Largest int from concatenated ints
You are encouraged to solve this task according to the task description, using any language you may know.
Given a set of positive integers, the task is to write a function to order the integers in such a way that the concatenation of the numbers forms the largest possible integer and return this integer.
Use the following two sets of integers as tests and show your program output here.
- {1, 34, 3, 98, 9, 76, 45, 4}
- {54, 546, 548, 60}
- Possible algorithms
- A solution could be found by trying all combinations and return the best.
- Another way to solve this is to note that in the best arrangement, for any two adjacent original integers X and Y, the concatenation X followed by Y will be numerically greater than or equal to the concatenation Y followed by X.
- Yet another way to solve this is to pad ints to the same size by repeating the digits then sort using these repeated ints as a sort key.
Cf:
- Algorithms: What is the most efficient way to arrange the given numbers to form the biggest number?.
- Constructing the largest number possible by rearranging a list
Ada
The algorithmic idea is to apply a twisted comparison function:
<lang Ada>function Order(Left, Right: Natural) return Boolean is
( (Img(Left) & Img(Right)) > (Img(Right) & Img(Left)) );</lang>
This function converts the parameters Left and Right to strings and returns True if (Left before Right) exceeds (Right before Left). It needs Ada 2012 -- the code for older versions of Ada would be more verbose.
The rest is straightforward: Run your favourite sorting subprogram that allows to use the function "Order" instead of standard comparison operators ("<" or ">" or so) and print the results:
<lang Ada>with Ada.Text_IO, Ada.Containers.Generic_Array_Sort;
procedure Largest_Int_From_List is
function Img(N: Natural) return String is
S: String := Integer'Image(N);
begin
return S(S'First+1 .. S'Last); -- First character is ' '
end Img;
function Order(Left, Right: Natural) return Boolean is
( (Img(Left) & Img(Right)) > (Img(Right) & Img(Left)) );
type Arr_T is array(Positive range <>) of Natural;
procedure Sort is new Ada.Containers.Generic_Array_Sort
(Positive, Natural, Arr_T, Order);
procedure Print_Sorted(A: Arr_T) is
B: Arr_T := A;
begin
Sort(B);
for Number of B loop
Ada.Text_IO.Put(Img(Number));
end loop;
Ada.Text_IO.New_Line;
end Print_Sorted;
begin
Print_Sorted((1, 34, 3, 98, 9, 76, 45, 4)); Print_Sorted((54, 546, 548, 60));
end Largest_Int_From_List;</lang>
AutoHotkey
<lang AutoHotkey>LargestConcatenatedInts(var){ StringReplace, var, A_LoopField,%A_Space%,, all Sort, var, D`, fConcSort StringReplace, var, var, `,,, all return var }
ConcSort(a, b){ m := a . b , n := b . a
return m < n ? 1 : m > n ? -1 : 0
}</lang> Examples:<lang AutoHotkey>d = ( 1, 34, 3, 98, 9, 76, 45, 4 54, 546, 548, 60 4 , 45, 54, 5 ) loop, parse, d, `n MsgBox % LargestConcatenatedInts(A_LoopField)</lang>
- Output:
998764543431 6054854654 554454
AWK
<lang awk> function cmp(i1, v1, i2, v2, u1, u2) { u1 = v1""v2; u2 = v2""v1;
return (u2 - u1)
} function largest_int_from_concatenated_ints(X) {
PROCINFO["sorted_in"]="cmp";
u=""; for (i in X) u=u""X[i]; return u }
BEGIN { split("1 34 3 98 9 76 45 4",X); print largest_int_from_concatenated_ints(X)
split("54 546 548 60",X); print largest_int_from_concatenated_ints(X) } </lang>
- Output:
998764543431 6054854654
BBC BASIC
<lang bbcbasic> DIM Nums%(10)
Nums%()=1,34,3,98,9,76,45,4
PRINT FNlargestint(8)
Nums%()=54,546,548,60
PRINT FNlargestint(4)
END
DEF FNlargestint(len%)
LOCAL i%,l$,a$,b$,sorted%
REPEAT
sorted%=TRUE
FOR i%=0 TO len%-2
a$=STR$Nums%(i%)
b$=STR$Nums%(i%+1)
IF a$+b$<b$+a$ SWAP Nums%(i%),Nums%(i%+1):sorted%=FALSE
NEXT
UNTIL sorted%
FOR i%=0 TO len%-1
l$+=STR$Nums%(i%)
NEXT
=l$</lang>
- Output:
998764543431 6054854654
Bracmat
<lang bracmat>( ( maxnum
= A Z F C
. !arg:#
| !arg
: %@?F
?
