Programming Riddle: How might you translate an Excel column name to a number?

Question

I was recently asked in a job interview to resolve a programming puzzle that I thought it would be interesting to share. It's about translating Excel column letters to actual numbers, if you recall, Excel names its columns with letters from A to Z, and then the sequence goes AA, AB, AC... AZ, BA, BB, etc.

You have to write a function that accepts a string as a parameter (like "AABCCE") and returns the actual column number.

The solution can be in any language.

Answer 1

I wrote this ages ago for some Python script:

def index_to_int(index):
    s = 0
    pow = 1
    for letter in index[::-1]:
        d = int(letter,36) - 9
        s += pow * d
        pow *= 26
    # excel starts column numeration from 1
    return s

Answer 2

Sounds like a standard reduce to me:

Python:

def excel2num(x): 
    return reduce(lambda s,a:s*26+ord(a)-ord('A')+1, x, 0)

C#:

int ExcelToNumber(string x) {
    return x.Aggregate(0, (s, c) => s * 26 + c - 'A' + 1 );
}

Answer 3

Read a column name from STDIN and print out its corresponding number:

perl -le '$x = $x * 26 - 64 + ord for <> =~ /./g; print $x'

Caveats: Assumes ASCII.

EDIT: Replaced " with ' so that your shell won't interpolate $x in the string.

Answer 4

Coincidentally I've solved the same problem using javascript

$(function() { //shorthand document.ready function
    var getNumber = function(x) {
        var result = 0;
        var multiplier = 1;
        for ( var i = x.length-1; i >= 0; i--)
        { 
            var value = ((x[i].charCodeAt(0) - "A".charCodeAt(0)) + 1);
            result = result + value * multiplier;
            multiplier = multiplier * 26;
        }
        return result;
    };
    
    $('#form').on('submit', function(e) { //use on if jQuery 1.7+
        e.preventDefault();  //prevent form from submitting
        var data = $("#number").val();
        $('#answer').text(getNumber(data));
    });
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<form id="form">
<input type="text" id="number"></input>
    <button>submit</button>
</form>
<p id="answer"></p>

    var getNumber = function(x) {
        var result = 0;
        var multiplier = 1;
        for ( var i = x.length-1; i >= 0; i--)
        { 
            var value = ((x[i].charCodeAt(0) - "A".charCodeAt(0)) + 1);
            result = result + value * multiplier;
            multiplier = multiplier * 26;
        }
        return result;
    };

http://jsfiddle.net/M7Xty/1/

Answer 5

Hah - written it already in our code base - about 3 different times :(

%% @doc Convert an string to a decimal integer
%% @spec b26_to_i(string()) -> integer()

b26_to_i(List) when is_list(List) ->
    b26_to_i(string:to_lower(lists:reverse(List)),0,0).

%% private functions
b26_to_i([], _Power, Value) -> 
    Value;

b26_to_i([H|T],Power,Value)->
    NewValue = case (H > 96) andalso (H < 123) of
                   true ->
                       round((H - 96) * math:pow(26, Power));
                   _    ->
                       exit([H | T] ++ " is not a valid base 26 number")
               end,
    b26_to_i(T, Power + 1, NewValue + Value).

The riddle is that it isn't actually a Base26 representation of a number (we are lying to ourselves in our function name here) because there is no 0 in it.

The sequence is: A, B, C ... Z, AA, AB, AC

and not: A, B, C ...Z, BA, BB, BC

(the language is Erlang, mais oui).

Answer 6

You can do this in C like this:

unsigned int coltonum(char * string)
{
   unsigned result = 0;
   char ch;

   while(ch = *string++)
      result = result * 26 + ch - 'A' + 1;

  return result;
}

No error checking, only works for upper case strings, string must be null terminated.

Answer 7

Get the column number from its name

Java:

public int getColNum (String colName) {

    //remove any whitespace
    colName = colName.trim();

    StringBuffer buff = new StringBuffer(colName);

    //string to lower case, reverse then place in char array
    char chars[] = buff.reverse().toString().toLowerCase().toCharArray();

    int retVal=0, multiplier=0;

    for(int i = 0; i < chars.length;i++){
        //retrieve ascii value of character, subtract 96 so number corresponds to place in alphabet. ascii 'a' = 97 
        multiplier = (int)chars[i]-96;
        //mult the number by 26^(position in array)
        retVal += multiplier * Math.pow(26, i);
    }
    return retVal;
}

Answer 8

Assuming column A = 1

int GetColumnNumber(string columnName)
{
  int sum = 0;
  int exponent = 0;
  for(int i = columnName.Length - 1; i>=0; i--)
  {
    sum += (columnName[i] - 'A' + 1) *  (GetPower(26, exponent));
    exponent++;
  }
  return sum;
}

int GetPower(int number, int exponent)
{
  int power = 1;
  for(int i=0; i<exponent; i++)
    power *= number;
  return power;
}

