Last letter-first letter

Last letter-first letter
You are encouraged to solve this task according to the task description, using any language you may know.

A certain childrens game involves starting with a word in a particular category. Each participant in turn says a word, but that word must begin with the final letter of the previous word. Once a word has been given, it cannot be repeated. If an opponent cannot give a word in the category, they fall out of the game. For example, with "animals" as the category,

Child 1: dog 
Child 2: goldfish
Child 1: hippopotamus
Child 2: snake
...

Task Description

Take the following selection of 70 English Pokemon names (extracted from Wikipedia's list of Pokemon) and generate the/a sequence with the highest possible number of Pokemon names where the subsequent name starts with the final letter of the preceding name. No Pokemon name is to be repeated.

audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
cresselia croagunk darmanitan deino emboar emolga exeggcute gabite
girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan
kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine
nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2
porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking
sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko
tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask

Extra brownie points for dealing with the full list of 646 names.

C

From the D version. <lang c>#include <stdlib.h>

1. include <string.h>
2. include <stdio.h>
3. include <inttypes.h>

typedef struct {

   uint16_t index;
   char last_char, first_char;

} Ref;

Ref* longest_path_refs; size_t longest_path_refs_len;

Ref* refs; size_t refs_len;

size_t n_solutions;

const char** longest_path; size_t longest_path_len;

/// tally statistics void search(size_t curr_len) {

   if (curr_len == longest_path_refs_len) {
       n_solutions++;
   } else if (curr_len > longest_path_refs_len) {
       n_solutions = 1;
       longest_path_refs_len = curr_len;
       memcpy(longest_path_refs, refs, curr_len * sizeof(Ref));
   }

   // recursive search
   intptr_t last_char = refs[curr_len - 1].last_char;
   for (size_t i = curr_len; i < refs_len; i++)
       if (refs[i].first_char == last_char) {
           Ref aux = refs[curr_len];
           refs[curr_len] = refs[i];
           refs[i] = aux;
           search(curr_len + 1);
           refs[i] = refs[curr_len];
           refs[curr_len] = aux;
       }

}

void find_longest_chain(const char* items[],

                       size_t items_len) {
   refs_len = items_len;
   refs = calloc(refs_len, sizeof(Ref));

   // enough space for all items
   longest_path_refs_len = 0;
   longest_path_refs = calloc(refs_len, sizeof(Ref));

   for (size_t i = 0; i < items_len; i++) {
       size_t itemsi_len = strlen(items[i]);
       if (itemsi_len <= 1)
           exit(1);
       refs[i].index = (uint16_t)i;
       refs[i].last_char = items[i][itemsi_len - 1];
       refs[i].first_char = items[i][0];
   }

   // try each item as possible start
   for (size_t i = 0; i < items_len; i++) {
       Ref aux = refs[0];
       refs[0] = refs[i];
       refs[i] = aux;
       search(1);
       refs[i] = refs[0];
       refs[0] = aux;
   }

   longest_path_len = longest_path_refs_len;
   longest_path = calloc(longest_path_len, sizeof(const char*));
   for (size_t i = 0; i < longest_path_len; i++)
       longest_path[i] = items[longest_path_refs[i].index];

   free(longest_path_refs);
   free(refs);

}

int main() {

   const char* pokemon[] = {"audino", "bagon", "baltoy", "banette",
   "bidoof", "braviary", "bronzor", "carracosta", "charmeleon",
   "cresselia", "croagunk", "darmanitan", "deino", "emboar",
   "emolga", "exeggcute", "gabite", "girafarig", "gulpin",
   "haxorus", "heatmor", "heatran", "ivysaur", "jellicent",
   "jumpluff", "kangaskhan", "kricketune", "landorus", "ledyba",
   "loudred", "lumineon", "lunatone", "machamp", "magnezone",
   "mamoswine", "nosepass", "petilil", "pidgeotto", "pikachu",
   "pinsir", "poliwrath", "poochyena", "porygon2", "porygonz",
   "registeel", "relicanth", "remoraid", "rufflet", "sableye",
   "scolipede", "scrafty", "seaking", "sealeo", "silcoon",
   "simisear", "snivy", "snorlax", "spoink", "starly", "tirtouga",
   "trapinch", "treecko", "tyrogue", "vigoroth", "vulpix",
   "wailord", "wartortle", "whismur", "wingull", "yamask"};
   size_t pokemon_len = sizeof(pokemon) / sizeof(pokemon[0]);