( #%@?C
& ( str$(!F !C)+-1*str$(!C !F):~<0
| !C:?F
)
& ~
)
?
| !arg:?A !F ?Z&!F maxnum$(!A !Z)
)
& out$(str$(maxnum$(1 34 3 98 9 76 45 4))) & out$(str$(maxnum$(54 546 548 60))) );</lang>
- Output:
998764543431 6054854654
C
<lang C>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
int catcmp(const void *a, const void *b) { char ab[32], ba[32]; sprintf(ab, "%d%d", *(int*)a, *(int*)b); sprintf(ba, "%d%d", *(int*)b, *(int*)a); return strcmp(ba, ab); }
void maxcat(int *a, int len) { int i; qsort(a, len, sizeof(int), catcmp); for (i = 0; i < len; i++) printf("%d", a[i]); putchar('\n'); }
int main(void) { int x[] = {1, 34, 3, 98, 9, 76, 45, 4}; int y[] = {54, 546, 548, 60};
maxcat(x, sizeof(x)/sizeof(x[0])); maxcat(y, sizeof(y)/sizeof(y[0]));
return 0; }</lang>
- Output:
998764543431 6054854654
C++
<lang cpp>#include <iostream>
- include <sstream>
- include <algorithm>
- include <vector>
- include <string>
std::string findLargestConcat ( std::vector< int > & mynumbers ) {
std::vector<std::string> concatnumbers ;
std::sort ( mynumbers.begin( ) , mynumbers.end( ) ) ;
do {
std::ostringstream numberstream ;
for ( int i : mynumbers )
numberstream << i ;
concatnumbers.push_back( numberstream.str( ) ) ; } while ( std::next_permutation( mynumbers.begin( ) ,
mynumbers.end( ) )) ;
return *( std::max_element( concatnumbers.begin( ) ,
concatnumbers.end( ) ) ) ; }
int main( ) {
std::vector<int> mynumbers = { 98, 76 , 45 , 34, 9 , 4 , 3 , 1 } ;
std::vector<int> othernumbers = { 54 , 546 , 548 , 60 } ;
std::cout << "The largest concatenated int is " <<
findLargestConcat( mynumbers ) << " !\n" ;
std::cout << "And here it is " << findLargestConcat( othernumbers )
<< " !\n" ;
return 0 ;
}</lang>
- Output:
The largest concatenated int is 998764543431 ! And here it is 6054854654 !
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
class Program {
static void Main(string[] args)
{
var source1 = new int[] { 1, 34, 3, 98, 9, 76, 45, 4 };
var source2 = new int[] { 54, 546, 548, 60 };
var largest1 = LargestPossibleSequence(source1);
var largest2 = LargestPossibleSequence(source2);
Console.WriteLine("The largest possible integer from set 1 is: {0}", largest1);
Console.WriteLine("The largest possible integer from set 2 is: {0}", largest2);
}
static long LargestPossibleSequence(int[] ints)
{
return long.Parse(string.Join("", ints.OrderBy(i => i, new IntConcatenationComparer()).Reverse()));
}
}
class IntConcatenationComparer : IComparer<int> {
public int Compare(int x, int y)
{
var xy = int.Parse(x.ToString() + y.ToString());
var yx = int.Parse(y.ToString() + x.ToString());
return xy - yx; }
} </lang>
- Output:
The largest possible integer from set 1 is: 998764543431 The largest possible integer from set 2 is: 6054854654
Clojure
<lang Clojure>(defn maxcat [coll]
(read-string
(apply str
(sort (fn [x y]
(apply compare
(map read-string [(str y x) (str x y)])))
coll))))
(prn (map maxcat [[1 34 3 98 9 76 45 4] [54 546 548 60]]))</lang>
- Output:
<pre>(998764543431 6054854654)
D
The three algorithms. Uses the second module from the Permutations Task. <lang d>import std.stdio, std.algorithm, std.conv, std.array, permutations2;
auto maxCat1(in int[] arr) pure @safe {
return arr.to!(string[]).permutations.map!join.reduce!max;
}
auto maxCat2(in int[] arr) pure nothrow @safe {
return arr.to!(string[]).sort!q{b ~ a < a ~ b}.join;
}
auto maxCat3(in int[] arr) /*pure nothrow @safe*/ {
immutable maxL = arr.reduce!max.text.length;
return arr.to!(string[])
.schwartzSort!(s => s.replicate(maxL/s.length + 1), "a > b")
.join;
}
void main() {
const lists = [[1, 34, 3, 98, 9, 76, 45, 4], [54, 546, 548, 60]]; [&maxCat1, &maxCat2, &maxCat3].map!(cat => lists.map!cat).writeln;
}</lang>
- Output:
[["998764543431", "6054854654"], ["998764543431", "6054854654"], ["998764543431", "6054854654"]]
Erlang
<lang Erlang> -module( largest_int_from_concatenated ).
-export( [ints/1, task/0] ).
ints( Ints ) -> Int_strings = [erlang:integer_to_list(X) || X <- Ints], Pad_ints = [{X ++ X, X} || X <- Int_strings], erlang:list_to_integer( lists:append([Int || {_Pad, Int} <- lists:reverse(lists:sort(Pad_ints))]) ).
