeated until the number is 0. Here is a drill that illustrates this concept:
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      num = 100
base = 7
digits = []
while num > 0:
    digits.append(str(num % base))
    num //= base
digits.reverse()
print("".join(digits))

    This concept is crucial because it forms the core logic of the solution. Without understanding base conversion, it would not be possible to solve this problem.

  3. Integrating the drills:

    • Start by checking if the number is zero using the condition checking drill. If it is, return “0”.
    • Next, check if the number is negative. If it is, use the negation operation to make it positive and remember that it was negative.
    • Then, use the base conversion drill to convert the number to base 7. This involves using a loop, arithmetic operations, and list manipulation.
    • Finally, use string manipulation to convert the list of digits to a string. If the original number was negative, prepend a “-” to the string.
    • By combining these drills in this order, you can create a solution to the problem.