   find_longest_chain(pokemon, pokemon_len);
   printf("Maximum path length: %u\n", longest_path_len);
   printf("Paths of that length: %u\n", n_solutions);
   printf("Example path of that length:\n");
   for (size_t i = 0; i < longest_path_len; i += 7) {
       printf("  ");
       for (size_t j = i; j < (i+7) && j < longest_path_len; j++)
           printf("%s ", longest_path[j]);
       printf("\n");
   }

   free(longest_path);

   return 0;

}</lang> Output:

Maximum path length: 23
Paths of that length: 1248
Example path of that length:
  machamp petilil landorus scrafty yamask kricketune emboar
  registeel loudred darmanitan nosepass simisear relicanth heatmor
  rufflet trapinch haxorus seaking girafarig gabite exeggcute
  emolga audino

Runtime: about 0.49 seconds, gcc compiler.

Approximate

For dealing with full list (646 names), here's an approximate method. Names are restricted to begin and end with a lower case letter, so for example in my input file "porygon2" is written as "porygon-two". It finds some chains with 300-odd length for 646 names, and found a chain with 23 for the 70 names (by luck, that is), and since it's basically a one-pass method, running time is next to none. C99 code. <lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <string.h>
3. include <ctype.h>

1. define forall(i, n) for (int i = 0; i < n; i++)

typedef struct edge { char s, e, *str; struct edge *lnk; } edge; typedef struct { edge* e[26]; int nin, nout, in[26], out[26];} node; typedef struct { edge *e, *tail; int len, has[26]; } chain;

node nodes[26]; edge *names, **tmp; int n_names;

/* add edge to graph */ void store_edge(edge *g) { if (!g) return; int i = g->e, j = g->s; node *n = nodes + j;

g->lnk = n->e[i];

n->e[i] = g, n->out[i]++, n->nout++; n = nodes + i, n->in[j]++, n->nin++; }

/* unlink an edge between nodes i and j, and return the edge */ edge* remove_edge(int i, int j) { node *n = nodes + i; edge *g = n->e[j]; if (g) { n->e[j] = g->lnk; g->lnk = 0; n->out[j]--, n->nout--;

n = nodes + j; n->in[i]--; n->nin--; } return g; }

void read_names() { FILE *fp = fopen("poke646", "rt"); int i, len; char *buf; edge *p;

if (!fp) abort();

fseek(fp, 0, SEEK_END); len = ftell(fp); buf = malloc(len + 1); fseek(fp, 0, SEEK_SET); fread(buf, 1, len, fp); fclose(fp);

buf[len] = 0; for (n_names = i = 0; i < len; i++) if (isspace(buf[i])) buf[i] = 0, n_names++;

if (buf[len-1]) n_names++;

memset(nodes, 0, sizeof(node) * 26); tmp = calloc(n_names, sizeof(edge*));

p = names = malloc(sizeof(edge) * n_names); for (i = 0; i < n_names; i++, p++) { if (i) p->str = names[i-1].str + len + 1; else p->str = buf;

len = strlen(p->str); p->s = p->str[0] - 'a'; p->e = p->str[len-1] - 'a'; if (p->s < 0 || p->s >= 26 || p->e < 0 || p->e >= 26) { printf("bad name %s: first/last char must be letter\n", p->str); abort(); } } printf("read %d names\n", n_names); }

void show_chain(chain *c) { printf("%d:", c->len); for (edge * e = c->e; e || !putchar('\n'); e = e->lnk) printf(" %s", e->str); }