task() -> [io:fwrite("Largest ~p from ~p~n", [ints(X), X]) || X <- [[1, 34, 3, 98, 9, 76, 45, 4], [54, 546, 548, 60]]]. </lang>
- Output:
8> largest_int_from_concatenated:task(). Largest 998764543431 from [1,34,3,98,9,76,45,4] Largest 6054854654 from [54,546,548,60]
Go
<lang go>// Variation of method 3. Repeat digits to at least the size of the longest, // then sort as strings. package main
import (
"fmt" "math/big" "sort" "strconv" "strings"
)
type c struct {
i int s, rs string
}
type cc []*c
func (c cc) Len() int { return len(c) } func (c cc) Less(i, j int) bool { return c[j].rs < c[i].rs } func (c cc) Swap(i, j int) { c[i], c[j] = c[j], c[i] }
// Function required by task. Takes a list of integers, returns big int. func li(is ...int) *big.Int {
ps := make(cc, len(is))
ss := make([]c, len(is))
ml := 0
for j, i := range is {
p := &ss[j]
ps[j] = p
p.i = i
p.s = strconv.Itoa(i)
if len(p.s) > ml {
ml = len(p.s)
}
}
for _, p := range ps {
p.rs = strings.Repeat(p.s, (ml+len(p.s)-1)/len(p.s))
}
sort.Sort(ps)
s := make([]string, len(ps))
for i, p := range ps {
s[i] = p.s
}
b, _ := new(big.Int).SetString(strings.Join(s, ""), 10)
return b
}
func main() {
fmt.Println(li(1, 34, 3, 98, 9, 76, 45, 4)) fmt.Println(li(54, 546, 548, 60))
}</lang>
- Output:
998764543431 6054854654
Groovy
<lang groovy>def largestInt = { c -> c.sort { v2, v1 -> "$v1$v2" <=> "$v2$v1" }.join() as BigInteger }</lang> Testing: <lang groovy>assert largestInt([1, 34, 3, 98, 9, 76, 45, 4]) == 998764543431 assert largestInt([54, 546, 548, 60]) == 6054854654</lang>
Haskell
Compare repeated string method
<lang Haskell>import Data.List (sortBy) import Data.Ord (comparing)
main = print (map maxcat [[1,34,3,98,9,76,45,4], [54,546,548,60]] :: [Integer])
where
sorted xs = let pad x = concat $ replicate (maxLen `div` length x + 1) x
maxLen = maximum $ map length xs
in sortBy (flip $ comparing pad) xs
maxcat = read . concat . sorted . map show</lang>
- Output:
[998764543431,6054854654]
Since repeating numerical string "1234" is the same as taking all the digits of 1234/9999 after the decimal point, the following does essentially the same as above: <lang haskell>import Data.List (sortBy) import Data.Ord (comparing) import Data.Ratio ((%))
nines = iterate ((+9).(*10)) 9
maxcat = foldl (\a (n,d)->a * (1 + d) + n) 0 .
sortBy (flip $ comparing $ uncurry (%)) . map (\a->(a, head $ dropWhile (<a) nines))
main = mapM_ (print.maxcat) [[1,34,3,98,9,76,45,4], [54,546,548,60]]</lang>
Sort on comparison of concatenated ints method
<lang Haskell>import Data.List (sortBy)
main = print (map maxcat [[1,34,3,98,9,76,45,4], [54,546,548,60]] :: [Integer])
where sorted = sortBy (\a b -> compare (b++a) (a++b))
maxcat = read . concat . sorted . map show</lang>
- Output as above.
Try all permutations method
<lang Haskell>import Data.List (sort, permutations)
main = print (map maxcat [[1,34,3,98,9,76,45,4], [54,546,548,60]] :: [Integer])
where maxcat = read . last . sort . map (concat . map show) . permutations</lang>
- Output as above.
Icon and Unicon
This solution only works in Unicon as it uses a Heap class to do the heavy lifting.
<lang unicon>import Collections # For the Heap (dense priority queue) class
procedure main(a)
write(lici(a))
end
procedure lici(a)
every (result := "") ||:= Heap(a,,cmp).gen() return result
end
procedure cmp(a,b)
return (a||b) > (b||a)
end</lang>
Sample runs:
->lici 1 34 3 98 9 76 45 4 998764543431 ->lici 54 546 548 60 6054854654 ->
J
Solution: <lang j>maxlen=: [: >./ #&> maxnum=: (0 ". ;)@(\: maxlen $&> ])@(8!:0)</lang> Usage: <lang j> maxnum&> 1 34 3 98 9 76 45 4 ; 54 546 548 60 998764543431 6054854654</lang>
Java
This example sets up a comparator to order the numbers using Collections.sort as described in method #3 (padding and reverse sorting).
It was also necessary to make a join method to meet the output requirements.
