Leetcode: Excel Sheet Column Title

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本文介绍了一种将正整数转换为Excel工作表中对应列标题的方法，例如1转换为A，26转换为Z，27转换为AA等。通过数学分析，详细解释了如何使用模运算和除法来实现这一转换过程。

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Question

Given a positive integer, return its corresponding column title as appear in an Excel sheet.

For example:

1 -> A
2 -> B
3 -> C
...
26 -> Z
27 -> AA
28 -> AB

Credits:
Special thanks to @ifanchu for adding this problem and creating all test cases.

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Analysis

This problem is to convert 1-26 to A-Z. Commonly, this kind of problem using ‘mod’ is in range [0,25].

The general equation is

a n * 26 n + a n - 1 * 26 n - 1 + . . . + a 1 * 261 + a 0

$a_n *26^n+a_{n-1}*26^{n-1} + ...+a_1 *26^1+a_0$
where

ai∈[1,26] $a_i\in[1,26]$

Each time we get the last digit by computing d=n%26. To convert it to be [0,25], we have to decrease the last digit of n by 1.
For example, after get $d = a_0 -1$ , we do n = n/26, so we have

a n * 26 n - 1 + a n - 1 * 26 n - 2 + . . . + a 1

$a_n *26^{n-1}+a_{n-1}*26^{n-2} + ...+a_1$
So by doing d=(n-1)%26, we get the number[0,25] for

a1 $a_1$ .

See solution v2

Solution

v1

The idea of this solution is to lend carry=1 to the lower digit if it is 26.

class Solution:
    # @param {integer} n
    # @return {string}
    def convertToTitle(self, n):
        res = []
        if n<=0:
            return res 

        while(n>0):
            d = n%26
            n = n/26
            if d==0:
                d = 26
                n = n -1 
            res = [ str(unichr(d+64)) ] + res

        return "".join(res)

v2

This is general solution

class Solution:
    # @param {integer} n
    # @return {string}
    def convertToTitle(self, n):
        res = []
        if n<=0:
            return res 

        while(n>0):
            d = (n-1)%26
            res = [ str(unichr(d+65)) ] + res
            n = n/26

        return "".join(res)