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Base 7

Difficulty: Easy

Problem Description

Given an integer num, return a string of its base 7 representation.

Key Insights

  • Base 7 representation uses digits from 0 to 6.
  • For negative numbers, the result should include a negative sign.
  • The conversion can be done using repeated division by 7, capturing remainders.

Space and Time Complexity

Time Complexity: O(log7(num))
Space Complexity: O(1)

Solution

To convert an integer to its base 7 representation, we can use a loop that repeatedly divides the number by 7, capturing the remainders. The remainders represent the digits in reverse order, so they need to be collected and reversed at the end. The algorithm handles negative numbers by first checking the sign and converting the absolute value of the number.

Code Solutions

def convertToBase7(num: int) -> str:
    if num == 0:
        return "0"
    
    negative = num < 0
    num = abs(num)
    base7 = []
    
    while num > 0:
        base7.append(str(num % 7))  # Get remainder
        num //= 7  # Divide by 7
    
    if negative:
        base7.append('-')  # Append negative sign if necessary
    
    return ''.join(reversed(base7))  # Reverse the list and join

# Example usage
print(convertToBase7(100))  # Output: "202"
print(convertToBase7(-7))   # Output: "-10"
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