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.
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 );
}
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
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.
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;
};
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.
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).
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
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;
}
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;
}
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;
}
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"));
}
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;
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;
}
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)
}
}
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;
}
…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;
// …
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]))
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.
Using Mr. Wizard's awesome Mathematica code, but getting rid of the cryptic pure function!
columnNumber[name_String] := FromDigits[ToCharacterCode[name] - 64, 26]
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?
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.
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') );
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))))))
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;
}
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]).
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.
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!