<lang java5>import java.util.*;
public class IntConcat {
private static Comparator<Integer> sorter = new Comparator<Integer>(){
@Override
public int compare(Integer o1, Integer o2){
String o1s = o1.toString();
String o2s = o2.toString();
if(o1s.length() == o2s.length()){
return o2s.compareTo(o1s);
}
int mlen = Math.max(o1s.length(), o2s.length());
while(o1s.length() < mlen * 2) o1s += o1s;
while(o2s.length() < mlen * 2) o2s += o2s;
return o2s.compareTo(o1s);
}
};
public static String join(List<?> things){
String output = "";
for(Object obj:things){
output += obj;
}
return output;
}
public static void main(String[] args){
List<Integer> ints1 = new ArrayList<Integer>(Arrays.asList(1, 34, 3, 98, 9, 76, 45, 4));
Collections.sort(ints1, sorter);
System.out.println(join(ints1));
List<Integer> ints2 = new ArrayList<Integer>(Arrays.asList(54, 546, 548, 60));
Collections.sort(ints2, sorter);
System.out.println(join(ints2));
}
}</lang>
<lang java5>import java.util.Comparator; import java.util.stream.Collectors; import java.util.stream.Stream;
public interface IntConcat {
public static Comparator<Integer> SORTER = (o1, o2) -> {
String o1s = o1.toString();
String o2s = o2.toString();
if (o1s.length() == o2s.length()) {
return o2s.compareTo(o1s);
}
int mlen = Math.max(o1s.length(), o2s.length());
while (o1s.length() < mlen * 2) {
o1s += o1s;
}
while (o2s.length() < mlen * 2) {
o2s += o2s;
}
return o2s.compareTo(o1s);
};
public static void main(String[] args) {
Stream<Integer> ints1 = Stream.of(
1, 34, 3, 98, 9, 76, 45, 4
);
System.out.println(ints1
.parallel()
.sorted(SORTER)
.map(String::valueOf)
.collect(Collectors.joining())
);
Stream<Integer> ints2 = Stream.of(
54, 546, 548, 60
);
System.out.println(ints2
.parallel()
.sorted(SORTER)
.map(String::valueOf)
.collect(Collectors.joining())
);
}
}</lang>
- Output:
998764543431 6054854654
JavaScript
<code>
maxCombine = function (list) {
list.sort(
function(x,y)
{
a = x.toString();
b = y.toString();
num1 = parseInt(a + b);
num2 = parseInt(b + a);
if (num1 < num2) return 1;
if (num1 > num2) return -1;
if (num1 == num2) return 0;
}
);
return list;
};
</code>
jq
Padding
For jq versions greater than 1.4, it may be necessary to change "sort_by" to "sort". <lang jq>def largest_int:
def pad(n): . + (n - length) * .[length-1:];
map(tostring)
| (map(length) | max) as $max
| map([., pad($max)])
| sort_by( .[1] )
| map( .[0] ) | reverse | join("") ;
- Examples:
([1, 34, 3, 98, 9, 76, 45, 4],
[54, 546, 548, 60]) | largest_int
</lang>
- Output:
$ /usr/local/bin/jq -n -M -r -f Largest_int_from_concatenated_ints.jq 998764543431 6054854654
Custom Sort
The following uses quicksort/1: <lang jq>def largest_int:
map(tostring)
| quicksort( .[0] + .[1] < .[1] + .[0] )
| reverse | join("") ;</lang>
Lua
<lang Lua>function icsort(numbers) table.sort(numbers,function(x,y) return (x..y) > (y..x) end) return numbers end
for _,numbers in pairs({{1, 34, 3, 98, 9, 76, 45, 4}, {54, 546, 548, 60}}) do print(('Numbers: {%s}\n Largest integer: %s'):format( table.concat(numbers,","),table.concat(icsort(numbers)) )) end</lang>
- Output:
Numbers: {1,34,3,98,9,76,45,4}
Largest integer: 998764543431
Numbers: {54,546,548,60}
Largest integer: 6054854654
Mathematica
<lang Mathematica>makeLargestInt[list_] := Module[{sortedlist},
sortedlist = Sort[list, Order[ToString[#1] <> ToString[#2], ToString[#2] <> ToString[#1]] < 0 &]; Map[ToString, sortedlist] // StringJoin // FromDigits ]
(* testing with two examples *) makeLargestInt[{1, 34, 3, 98, 9, 76, 45, 4}] makeLargestInt[{54, 546, 548, 60}]</lang>
- Output:
998764543431 6054854654
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary
runSample(arg) return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method largestInt(il) public static
ri = wa = -- put the list into an indexed string wa[0] = il.words loop ww = 1 to wa[0] wa[ww] = il.word(ww) end ww
-- order the list
loop wx = 1 to wa[0] - 1
loop wy = wx + 1 to wa[0]
xx = wa[wx]
yy = wa[wy]
xy = xx || yy
yx = yy || xx
if xy < yx then do
-- swap xx and yy
wa[wx] = yy
wa[wy] = xx
end
end wy
end wx
-- rebuild list from indexed string loop ww = 1 to wa[0] ri = ri wa[ww] end ww return ri.space(0) -- concatenate the list elements into a single numeric
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method runSample(arg) private static
ints = [ - '1 34 3 98 9 76 45 4', - '54 546 548 60' - ] loop il over ints say largestInt(il).right(20) ':' il.space(1, ',') end il return
</lang>
- Output:
998764543431 : 1,34,3,98,9,76,45,4
6054854654 : 54,546,548,60
Nim
<lang nim>import algorithm, sequtils, strutils, future
proc maxNum(x: seq[int]): string =
var c = x.mapIt(string, $it) c.sort((x, y) => cmp(y&x, x&y)) c.join()
echo maxNum(@[1, 34, 3, 98, 9, 76, 45, 4]) echo maxNum(@[54, 546, 548, 60])</lang>
- Output:
998764543431 6054854654
OCaml
<lang ocaml>let myCompare a b = compare (b ^ a) (a ^ b) let icsort nums = String.concat "" (List.sort myCompare (List.map string_of_int nums))</lang>
- testing
# icsort [1;34;3;98;9;76;45;4];; - : string = "998764543431" # icsort [54;546;548;60];; - : string = "6054854654"
Oforth
<lang Oforth>func: largestInt { map(#asString) sortWith(#[ dup2 + tor swap + > ]) sum asInteger }</lang>
- Output:
[ [1, 34, 3, 98, 9, 76, 45, 4], [54, 546, 548, 60] ] map(#largestInt) println [998764543431, 6054854654]
Pascal
tested with freepascal.Used a more extreme example 3.