Answer 9

Get a column name from an int in Java(read more here):

public String getColName (int colNum) {

   String res = "";

   int quot = colNum;
   int rem;        
    /*1. Subtract one from number.
    *2. Save the mod 26 value.
   *3. Divide the number by 26, save result.
   *4. Convert the remainder to a letter.
   *5. Repeat until the number is zero.
   *6. Return that bitch...
   */
    while(quot > 0)
    {
        quot = quot - 1;
        rem = quot % 26;
        quot = quot / 26;

        //cast to a char and add to the beginning of the string
        //add 97 to convert to the correct ascii number
        res = (char)(rem+97) + res;            
    }   
    return res;
}

Answer 10

Caveat: both of these versions assume only uppercase letters A to Z. Anything else causes a miscalculation. It wouldn't be hard to add a bit of error checking and/or uppercasing to improve them.

Scala

def excel2Number(excel : String) : Int = 
  (0 /: excel) ((accum, ch) => accum * 26 + ch - 'A' + 1)

Haskell

excel2Number :: String -> Int
excel2Number = flip foldl 0 $ \accum ch -> accum * 26 + fromEnum ch - fromEnum 'A' + 1

Answer 11

Another Delphi one:

function ExcelColumnNumberToLetter(col: Integer): string;
begin
  if (col <= 26) then begin
    Result := Chr(col + 64);
  end
  else begin
    col := col-1;
    Result := ExcelColumnNumberToLetter(col div 26) + ExcelColumnNumberToLetter((col mod 26) + 1);
  end;
end;

Answer 12

Another Java:

public static int convertNameToIndex(String columnName) {
    int index = 0;
    char[] name = columnName.toUpperCase().toCharArray();

    for(int i = 0; i < name.length; i++) {
        index *= 26;
        index += name[i] - 'A' + 1;
    }

    return index;
}

Answer 13

Easy Java solution -->

public class ColumnName {

public static int colIndex(String col)
{   int index=0;
    int mul=0;
    for(int i=col.length()-1;i>=0;i--)
    {   
        index  += (col.charAt(i)-64) * Math.pow(26, mul);
        mul++;
    }
    return index;
}

public static void main(String[] args) {

    System.out.println(colIndex("AAA"));

}

Answer 14

Does it help to think of the string as the reverse of the column number in base 26 with digits represented by A, B, ... Z?

Answer 15

This is basically a number in base 26, with the difference that the number doesn't use 0-9 and then letters but only letters.

Answer 16

Here's a CFML one:

<cffunction name="ColToNum" returntype="Numeric">
    <cfargument name="Input" type="String" />
    <cfset var Total = 0 />
    <cfset var Pos = 0 />

    <cfloop index="Pos" from="1" to="#Len(Arguments.Input)#">
        <cfset Total += 26^(Pos-1) * ( Asc( UCase( Mid(Arguments.Input,Pos,1) ) ) - 64 ) />
    </cfloop>

    <cfreturn Total />
</cffunction>

<cfoutput>
    #ColToNum('AABCCE')#
</cfoutput>

And because I'm in an odd mood, here's a CFScript version:

function ColToNum ( Input )
{
    var Total = 0;

    for ( var Pos = 1 ; Pos <= Len(Arguments.Input) ; Pos++ )
    {
        Total += 26^(Pos-1) * ( Asc( UCase( Mid(Arguments.Input,Pos,1) ) ) - 64 );
    }

    return Total;
}

WriteOutput( ColToNum('AABCCE') );

Answer 17

another [more cryptic] erlang example:

col2int(String) -> col2int(0,String).
col2int(X,[A|L]) when A >= 65, A =< 90 ->
col2int(26 * X + A - 65 + 1, L);
col2int(X,[]) -> X.

and inverse function:

int2col(Y) when Y > 0 -> int2col(Y,[]).
int2col(0,L) -> L;
int2col(Y,L) when Y rem 26 == 0 -> 
   int2col(Y div 26 - 1,[(26+65-1)|L]);
int2col(Y,L) ->
   P = Y rem 26,
   int2col((Y - P) div 26,[P + 65-1|L]).

Answer 18

Delphi:

// convert EXcel column name to column number 1..256
// case-sensitive; returns 0 for illegal column name
function cmColmAlfaToNumb( const qSRC : string ) : integer;
var II : integer;
begin
   result := 0;
   for II := 1 to length(qSRC) do begin
      if (qSRC[II]<'A')or(qSRC[II]>'Z') then begin
         result := 0;
         exit;
      end;
      result := result*26+ord(qSRC[II])-ord('A')+1;
   end;
   if result>256 then result := 0;
end;

-Al.

Answer 19

Slightly related, the better challenge is the other way around: given the column number, find the column label as string.