/* Which next node has most enter or exit edges. */ int widest(int n, int out) { if (nodes[n].out[n]) return n;

int mm = -1, mi = -1; forall(i, 26) { if (out) { if (nodes[n].out[i] && nodes[i].nout > mm) mi = i, mm = nodes[i].nout; } else { if (nodes[i].out[n] && nodes[i].nin > mm) mi = i, mm = nodes[i].nin; } }

return mi; }

void insert(chain *c, edge *e) { e->lnk = c->e; if (!c->tail) c->tail = e; c->e = e; c->len++; }

void append(chain *c, edge *e) { if (c->tail) c->tail->lnk = e; else c->e = e; c->tail = e; c->len++; }

edge * shift(chain *c) { edge *e = c->e; if (e) { c->e = e->lnk; if (!--c->len) c->tail = 0; } return e; }

chain* make_chain(int s) { chain *c = calloc(1, sizeof(chain));

/* extend backwards */ for (int i, j = s; (i = widest(j, 0)) >= 0; j = i) insert(c, remove_edge(i, j));

/* extend forwards */ for (int i, j = s; (i = widest(j, 1)) >= 0; j = i) append(c, remove_edge(j, i));

for (int step = 0;; step++) { edge *e = c->e;

for (int i = 0; i < step; i++) if (!(e = e->lnk)) break; if (!e) return c;

int n = 0; for (int i, j = e->s; (i = widest(j, 0)) >= 0; j = i) { if (!(e = remove_edge(i, j))) break; tmp[n++] = e; }

if (n > step) { forall(i, step) store_edge(shift(c)); forall(i, n) insert(c, tmp[i]); step = -1; } else while (--n >= 0) store_edge(tmp[n]); } return c; }

int main(void) { int best = 0; read_names();

forall(i, 26) { /* rebuild the graph */ memset(nodes, 0, sizeof(nodes)); forall(j, n_names) store_edge(names + j);

/* make a chain from node i */ chain *c = make_chain(i); if (c->len > best) { show_chain(c); best = c->len; } free(c); }

printf("longest found: %d\n", best); return 0; }</lang>output<lang>read 646 names 307: voltorb breloom magikarp palpito... 308: voltorb bayleef forretress swinub b... 310: voltorb bayleef forretress sw... 312: voltorb breloom mandibuzz zek... 320: voltorb beldum mandibuzz zekrom m... 322: voltorb beldum mandibuzz zekrom murk... 323: voltorb breloom mandibuzz zekr... longest found: 323</lang>

C#

<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Text;

namespace ConsoleApplication1 {

   class Program
   {
       static void Main(string[] args)
       {
           string pokemon_names = @"audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon

cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask";

           string[] pokemon = pokemon_names.Split(new char[]{' ','\n'});
           List<string> chain = new List<string>(pokemon.Length);

           for (int i = 0; i < pokemon.Length; i++)
           {
               swap(ref pokemon[0], ref pokemon[i]);
               Search( pokemon, chain, 1 );               
               swap(ref pokemon[0], ref pokemon[i]);
           }

           foreach (string s in chain)
               Console.WriteLine(s);

           Console.ReadKey();
       }

       static void Search(string[] pokemon, List<string> longest_chain, int len )
       {
           if (len > longest_chain.Count)
           {
               longest_chain.Clear();
               for (int i = 0; i < len; i++)
                   longest_chain.Add(pokemon[i]);
           }

           char lastchar = pokemon[len - 1][pokemon[len-1].Length - 1];
           for (int i = len; i < pokemon.Length; i++)
           {
               if (pokemon[i][0] == lastchar)
               {
                   swap(ref pokemon[i], ref pokemon[len]);
                   Search(pokemon, longest_chain, len + 1);
                   swap(ref pokemon[i], ref pokemon[len]);
               }
           }
       }

       static void swap(ref string s1, ref string s2)
       {
           string tmp = s1;
           s1 = s2;
           s2 = tmp;
       }
   }