algorithm 3
<lang pascal>const
base = 10; MaxDigitCnt = 11; source1 : array[0..7] of integer = (1, 34, 3, 98, 9, 76, 45, 4); source2 : array[0..3] of integer = (54,546,548,60); source3 : array[0..3] of integer = (60, 54,545454546,0);
type
tdata = record
datOrg,
datMod : LongWord;
datStrOrg : string[MaxDigitCnt];
end;
tArrData = array of tData;
procedure DigitCount(var n: tdata); begin
with n do //InttoStr is very fast str(datOrg,datStrOrg);
end;
procedure InsertData(var n: tdata;data:LongWord); begin
n.datOrg := data; DigitCount(n);
end;
function FindMaxLen(const ArrData:tArrData): LongWord; var
cnt : longInt; res,t : LongWord;
begin
res := 0;// 1 is minimum
for cnt := High(ArrData) downto Low(ArrData) do
begin
t := length(ArrData[cnt].datStrOrg);
IF res < t then
res := t;
end;
FindMaxLen := res;
end;
procedure ExtendCount(var ArrData:tArrData;newLen: integer); var
cnt, i,k : integer;
begin
For cnt := High(ArrData) downto Low(ArrData) do
with ArrData[cnt] do
begin
datMod := datOrg;
i := newlen-length(datStrOrg);
k := 1;
while i > 0 do
begin
datMod := datMod *Base+Ord(datStrOrg[k])-Ord('0');
inc(k);
IF k >length(datStrOrg) then
k := 1;
dec(i);
end;
end;
end;
procedure SortArrData(var ArrData:tArrData); var
i, j,idx : integer; tmpData : tData;
begin
For i := High(ArrData) downto Low(ArrData)+1 do
begin
idx := i;
j := i-1;
For j := j downto Low(ArrData) do
IF ArrData[idx].datMod < ArrData[j].datMod then
idx := j;
IF idx <> i then
begin
tmpData := ArrData[idx];
ArrData[idx]:= ArrData[i];
ArrData[i] := tmpData;
end;
end;
end;
procedure ArrDataOutput(const ArrData:tArrData); var
i,l : integer; s : string;
begin { the easy way
For i := High(ArrData) downto Low(ArrData) do
write(ArrData[i].datStrOrg);
writeln;
*}
l := 0;
For i := High(ArrData) downto Low(ArrData) do
inc(l,length(ArrData[i].datStrOrg));
setlength(s,l);
l:= 1;
For i := High(ArrData) downto Low(ArrData) do
with ArrData[i] do
begin
move(datStrOrg[1],s[l],length(datStrOrg));
inc(l,length(datStrOrg));
end;
writeln(s);
end;
procedure HighestInt(var ArrData:tArrData); begin
ExtendCount(ArrData,FindMaxLen(ArrData)); SortArrData(ArrData); ArrDataOutput(ArrData);
end;
var
i : integer; tmpData : tArrData;
begin
// Source1 setlength(tmpData,length(source1)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source1[i]); HighestInt(tmpData); // Source2 setlength(tmpData,length(source2)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source2[i]); HighestInt(tmpData); // Source3 setlength(tmpData,length(source3)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source3[i]); HighestInt(tmpData);
end.</lang>
- Output:
998764543431 6054854654 60545454546540
Inspired by Haskell
generate the repetition by dividing /(10^CountDigits-1) http://rosettacode.org/wiki/Largest_int_from_concatenated_ints#Compare_repeated_string_method
<lang pascal>const
base = 10; MaxDigitCnt = 11; source1 : array[0..7] of LongInt = (10 , 34, 3, 98, 9, 76, 45, 4); source2 : array[0..3] of LongInt = (54,546,548,60); source3 : array[0..3] of LongInt = (0,2121212122,21,60);
type
tdata = record
datMod : double;
datOrg : LongInt;
//InttoStr is very fast and the string is always needed
datStrOrg : string[MaxDigitCnt];
end;
tArrData = array of tData;
procedure InsertData(var n: tdata;data:LongWord); begin
with n do begin datOrg := data; str(datOrg,datStrOrg); end;
end;
function FindMaxLen(const ArrData:tArrData): LongWord; var
cnt : longInt; res,t : LongWord;
begin
res := 0;// 1 is minimum
for cnt := High(ArrData) downto Low(ArrData) do
begin
t := length(ArrData[cnt].datStrOrg);
IF res < t then
res := t;
end;
FindMaxLen := res;
end;
procedure ExtendData(var ArrData:tArrData;newLen: integer); var
cnt, i : integer;
begin
For cnt := High(ArrData) downto Low(ArrData) do
with ArrData[cnt] do
begin
//generating 10^length(datStrOrg)
datMod := 1;
i := length(datStrOrg);
// i always >= 1
repeat
datMod := base*datMod;
dec(i);
until i <= 0;
// 1/(datMod-1.0) = 1/(9...9)
datMod := datOrg/(datMod-1.0)+datOrg;
i := newlen-length(datStrOrg);
For i := i downto 1 do
datMod := datMod*Base;
end;
end;
procedure SortArrData(var ArrData:tArrData); //selection sort var
i, j,idx : integer; tmpData : tData;
begin
For i := High(ArrData) downto Low(ArrData)+1 do
begin
idx := i;
j := i-1;
//select max
For j := j downto Low(ArrData) do
IF ArrData[idx].datMod < ArrData[j].datMod then
idx := j;
//finally swap
IF idx <> i then
begin
tmpData := ArrData[idx];
ArrData[idx]:= ArrData[i];
ArrData[i] := tmpData;
end;
end;
end;
procedure ArrDataOutput(const ArrData:tArrData); var
i : integer;
begin { the easy way}
For i := High(ArrData) downto Low(ArrData) do write(ArrData[i].datStrOrg); writeln;
end;
procedure HighestInt(var ArrData:tArrData); begin
ExtendData(ArrData,FindMaxLen(ArrData)); SortArrData(ArrData); ArrDataOutput(ArrData);
end;
var
i : integer; tmpData : tArrData;
begin
// Source1 setlength(tmpData,length(source1)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source1[i]); HighestInt(tmpData); // Source2 setlength(tmpData,length(source2)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source2[i]); HighestInt(tmpData); // Source3 setlength(tmpData,length(source3)); For i := low(tmpData) to high(tmpData) do InsertData(tmpData[i],source3[i]); HighestInt(tmpData);
end.</lang>
- Output:
9987645434310 6054854654 602121212122210>
PARI/GP
Sorts then joins. Most of the noise comes from converting a vector of integers into a concatenated integer: eval(concat(apply(n->Str(n),v))). Note that the short form eval(concat(apply(Str,v))) is not valid here because Str is variadic.
