#504

Easy

LeetCode Problem Workspace

Base 7

Convert any given integer to its base 7 string representation using efficient math and string manipulation techniques.

Problem Statement

Given an integer num, return its string representation in base 7. Negative numbers should start with a '-' sign. Implement an efficient method combining arithmetic and string operations.

For example, if num = 100, the output should be "202" because 100 in base 7 is 2 7^2 + 0 7^1 + 2*7^0. Similarly, num = -7 should return "-10".

Examples

Example 1

Input: num = 100

Output: "202"

Example details omitted.

Example 2

Input: num = -7

Output: "-10"

Example details omitted.

Constraints

-107 <= num <= 107

Solution Approach

Use repeated division and modulo

Divide the number by 7 repeatedly, storing the remainder each time. Build the base 7 digits in reverse order, then join them into a final string. This ensures correct digit order for the base 7 representation.

Handle negative numbers carefully

If the input number is negative, compute the base 7 string for its absolute value, then prepend a '-' sign. This avoids sign errors that commonly appear in naive implementations.

Convert remainders to string efficiently

Each remainder from the division corresponds to a single base 7 digit. Convert integers to string using standard methods and concatenate them efficiently to minimize string-building overhead.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(log7|num|) because each division reduces the number by a factor of 7. Space complexity is also O(log7|num|) to store the resulting digits in a string.

What Interviewers Usually Probe

Are you handling negative numbers correctly with a leading '-' sign?
Can you perform the conversion without using built-in base functions?
Are you efficiently building the string from the remainders to avoid order issues?

Common Pitfalls or Variants

Common pitfalls

Forgetting to prepend '-' for negative numbers can cause incorrect output.
Reversing the digits incorrectly when joining remainders results in wrong base 7 string.
Using float division instead of integer division may produce unexpected results.

Follow-up variants

Convert an integer to any arbitrary base k as a string.
Handle very large integers efficiently using string concatenation only.
Convert a list of integers to their base 7 strings in batch processing.

FAQ

What is the Base 7 problem about?

It requires converting a given integer into its base 7 string representation, handling both positive and negative numbers.

Can I use built-in functions to solve Base 7?

While some languages offer base conversion utilities, interview best practice is implementing repeated division and modulo manually.

How do negative numbers affect Base 7 conversion?

Compute the conversion on the absolute value, then prepend a '-' to ensure correct output.

What is the time complexity for Base 7 conversion?

The time complexity is O(log7|num|) because each division reduces the number by a factor of 7.

Does Base 7 conversion tie to a common interview pattern?

Yes, it exemplifies the 'Math plus String' pattern, combining arithmetic digit extraction with careful string construction.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def convertToBase7(self, num: int) -> str:
        if num == 0:
            return '0'
        if num < 0:
            return '-' + self.convertToBase7(-num)
        ans = []
        while num:
            ans.append(str(num % 7))
            num //= 7
        return ''.join(ans[::-1])

Continue Practicing

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