}</lang>

machamp
petilil
landorus
sableye
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
scrafty
yamask
kricketune
exeggcute
emolga
audino

D

Modified from the Go version: <lang d>import std.stdio, std.algorithm, std.string;

void search(string[] items, in int len, ref string[] longest) pure {

   if (len > longest.length)
       longest = items[0 .. len].dup;
   const lastChar = items[len - 1][$ - 1];
   foreach (ref item; items[len .. $])
       if (item[0] == lastChar) {
           swap(items[len], item);
           search(items, len + 1, longest);
           swap(items[len], item);
       }

}

void main() {

   auto pokemon = "audino bagon baltoy banette bidoof braviary

bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".split();

   string[] solution;
   foreach (ref name; pokemon) {
       swap(pokemon[0], name);
       search(pokemon, 1, solution);
       swap(pokemon[0], name);
   }
   foreach (name; solution)
       writeln(name);

}</lang> Output:

machamp
petilil
landorus
scrafty
yamask
kricketune
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
seaking
girafarig
gabite
exeggcute
emolga
audino

Runtime: about 1 second, dmd compiler.

Faster version

<lang d>import std.stdio, std.algorithm, std.string,

      std.range, std.typecons;

alias Tuple!(string,"word", bool,"unused") Pair; int nSolutions;

void search(Pair[][] sequences, in size_t minHead,

           in string currWord, string[] currentPath,
           size_t currentPathLen,
           ref string[] longestPath) {

   currentPath[currentPathLen] = currWord;
   currentPathLen++;

   if (currentPathLen == longestPath.length) {
       nSolutions++;
   }  else if (currentPathLen > longestPath.length) {
       nSolutions = 1;
       longestPath = currentPath[0 .. currentPathLen].dup;
   }

   // recursive search
   size_t lastCharIndex = currWord[$ - 1] - minHead;
   if (lastCharIndex < sequences.length)
       foreach (ref pair; sequences[lastCharIndex])
           if (pair.unused) {
               pair.unused = false;
               search(sequences, minHead, pair.word, currentPath,
                      currentPathLen, longestPath);
               pair.unused = true;
           }

}

string[] findLongestChain(in string[] words) {

   auto heads = map!q{ a[0] }(words);
   size_t minHead = reduce!min(heads);
   size_t maxHead = reduce!max(heads);
   auto sequences = new Pair[][](maxHead - minHead + 1, 0);
   foreach (word; words)
       sequences[word[0] - minHead] ~= Pair(word, true);

   auto currentPath = new string[words.length];
   string[] longestPath;

   // try each item as possible start
   foreach (seq; sequences)
       foreach (ref pair; seq) {
           pair.unused = false;
           search(sequences, minHead, pair.word,
                  currentPath, 0, longestPath);
           pair.unused = true;
      }

   return longestPath;

}

void main() {

   auto pokemon = "audino bagon baltoy banette bidoof braviary

bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".toLower().split();

   // remove duplicates
   pokemon.length -= copy(uniq(pokemon.sort()), pokemon).length;

   /*const*/ auto sol = findLongestChain(pokemon);
   writeln("Maximum path length: ", sol.length);
   writeln("Paths of that length: ", nSolutions);
   writeln("Example path of that length:");
   foreach (ch; std.range.chunks(sol, 7))
       writeln("  ", ch.join(" "));

}</lang> Output:

Maximum path length: 23
Paths of that length: 1248
Example path of that length:
  machamp petilil landorus scrafty yamask kricketune emboar
  registeel loudred darmanitan nosepass simisear relicanth heatmor
  rufflet trapinch haxorus seaking girafarig gabite exeggcute
  emolga audino

Runtime: about 0.20 seconds, dmd compiler.