<lang parigp>large(v)=eval(concat(apply(n->Str(n),vecsort(v,(x,y)->eval(Str(y,x,"-",x,y)))))); large([1, 34, 3, 98, 9, 76, 45, 4]) large([54, 546, 548, 60])</lang>
- Output:
%1 = 998764543431 %2 = 6054854654
Perl
<lang perl>sub maxnum {
join , sort { "$b$a" cmp "$a$b" } @_
}
print maxnum(1, 34, 3, 98, 9, 76, 45, 4), "\n"; print maxnum(54, 546, 548, 60), "\n";</lang>
- Output:
998764543431 6054854654
Perl 6
<lang perl6>sub maxnum(@x) {
[~] @x.sort: -> $a, $b { $b ~ $a leg $a ~ $b }
}
say maxnum <1 34 3 98 9 76 45 4>; say maxnum <54 546 548 60>;</lang>
- Output:
998764543431 6054854654
PHP
<lang php>function maxnum($nums) {
usort($nums, function ($x, $y) { return strcmp("$y$x", "$x$y"); });
return implode(, $nums);
}
echo maxnum(array(1, 34, 3, 98, 9, 76, 45, 4)), "\n"; echo maxnum(array(54, 546, 548, 60)), "\n";</lang>
- Output:
998764543431 6054854654
PicoLisp
Here are solutions for all three algorithms.
The third solution actually avoids padding the numbers, by converting them into circular lists and comparing these. As a drawback, however, this works only for unique lists (as the comparison of identical numbers would not terminate), so a better solution might involve additional checks. <lang PicoLisp>(load "@lib/simul.l") # For 'permute'</lang>
Algorithm 1
<lang PicoLisp>(for L '((1 34 3 98 9 76 45 4) (54 546 548 60))
(prinl (maxi format (permute L))) )</lang>
Algorithm 2
<lang PicoLisp>(for L '((1 34 3 98 9 76 45 4) (54 546 548 60))
(prinl
(sort L
'((A B)
(>
(format (pack A B))
(format (pack B A)) ) ) ) ) )</lang>
Algorithm 3
<lang PicoLisp>(for L '((1 34 3 98 9 76 45 4) (54 546 548 60))
(prinl
(flip
(by '((N) (apply circ (chop N))) sort L) ) ) )</lang>
- Output:
in all three cases
998764543431 6054854654
PL/I
<lang pli> /* Largest catenation of integers 16 October 2013 */ /* Sort using method 2, comparing pairs of adjacent integers. */
Largest: procedure options (main);
declare s(*) char (20) varying controlled, n fixed binary;
get (n);
allocate s(n);
get list (s);
s = trim(s);
put skip edit (s) (a, x(1));
put skip list ('Largest integer=', Largest_integer());
largest_integer: procedure () returns (char(100) varying);
declare sorted bit (1);
declare (true value ('1'b), false value ('0'b)) bit (1);
declare i fixed binary;
declare temp character(20) varying;
do until (sorted);
sorted = true;
do i = 1 to n-1;
if char(s(i)) || char(s(i+1)) < char(s(i+1)) || char(s(i)) then
do;
temp = s(i); s(i) = s(i+1); s(i+1) = temp; sorted = false;
end;
end;
end;
return (string(s));
end largest_integer; end Largest; </lang>
54 546 548 60 Largest integer= 6054854654 1 34 3 98 9 76 45 4 Largest integer= 998764543431
Prolog
Works with SWI-Prolog 6.5.3.
All permutations method
<lang Prolog>largest_int_v1(In, Out) :- maplist(name, In, LC), aggregate(max(V), get_int(LC, V), Out).
get_int(LC, V) :-
permutation(LC, P),
append(P, LV),
name(V, LV).
</lang>
- Output:
?- largest_int_v1([1, 34, 3, 98, 9, 76, 45, 4], Out). Out = 998764543431. ?- largest_int_v1([54, 546, 548, 60], Out). Out = 6054854654.
Method 2
<lang Prolog>largest_int_v2(In, Out) :- maplist(name, In, LC), predsort(my_sort,LC, LCS), append(LCS, LC1), name(Out, LC1).
my_sort(R, L1, L2) :-
append(L1, L2, V1), name(I1, V1),
append(L2, L1, V2), name(I2, V2),
( I1 < I2, R = >; I1 = I2, R = '='; R = <).
