Excel Sheet Column Title

Intuition

• The Arabs invented the number 0.
• This number is useful in exactly this case, since it allows for you to convert the column number to a mapping from A to Z, with A starting at 0 and Z ending at 25.
• This is useful to avoid the edge case of getting 0, but 0 mapping to Z, which causes a bunch of problems, such as the number 1 mapping to A, but not needing A since we already found Z from the remainder being 0.

Complexity

Runtime

$O(lo{g}_{26}N)$ since we are dividing by 26 each time until we reach 0, meaning $\frac{N}{26^k}$, which becomes $lo{g}_{26}N$.

Space

$O(N)$ to store result, or $O(1)$ if you don’t consider the result as part of the space complexity.

Code

class Solution:
    def convertToTitle(self, columnNumber: int) -> str:
        res = deque()
        while columnNumber > 0:
            columnNumber -= 1
            columnNumber, remainder = divmod(columnNumber, 26)
            res.appendleft(chr(ord('A') + remainder))
 
        return ''.join(res)

Notes

Cards

START Basic Front: Excel Sheet Column Title Back: Subtract by 1 to convert to base 26, with A starting at 0 and Z ending at 25, thereby making divmod work.

END

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References

Excel Sheet Column Title