Delphi

Visual implementation, this unit is a VCL Form with a Memo, a Button, a Checkbox, a DataGrid, a DBMemo, a DataSource and a ClientDataSet with tree fields (length integer,count integer,list memo): <lang delphi>unit Unit1;

interface

uses

 Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
 Dialogs, StdCtrls, DBCtrls, DB, DBClient, Grids, DBGrids, ExtCtrls;

type

 TLastLFirstL = class(TForm)
   Panel1: TPanel;
   Button1: TButton;
   Memo1: TMemo;
   DataSource1: TDataSource;
   ClientDataSet1: TClientDataSet;
   ClientDataSet1Longitud: TIntegerField;
   ClientDataSet1Cantidad: TIntegerField;
   ClientDataSet1Lista: TMemoField;
   Panel2: TPanel;
   DBMemo1: TDBMemo;
   DBGrid1: TDBGrid;
   Splitter1: TSplitter;
   CheckBox1: TCheckBox;
   procedure FormCreate(Sender: TObject);
   procedure Button1Click(Sender: TObject);
   procedure FormDestroy(Sender: TObject);
 private
   { Private declarations }
   FPokemons:TStrings; //internal list of words, taken from memo
   FIndex:TStrings; //index of words, based on starting letter
   FCurrList:TStrings; //current list of words being made
   FMax:integer; //max length of list found so far
   FCount:array of array[boolean]of integer; //counting of lists length ocurrences
 protected
   procedure BuildIndex; //build FIndex based on FPokemons contents
   procedure ClearIndex; //empty FIndex
   procedure PokeChain(starting:Char;mylevel:integer); //recursive procedure that builds words lists
   procedure BuildChains; //starts the lists building, by calling PokeChain for every FPokemons
   procedure AddCurrList; //called each time a list is "finished" (no more words to add to it)
 public
   { Public declarations }
 end;

var

 LastLFirstL: TLastLFirstL;

implementation

{$R *.dfm}

{ TForm1 }

{ if the actual list is the longest found so far it is added to the dataset, otherwise its ocurrence is just counted} procedure TLastLFirstL.AddCurrList; var

 i,cc: integer;
 foundit:boolean;

begin

 with ClientDataSet1 do begin
   cc := FCurrList.Count;
   if cc <= FMax then begin //count it
     foundit := false;
     for i := 0 to High(FCount) do begin
       foundit := FCount[i][false] = cc;
       if foundit then begin
         FCount[i][true] := FCount[i][true] + 1;
         break;
       end;
     end;
     if not foundit then begin
       //length that we never add to the dataset
       i := High(FCount);
       SetLength(FCount,i+2);
       Inc(i);
       FCount[i][false] := cc;
       FCount[i][true] := 1;
     end;
     exit;
   end;
   //new longest list is FCurrList, add it to the dataset
   FMax := cc;
   SetLength(FCount,High(Fcount)+2); //make room for ocurrence count
   FCount[High(FCount)][false] := cc;
   FCount[High(FCount)][true] := 1;
   //actual dataset adding
   Append;
   Fields[0].AsInteger := cc;
   Fields[1].AsInteger := 0;
   Fields[2].AsString := FCurrList.Text; //first one is example one
   Post;
 end;

end;

{} procedure TLastLFirstL.BuildChains; var

 stSeen:array of array[boolean] of char;
 poke:string;
 i:integer;
 tc:int64;
 filteqs:boolean;
 k: Integer;