% particular case 95 958 my_sort(>, [H1], [H1, H2 | _]) :- H1 > H2.
my_sort(<, [H1], [H1, H2 | _]) :- H1 < H2.
my_sort(R, [H1], [H1, H1 | T]) :- my_sort(R, [H1], [H1 | T]).
% particular case 958 95 my_sort(>, [H1, H2 | _], [H1]) :- H1 > H2.
my_sort(<, [H1, H2 | _], [H1]) :- H1 < H2.
my_sort(R, [H1, H1 | T], [H1]) :- my_sort(R, [H1 | T], [H1]) . </lang>
- Output:
?- largest_int_v2([1, 34, 3, 98, 9, 76, 45, 4], Out). Out = 998764543431 . ?- largest_int_v2([54, 546, 548, 60], Out). Out = 5486054654 .
Python
Python: Sort on comparison of concatenated ints method
This also shows one of the few times where cmp= is better than key= on sorted()
<lang python>try:
cmp # Python 2 OK or NameError in Python 3
def maxnum(x):
return .join(sorted((str(n) for n in x),
cmp=lambda x,y:cmp(y+x, x+y)))
except NameError:
# Python 3
from functools import cmp_to_key
def cmp(x, y):
return -1 if x<y else ( 0 if x==y else 1)
def maxnum(x):
return .join(sorted((str(n) for n in x),
key=cmp_to_key(lambda x,y:cmp(y+x, x+y))))
for numbers in [(1, 34, 3, 98, 9, 76, 45, 4), (54, 546, 548, 60):
print('Numbers: %r\n Largest integer: %15s' % (numbers, maxnum(numbers)))</lang>
- Output:
Numbers: (1, 34, 3, 98, 9, 76, 45, 4) Largest integer: 998764543431 Numbers: (54, 546, 548, 60) Largest integer: 6054854654
Python: Compare repeated string method
<lang python>def maxnum(x):
maxlen = len(str(max(x)))
return .join(sorted((str(v) for v in x), reverse=True,
key=lambda i: i*(maxlen * 2 // len(i))))
for numbers in [(212, 21221), (1, 34, 3, 98, 9, 76, 45, 4), (54, 546, 548, 60)]:
print('Numbers: %r' % (numbers, maxnum(numbers)))</lang>
- Output:
Numbers: (212, 21221) Largest integer: 21221221 Numbers: (1, 34, 3, 98, 9, 76, 45, 4) Largest integer: 998764543431 Numbers: (54, 546, 548, 60) Largest integer: 6054854654
<lang python>from fractions import Fraction from math import log10
def maxnum(x):
return .join(str(n) for n in sorted(x, reverse=True,
key=lambda i: Fraction(i, 10**(int(log10(i))+1)-1)))
for numbers in [(1, 34, 3, 98, 9, 76, 45, 4), (54, 546, 548, 60)]:
print('Numbers: %r\n Largest integer: %15s' % (numbers, maxnum(numbers)))</lang>
- Output as first Python example, above.
Python: Try all permutations method
<lang python>from itertools import permutations def maxnum(x):
return max(int(.join(n) for n in permutations(str(i) for i in x)))
for numbers in [(1, 34, 3, 98, 9, 76, 45, 4), (54, 546, 548, 60)]:
print('Numbers: %r\n Largest integer: %15s' % (numbers, maxnum(numbers)))</lang>
- Output as above.
Racket
<lang Racket>
- lang racket
(define (largest-int ns)
(string->number (apply ~a (sort ns (λ(x y) (string>? (~a x y) (~a y x)))))))
(map largest-int '((1 34 3 98 9 76 45 4) (54 546 548 60)))
- -> '(998764543431 6054854654)
</lang>
REXX
The algorithm used is based on exact comparisons (left to right) with right digit fill of the left digit. This allows the integers to be of any size.
