Excel column name from a given column number

Given a positive integer n, return its corresponding Excel column title. In Excel, column titles follow this pattern:

A, B, C, ..., Z, AA, AB, ..., AZ, BA, ..., ZZ, AAA, AAB, ...

This is similar to a base-26 numbering system, but instead of digits 0–25, the letters A–Z represent values 1–26.

Examples:

Input: n = 28
Output: AB
Explanation: 1 to 26 are A to Z, then 27 is AA and 28 is AB.

Input: n = 13
Output: M
Explanation: M is the 13th character of alphabet.

Input: n = 5473578
Output: KYJZF

Recursive Base-26 Conversion – O(log₂₆ n) Time and O(log₂₆ n) Space

The idea is to use recursion to convert the given column number into its corresponding alphabetic name using base 26.

• Divide the number by 26 and find the corresponding letter using the remainder, handling the remainder 0 as 'Z'.
• Recursively process the remaining number or quotient.
• Combine the letters in the correct order to get the column name.

Working of Approach:

• Establish a base case that returns an empty string when the number becomes zero.
• Recursively divide the number by 26 to break it down to its smallest components.
• Decrement the number before calculating the remainder to handle the 1-indexing.
• Convert the remainder to its corresponding alphabetic character by adding it to 'A'.
• Concatenate the recursive call result with the generated character to build the column name.

#include <bits/stdc++.h>
using namespace std;

string colName(int n)
{

    // base case
    if (n == 0)
        return "";

    // decrement n to handle 1 based indexing
    n--;

    return colName(n / 26) + (char)(n % 26 + 'A');
}

int main()
{
    int n = 702;
    cout << colName(n);
    return 0;
}

class GFG {

    static String colName(int n)
    {

        // base case
        if (n == 0)
            return "";

        // decrement n to handle 1 based indexing
        n--;

        return colName(n / 26) + (char)(n % 26 + 'A');
    }

    public static void main(String[] args)
    {
        int n = 702;
        System.out.println(colName(n));
    }
}

def colName(n):

    # base case
    if n == 0:
        return ""

    # decrement n to handle 1 based indexing
    n -= 1

    return colName(n // 26) + chr(n % 26 + ord('A'))


if __name__ == "__main__":
    n = 702
    print(colName(n))

using System;

class GFG {

    static string colName(int n)
    {

        // base case
        if (n == 0)
            return "";

        // decrement n to handle 1 based indexing
        n--;

        return colName(n / 26) + (char)(n % 26 + 'A');
    }

    static void Main()
    {
        int n = 702;
        Console.WriteLine(colName(n));
    }
}

function colName(n)
{

    // base case
    if (n === 0)
        return "";

    // decrement n to handle 1 based indexing
    n--;

    return colName(Math.floor(n / 26))
           + String.fromCharCode(n % 26
                                 + "A".charCodeAt(0));
}

// Driver Code
let n = 702;
console.log(colName(n));

ZZ

Iterative Base-26 Conversion – O(log₂₆ n) Time and O(log₂₆ n) Space

Idea: The idea is to convert the given number into a column name using a base-26 system, where letters from A to Z represent values from 1 to 26.

• Divide the number by 26 and use the remainder to find the corresponding letter.
• If the remainder is 0, use 'Z' and adjust the number accordingly.
• Repeat until the number becomes 0, then reverse the result to get the correct column name.

Note that subtraction of 1 when encountering a remainder of 0 (which maps to 'Z') is crucial because Excel's column naming system is essentially a 1-indexed, base-26 numbering scheme. By subtracting 1 during the division process, the algorithm ensures that these multiples correctly map to 'Z', 'AZ', 'BZ', and so on.

Working of Approach:

• Find the remainder when dividing the column number by 26 to determine the current letter.
• If the remainder is non-zero, convert it to the corresponding letter by subtracting 1 and adding 'A'.
• If the remainder is 0, append 'Z' and adjust the number by subtracting 1 from the integer division result.
• Continuously divide the number by 26 to move to the next digit.
• Reverse the generated string to get the correct column name.

Let us understand with an example, n = 3588

• n = 3588, n % 26 = 0: 0 corresponds to 'Z'. The resultant string will be "Z". Divide n by 26 and subtract 1 from it, so n = 137.
• n = 137, n % 26 = 7: 7 corresponds to 'G'. The resultant string will be "ZG". Divide n by 26, so n = 5.
• n = 5, n % 26 = 5: 5 corresponds to 'E'. The resultant string will be "ZGE". Divide n by 26, so n = 0.
• n = 0, stop the process.
• As the string is generated from right to left, reverse it to get the correct column name. The final string will be "EGZ".

#include <bits/stdc++.h>
using namespace std;

string colName(int n)
{
    string res = "";

    while (n > 0)
    {

        // Find remainder
        int rem = n % 26;

        // If remainder is 0, then a 'Z'
        // must be there in output
        if (rem == 0)
        {
            res += 'Z';
            n = (n / 26) - 1;
        }

        // If remainder is non-zero
        else
        {
            res += (rem - 1) + 'A';
            n = n / 26;
        }
    }

    // Reverse the string
    reverse(res.begin(), res.end());

    return res;
}

int main()
{
    int n = 702;
    cout << colName(n);
    return 0;
}

import java.util.*;

class GFG {

    static String colName(int n)
    {
        StringBuilder res = new StringBuilder();

        while (n > 0) {

            // Find remainder
            int rem = n % 26;

            // If remainder is 0, then a 'Z'
            // must be there in output
            if (rem == 0) {
                res.append('Z');
                n = (n / 26) - 1;
            }

            // If remainder is non-zero
            else {
                res.append((char)((rem - 1) + 'A'));
                n = n / 26;
            }
        }

        // Reverse the string
        res.reverse();

        return res.toString();
    }

    public static void main(String[] args)
    {
        int n = 702;
        System.out.println(colName(n));
    }
}

def colName(n):
    res = ""

    while n > 0:

        # Find remainder
        rem = n % 26

        # If remainder is 0, then a 'Z'
        # must be there in output
        if rem == 0:
            res += 'Z'
            n = (n // 26) - 1

        # If remainder is non-zero
        else:
            res += chr((rem - 1) + ord('A'))
            n //= 26

    # Reverse the string
    return res[::-1]


if __name__ == "__main__":
    n = 702
    print(colName(n))

using System;

class GFG {

    static string colName(int n)
    {
        string res = "";

        while (n > 0) {

            // Find remainder
            int rem = n % 26;

            // If remainder is 0, then a 'Z'
            // must be there in output
            if (rem == 0) {
                res += 'Z';
                n = (n / 26) - 1;
            }

            // If remainder is non-zero
            else {
                res += (char)((rem - 1) + 'A');
                n /= 26;
            }
        }

        // Reverse the string
        char[] charArray = res.ToCharArray();
        Array.Reverse(charArray);

        return new string(charArray);
    }

    static void Main()
    {
        int n = 702;
        Console.WriteLine(colName(n));
    }
}

function colName(n)
{
    let res = "";

    while (n > 0) {

        // Find remainder
        let rem = n % 26;

        // If remainder is 0, then a 'Z'
        // must be there in output
        if (rem === 0) {
            res += "Z";
            n = Math.floor(n / 26) - 1;
        }

        // If remainder is non-zero
        else {
            res += String.fromCharCode((rem - 1)
                                       + "A".charCodeAt(0));
            n = Math.floor(n / 26);
        }
    }

    // Reverse the string
    return res.split("").reverse().join("");
}

// Driver Code
let n = 702;
console.log(colName(n));

ZZ

Related Article : Find the Excel column number from the column title