begin

 //do some cleaning before starting
 while not ClientDataSet1.IsEmpty do
   ClientDataSet1.Delete;
 Finalize(FCount);
 FMax := 0;
 filteqs := CheckBox1.Checked;
 //measure time
 tc := gettickcount;
 //each word is given the opportunity of starting a list
 if filteqs then begin
   //ignore words with same start and end as others already seen
   filteqs := False;
   for i := 0 to FPokemons.Count - 1 do begin
     poke := FPokemons[i];
     for k := 0 to High(stSeen) do begin
       filteqs := (stSeen[k][false] = poke[1]) and (stSeen[k][true] = poke[length(poke)]);
       if filteqs then
         break;
     end;
     if filteqs then //already seen equivalent
       continue;
     FPokemons.Objects[i] := Pointer(1);
     FCurrList.Clear; //new list of words
     FCurrList.Add(poke);
     PokeChain(poke[length(poke)],2); //continue the list
     //register as seen, for future equivalents
     k := High(stSeen);
     SetLength(stSeen,k+2);
     Inc(k);
     stSeen[k][false] := poke[1];
     stSeen[k][true] := poke[length(poke)];
     FPokemons.Objects[i] := nil;
   end;
   Finalize(stSeen);
 end else begin
   for i := 0 to FPokemons.Count - 1 do begin
     poke := FPokemons[i];
     FPokemons.Objects[i] := Pointer(1);
     FCurrList.Clear; //new list of words
     FCurrList.Add(poke);
     PokeChain(poke[length(poke)],2); //continue the list
     FPokemons.Objects[i] := nil;
   end;
 end;
 tc := gettickcount - tc; //don't consider dataset counting as part of the process
 //set actual counting of ocurrences on the dataset
 for i := 0 to High(FCount) do with ClientDataSet1 do begin
   if Locate('Longitud',FCount[i][false],[]) then
     Edit
   else begin
     Append;
     Fields[0].AsInteger := FCount[i][false];
     Fields[2].AsString := 'No example preserved';
   end;
   Fields[1].AsInteger := FCount[i][true];
   Post;
 end;
 ClientDataSet1.IndexFieldNames := 'Longitud';
 //show time taken
 Panel1.Caption := IntToStr(tc div 1000) + '.' + IntToStr(tc - (tc div 1000) * 1000) + ' segs.';

end;

{ builds an index based on the first letter of every word in consideration, because all we care about is the first and the last letter of every word. The index is a TStrings where each element is the starting letter and the corresponding object is a TList with all the indices of the words that starts with that letter. } procedure TLastLFirstL.BuildIndex; var

 i,ii: Integer;
 poke:string;
 st,ed:char;
 List:TList;
 k: Integer;
 found:boolean;

begin

 ClearIndex; //just in case is not the first execution
 if not Assigned(FIndex) then // just in case IS the first execution
   FIndex := TStringList.Create;
 for i := 0 to FPokemons.Count - 1 do begin
   poke := FPokemons[i];
   st := poke[1];
   ed := poke[Length(poke)];
   ii := FIndex.IndexOf(st);
   if ii<0 then //first time we see this starting letter
     ii := FIndex.AddObject(st,TList.Create);
   List := TList(FIndex.Objects[ii]);
   found := false;
   if CheckBox1.Checked then begin //ignore equivalent words (same start, same end)
     //all the List are words with the same start, so lets check the end
     for k := 0 to List.Count - 1 do begin
       poke := FPokemons[integer(List[k])];
       found := poke[Length(poke)] = ed;
       if found then
         break;
     end;
   end;
   if not found then // not checking equivalents, or firts time this end is seen
     List.Add(Pointer(i));
 end;

end;

{ do your thing! } procedure TLastLFirstL.Button1Click(Sender: TObject); begin

 Panel1.Caption := 'Calculating..';
 FPokemons.Assign(Memo1.Lines); //words in the game
 BuildIndex;
 BuildChains;

end;

{ frees all the TList used by the index, clears the index } procedure TLastLFirstL.ClearIndex; var

 i:integer;

begin

 if not Assigned(FIndex) then
   exit;
 for i := 0 to FIndex.Count - 1 do begin
   TList(FIndex.Objects[i]).Free;
 end;
 FIndex.Clear;

end;

procedure TLastLFirstL.FormCreate(Sender: TObject); begin

 FPokemons := TStringList.Create;
 FCurrList := TStringList.Create;

end;

procedure TLastLFirstL.FormDestroy(Sender: TObject); begin

 FCurrList.Free;
 FPokemons.Free;
 ClearIndex; //IMPORTANT!
 FIndex.Free;

end;