This REXX version works with any integer (negative, zero, positive), and does some basic error checking to verify that the numbers are integers (and normalizes the integers). <lang rexx>/*REXX pgm constructs largest integer from a list using concatenation.*/ @. = /*used to signify end-of-lists. */ @.1 = '{1, 34, 3, 98, 9, 76, 45, 4}' /*the first list of integers. */ @.2 = '{54, 546, 548, 60}' /* " second " " " */ @.3 = '{ 4, 45, 54, 5}' /* " third " " " */
/* [↓] process all the lists. */
do j=1 while @.j\==; $= /*keep truckin' until exhausted. */
z=space(translate(@.j, , '])},{([')) /*perform scrubbing on the list. */
_=length(space(z,0)) + 1 /*determine the largest possible#*/
if _>digits() then numeric digits _ /*ensure 'nuff digits for the #. */
/* [↓] examine each num in list.*/
do while z\==; index=1 /*keep examining list until done.*/
big=isOK(word(z,1)) /*assume first number is biggest.*/
do k=2 to words(z); x=isOK(word(z,k)) /*get an integer.*/
x1=left(x,1); L=max(length(big), length(x)) /*get max length.*/
if left(x, L, x1) <<= left(big, L, left(big,1)) then iterate
big=x; index=k /*we found a new biggie (& index)*/
end /*k*/ /* [↑] find max concatenated int*/
z=space(delword(z, index, 1)) /*remove the "maximum" from list.*/ $=$ || big /*append the "maximum" number. */ end /*while z ···*/ /* [↑] process all nums in list.*/
say right($,digits()) ' max for: ' @.j /*show max integer & list.*/ end /*j*/ /* [↑] process each list of nums*/
exit /*stick a fork in it, we're done.*/ /*───────────────────────────────────ISOK subroutine────────────────────*/ isOK: parse arg ?; if datatype(?,'W') then return abs(?)/1 /*normalize*/ say; say '***error!*** number ' ? "isn't an integer."; say; exit 13</lang>
- Output:
998764543431 max for: {1, 34, 3, 98, 9, 76, 45, 4}
6054854654 max for: {54, 546, 548, 60}
554454 max for: { 4, 45, 54, 5}
Ruby
Sort on comparison of concatenated ints method
<lang Ruby>def icsort nums
nums.sort { |x, y| "#{y}#{x}" <=> "#{x}#{y}" }
end
[[54, 546, 548, 60], [1, 34, 3, 98, 9, 76, 45, 4]].each do |c|
p c # prints nicer in Ruby 1.8 puts icsort(c).join
end</lang>
- Output:
[54, 546, 548, 60] 6054854654 [1, 34, 3, 98, 9, 76, 45, 4] 998764543431
Compare repeated string method
<lang ruby>def icsort nums
maxlen = nums.max.to_s.length
nums.map{ |x| x.to_s }.sort_by { |x| x * (maxlen * 2 / x.length) }.reverse
end
[[54, 546, 548, 60], [1, 34, 3, 98, 9, 76, 45, 4]].each do |c|
p c # prints nicer in Ruby 1.8 puts icsort(c).join
end</lang>
- Output as above.
<lang ruby>require 'rational' #Only needed in Ruby < 1.9
def icsort nums
nums.sort_by { |i| Rational(i, 10**(Math.log10(i).to_i+1)-1) }.reverse
end
[[54, 546, 548, 60], [1, 34, 3, 98, 9, 76, 45, 4]].each do |c|
p c # prints nicer in Ruby 1.8 puts icsort(c).join
end</lang>
- Output as above.
Run BASIC
<lang runbasic>a1$ = "1, 34, 3, 98, 9, 76, 45, 4" a2$ = "54,546,548,60"
print "Max Num ";a1$;" = ";maxNum$(a1$) print "Max Num ";a2$;" = ";maxNum$(a2$)
function maxNum$(a1$) while word$(a1$,i+1,",") <> ""
i = i + 1 a$(i) = trim$(word$(a1$,i,","))
wend
s = 1 while s = 1
s = 0 for j = 1 to i -1 if a$(j)+a$(j+1) < a$(j+1)+a$(j) then h$ = a$(j) a$(j) = a$(j+1) a$(j+1) = h$ s = 1 end if next j
wend
for j = 1 to i
maxNum$ = maxNum$ ; a$(j)
next j end function</lang>
- Output:
Max Num 1, 34, 3, 98, 9, 76, 45, 4 = 998764543431 Max Num 54,546,548,60 = 6054854654
Scala
<lang Scala>object LIFCI extends App {
def lifci(list: List[Long]) = list.permutations.map(_.mkString).max
println(lifci(List(1, 34, 3, 98, 9, 76, 45, 4))) println(lifci(List(54, 546, 548, 60)))
}</lang>
- Output:
998764543431 6054854654
Scheme
<lang Scheme>(define (cat . nums) (apply string-append (map number->string nums)))
(define (my-compare a b) (string>? (cat a b) (cat b a)))
(map (lambda (xs) (string->number (apply cat (sort xs my-compare))))
'((1 34 3 98 9 76 45 4) (54 546 548 60)))</lang>
- Output:
(998764543431 6054854654)
Sidef
<lang ruby>func maxnum(nums) {
nums.sort {|x,y| "#{y}#{x}" <=> "#{x}#{y}" };
}
[[54, 546, 548, 60], [1, 34, 3, 98, 9, 76, 45, 4]].each { |c|
say maxnum(c).join.to_num;
}</lang>
- Output:
6054854654 998764543431
Tcl
<lang tcl>proc intcatsort {nums} {
lsort -command {apply {{x y} {expr {"$y$x" - "$x$y"}}}} $nums
}</lang> Demonstrating: <lang tcl>foreach collection {
{1 34 3 98 9 76 45 4}
{54 546 548 60}
} {
set sorted [intcatsort $collection] puts "\[$collection\] => \[$sorted\] (concatenated: [join $sorted ""])"
}</lang>
- Output:
[1 34 3 98 9 76 45 4] => [9 98 76 45 4 34 3 1] (concatenated: 998764543431) [54 546 548 60] => [60 548 546 54] (concatenated: 6054854654)
Vim Script
This solution is intended to be run as an Ex command within a buffer containing the integers to be processed, one per line. <lang Vim>%s/\(.\+\)/\1\1/ | sort! | %s/\(.\+\)\1\n/\1/</lang>
- Demonstration
<lang Bash>$ paste -s nums 1 34 3 98 9 76 45 4 $ vim -S icsort.vim nums 998764543431</lang>
zkl
<lang zkl>fcn bigCI(ns){
ns.apply("toString").sort(fcn(a,b){ (a+b)>(b+a) }).concat();
}</lang> <lang zkl>bigCI(T(1, 34, 3, 98, 9, 76, 45, 4)).println(); bigCI(T(54, 546, 548, 60)).println();</lang>
- Output:
998764543431 6054854654