Qt version as what I implemented for KOffice:

QString columnLabel( unsigned column )
{
  QString str;
  unsigned digits = 1;
  unsigned offset = 0;

  column--;
  for( unsigned limit = 26; column >= limit+offset; limit *= 26, digits++ )
    offset += limit;

  for( unsigned c = column - offset; digits; --digits, c/=26 )
    str.prepend( QChar( 'A' + (c%26) ) );

  return str;
}

Answer 20

Common Lisp:

(defun excel->number (string)
  "Converts an Excel column name to a column number."
  (reduce (lambda (a b) (+ (* a 26) b))
          string
          :key (lambda (x) (- (char-int x) 64))))

edit: the inverse operation:

(defun number->excel (number &optional acc)
  "Converts a column number to Excel column name."
  (if (zerop number)
      (concatenate 'string acc)
      (multiple-value-bind (rest current) (floor number 26)
        (if (zerop current)
            (number->excel (- rest 1) (cons #\Z acc))
            (number->excel rest (cons (code-char (+ current 64)) acc))))))

Answer 21

This version is purely functional and permits alternative 'code' sequences, for example if you wanted to only uses the letters 'A' to 'C'. In Scala, with a suggestion from dcsobral.

def columnNumber(name: String) = {
    val code = 'A' to 'Z'

    name.foldLeft(0) { (sum, letter) =>
        (sum * code.length) + (code.indexOf(letter) + 1)
    }
}

Answer 22

def ExcelColumnToNumber(ColumnName):
    ColNum = 0
    for i in range(0, len(ColumnName)):
        # Easier once formula determined: 'PositionValue * Base^Position'
        # i.e. AA=(1*26^1)+(1*26^0)   or  792=(7*10^2)+(9*10^1)+(2*10^0)
        ColNum += (int(ColumnName[i],36) -9) * (pow(26, len(ColumnName)-i-1))
    return ColNum

p.s. My first Python script!

Answer 23

In Mathematica:

FromDigits[ToCharacterCode@# - 64, 26] &

Answer 24

Using Mr. Wizard's awesome Mathematica code, but getting rid of the cryptic pure function!

columnNumber[name_String] := FromDigits[ToCharacterCode[name] - 64, 26]

Answer 25

Wikipedia has good explanations and algos

http://en.wikipedia.org/wiki/Hexavigesimal

public static String toBase26(int value){
    // Note: This is a slightly modified version of the Alphabet-only conversion algorithm

    value = Math.abs(value);
    String converted = "";

    boolean iteration = false;

    // Repeatedly divide the number by 26 and convert the
    // remainder into the appropriate letter.
    do {
        int remainder = value % 26;

        // Compensate for the last letter of the series being corrected on 2 or more iterations.
        if (iteration && value < 25) {
            remainder--;
        }

        converted = (char)(remainder + 'A') + converted;
        value = (value - remainder) / 26;

        iteration = true;
    } while (value > 0);

    return converted;    
}

Answer 26

…just needed a solution for PHP. This is what I came up with:

/**
 * Calculates the column number for a given column name.
 *
 * @param string $columnName the column name: "A", "B", …, "Y", "Z", "AA", "AB" … "AZ", "BA", … "ZZ", "AAA", …
 *
 * @return int the column number for the given column name: 1 for "A", 2 for "B", …, 25 for "Y", 26 for "Z", 27 for "AA", … 52 for "AZ", 53 for "BA", … 703 for "AAA", …
 */
function getColumnNumber($columnName){
    //  the function's result
    $columnNumber = 0;

    //  at first we need to lower-case the string because we calculate with the ASCII value of (lower-case) "a"
    $columnName = strtolower($columnName);
    //  ASCII value of letter "a"
    $aAsciiValue = ord('a') - 1;

    //  iterate all characters by splitting the column name
    foreach (str_split($columnName) as $character) {
        //  determine ASCII value of current character and substract with that one from letter "a"
        $characterNumberValue = ord($character) - $aAsciiValue;

        //  through iteration and multiplying we finally get the previous letters' values on base 26
        //  then we just add the current character's number value
        $columnNumber = $columnNumber * 26 + $characterNumberValue;
    }

    //  return the result
    return $columnNumber;
}

Of course the script can be shortened a little by just combining some stuff into one line of code within the foreach loop:

//  …
$columnNumber = $columnNumber * 26 + ord($character) - ord('a') + 1;
//  …

Answer 27

In Python, without reduce:

def transform(column_string):
    return sum((ascii_uppercase.index(letter)+1) * 26**position for position, letter in enumerate(column_string[::-1]))

Answer 28

Here is another version of this code in Python:

keycode=1
for i in range (1,len(word)):
    numtest[i]=word[i-1]
    keycode = keycode*26*int(wordtest[numtest[i]])
last=word[-1:]
keycode=keycode+int(wordtest[last])
print(keycode)
print(bin(keycode))
#Numtest and wordtest are dictionaries.