{where the magic happens. Recursive procedure that adds a word to the current list of words. Receives the starting letter of the word to add, and the "position" of the word in the chain. The position is used to ensure a word is not used twice for the list. } procedure TLastLFirstL.PokeChain(starting: Char;mylevel:integer); var

 i,ii,plevel:integer;
 List:TList;
 didit:boolean;

begin

 application.processMessages; //don't let the interface die..
 didit := False; //if we can't add another word, then we have reached the maximun length for the list
 ii := FIndex.IndexOf(starting);
 if ii >= 0 then begin //there are words with this starting letter
   List := TList(FIndex.Objects[ii]);
   for i := 0 to List.Count - 1 do begin
     ii := integer(List[i]);
     plevel := integer(FPokemons.Objects[ii]); // if the integer stored in the Object property is lower than mylevel, then this word is already in the list
     if (plevel > mylevel) or (plevel = 0) then begin // you can use the word
       //a try finally would be a good thing here, but...
       FCurrList.Add(FPokemons[ii]); //add the word to the list
       FPokemons.Objects[ii] := Pointer(mylevel); //signal is already in the list
       PokeChain(FPokemons[ii][length(FPokemons[ii])],mylevel+1); //add more words to the list
       FcurrList.Delete(FCurrList.Count-1); //already did my best, lets try with another word
       FPokemons.Objects[ii] := nil; //unsignal it, so it can be used "later"
       didit := True; //we did add one word to the list
     end;
   end;
 end;
 if not didit then //there is no way of making the list longer, process it
   AddCurrList;

end;

end.</lang> Runtime varies depending if you run the "optimized" version or not. Ranges from 6 to 18 seconds.

NOTE: "optimized" version is actually a different algorithm, but in most cases returns the same results.

Go

Depth first, starting with each possible name. <lang go>package main

import (

   "fmt"
   "strings"

)

var pokemon = `audino bagon baltoy...67 names omitted...`

func main() {

   // split text into slice representing directed graph
   var d []string
   for _, l := range strings.Split(pokemon, "\n") {
       d = append(d, strings.Fields(l)...)
   }
   fmt.Println("searching", len(d), "names...")
   // try each name as possible start
   for i := range d {
       d[0], d[i] = d[i], d[0]
       search(d, 1, len(d[0]))
       d[0], d[i] = d[i], d[0]
   }
   fmt.Println("maximum path length:", len(ex))
   fmt.Println("paths of that length:", nMax)
   fmt.Print("example path of that length:")
   for i, n := range ex {
       if i%6 == 0 {
           fmt.Print("\n   ")
       }
       fmt.Print(n, " ")
   }
   fmt.Println()

}

var ex []string var nMax int

func search(d []string, i, ncPath int) {

   // tally statistics
   if i == len(ex) {
       nMax++
   } else if i > len(ex) {
       nMax = 1
       ex = append(ex[:0], d[:i]...)
   }
   // recursive search
   lastName := d[i-1]
   lastChar := lastName[len(lastName)-1]
   for j := i; j < len(d); j++ {
       if d[j][0] == lastChar {
           d[i], d[j] = d[j], d[i]
           search(d, i+1, ncPath+1+len(d[i]))
           d[i], d[j] = d[j], d[i]
       }
   }

}</lang> Output:

searching 70 names...
maximum path length: 23
paths of that length: 1248
example path of that length:
   machamp petilil landorus scrafty yamask kricketune 
   emboar registeel loudred darmanitan nosepass simisear 
   relicanth heatmor rufflet trapinch haxorus seaking 
   girafarig gabite exeggcute emolga audino 

