9.35 Excel Sheet Column Number

Source: src/main/kotlin/string/ExcelSheetToColumnNumber.kt Pattern: base-26 decoding · Core page

The Problem

“AB” → 28 (A=1, B=2, … base-26 without zero).

• Constraints: n ≤ 7.

Examples

Input:  columnTitle = "AB"   -> Output: 28
Input:  columnTitle = "ZY"   -> Output: 701

Intuition — Horner’s rule in base 26

var base = 1
var sum = 0

for (i in columnTitle.length - 1 downTo 0) {
    sum += (columnTitle[i] - 'A' + 1) * base
    base *= 26
}
return sum

Approach 1 — Horner decode (the repo’s version, optimal)

Approach 2 — Forward Horner (cleaner)

sum = sum * 26 + (c - 'A' + 1) left to right.

class ExcelSheetToColumnNumber {
    /**
     * @param columnTitle column title
     * @return            column number
     */
    fun titleToNumber(columnTitle: String): Int {
        var result = 0

        for (ch in columnTitle) {
            result = result * 26 + (ch - 'A' + 1)
        }
        return result
    }
}

public class ExcelSheetColumnNumber {
    /**
     * @param columnTitle column title
     * @return            column number
     */
    public int titleToNumber(String columnTitle) {
        int result = 0;

        for (char c : columnTitle.toCharArray()) {
            result = result * 26 + (c - 'A' + 1);
        }
        return result;
    }
}

#include <string>

class ExcelSheetColumnNumber {
public:
    /**
     * @param columnTitle column title
     * @return            column number
     */
    int titleToNumber(std::string columnTitle) {
        int result = 0;

        for (char c : columnTitle) {
            result = result * 26 + (c - 'A' + 1);
        }
        return result;
    }
};

def title_to_number(column_title: str) -> int:
    """
    @param column_title: column title
    @return:             column number
    """
    result = 0

    for ch in column_title:
        result = result * 26 + (ord(ch) - ord("A") + 1)

    return result

#![allow(unused)]
fn main() {
impl Solution {
    /// @param column_title column title
    /// @return             column number
    pub fn title_to_number(column_title: String) -> i32 {
        column_title.bytes().fold(0, |acc, b| acc * 26 + (b - b'A' + 1) as i32)
    }
}
}

Reading the code — what’s actually happening

fun titleToNumber(columnTitle: String): Int {
    var result = 0
    for (ch in columnTitle) {
        result = result * 26 + (ch - 'A' + 1)
    }
    return result
}

Think of reading a number left to right: "AB" is like reading "28" digit by digit — each new digit shifts the accumulated value left by one place. The only difference is the base: here it’s 26, and the “digits” are letters where 'A' = 1, 'B' = 2, …, 'Z' = 26.

• ch - 'A' + 1 converts a letter to its 1-based value. 'A' is the zero point, so 'C' - 'A' = 2, plus 1 → 3. That +1 is the “no zero digit” quirk: Excel’s alphabet has no zero, so 'A' is 1, not 0.
• result = result * 26 + value is Horner’s rule. When we see 'A', result goes 0 → 1. When we see 'B', we multiply the old 1 by 26 (shifting "A" into the high place, like "1" becoming "10" in decimal) and add 'B'’s value 2 → 1 * 26 + 2 = 28. This is exactly how "28" would parse in base 10: 2 * 10 + 8.
• Why does the right-to-left version also work? The alternative approach multiplies a running base (1, 26, 676, …) by each letter from the end: 'B' * 1 + 'A' * 26 = 2 + 26 = 28. Same math, opposite direction. The left-to-right Horner version is preferred because it needs no base variable and no reverse iteration.

For "ZY": 'Z' → 26, then 26 * 26 + 25 = 701 ✓.

Dry run

Input: columnTitle = "AB".

A: 0*26+1 = 1.  B: 1*26+2 = 28.
Output: 28 ✓

Complexity

Time. One pass:

$$ T(n) = O(n) $$

Space. Constants:

$$ S(n) = O(1) $$

Variants & follow-ups

• Excel Sheet Column Title — the inverse (encode).
• Interview follow-up: “Why is this not plain base-26?” There’s no zero digit — ‘A’ is 1, not 0. Horner still works because each position contributes (c−A+1) at its weight.