Haskell

Note: This takes ~80 seconds to complete on my machine. <lang Haskell>import Data.List import qualified Data.ByteString.Char8 as B

allPokemon :: [B.ByteString] allPokemon = map B.pack $ words

   "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon \
   \cresselia croagunk darmanitan deino emboar emolga exeggcute gabite \
   \girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan \
   \kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine \
   \nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 \
   \porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking \
   \sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko \
   \tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"

growChains :: B.ByteString -> [B.ByteString] growChains pcs

   | nextChainSet == [] = head pcs
   | otherwise = growChains nextChainSet
 where nextChainSet = pcs >>= findLinks
       findLinks pc = map (\x -> pc ++ [x]) $ filter (isLink $ last pc) (allPokemon \\ pc)
       isLink pl pr = B.last pl == B.head pr

main = mapM_ B.putStrLn $ growChains $ map (\x -> [x]) allPokemon</lang> Output:

machamp
petilil
landorus
scrafty
yamask
kricketune
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
seaking
girafarig
gabite
exeggcute
emolga
audino

A simpler version (no ByteString), about 2.4 times slower (GHC -O3), same output: <lang Haskell>import Data.List

allPokemon = words

   "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon \
   \cresselia croagunk darmanitan deino emboar emolga exeggcute gabite \
   \girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan \
   \kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine \
   \nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 \
   \porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking \
   \sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko \
   \tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask"

growChains :: String -> [String] growChains pcs

   | nextChainSet == [] = head pcs
   | otherwise = growChains nextChainSet
 where nextChainSet = pcs >>= findLinks
       findLinks pc = map (\x -> pc ++ [x]) $ filter (isLink $ last pc) (allPokemon \\ pc)
       isLink pl pr = last pl == head pr

main = mapM_ putStrLn $ growChains $ map (\x -> [x]) allPokemon</lang>

J

Here, we use a brute force breadth-first search. Unless we know ahead of time how long "longest" is, we must try all possibilities to ensure that an unchecked possibility is not longer than a possibility which we have found.

<lang j>pokenames=: ;:0 :0-.LF

audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
cresselia croagunk darmanitan deino emboar emolga exeggcute gabite
girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan
kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine
nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2
porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking
sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko
tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask

)

seqs=: 3 :0

 links=. <@I. _1 =/&({&>&y) 0  
 next=. ,.i.#links
 while.#next do.
    r=. next
    assert. 1e9>*/8,$r
    next=. (#~ (-: ~.)"1) >;<@(] <@,"1 0 links {::~ {:)"1 r
 end.
 r

)</lang>

The line assert. 1e9>*/8,$r was added to avoid a very bad behavior from microsoft windows which appeared on different arguments, when intermediate results became too large (the machine would have to be rebooted when intermediate results became an order of magnitude larger than the available physical memory). By ensuring that the program would end before consuming that much virtual memory, this behavior from the operating system can be avoided.

With this procedure we are able to conduct the entire search for this list of names:

<lang j>$R=: seqs pokenames 1248 23</lang>

With this data set, we have 1248 sequences of names which have the longest possible length, and those sequences are 23 names long. Here's one of them:

<lang j> >pokenames {~{.R machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino </lang>

OpenEdge/Progress

The following gets the job done, but the time taken (40 minutes) is somewhat worrying when compared to other language solutions. So I am not going after the brownie points just yet...

<lang progress>DEFINE VARIABLE cpokemon AS CHARACTER INITIAL "audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon ~ cresselia croagunk darmanitan deino emboar emolga exeggcute gabite ~ girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan ~ kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine ~ nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 ~ porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking ~ sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko ~ tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask".

DEFINE TEMP-TABLE tt NO-UNDO

  FIELD cname    AS CHARACTER
  FIELD cfirst   AS CHARACTER
  FIELD clast    AS CHARACTER
  FIELD lused    AS LOGICAL
  FIELD ilength  AS INTEGER
  FIELD imax     AS INTEGER
  FIELD cchain   AS CHARACTER

INDEX ttname cname INDEX ttfirst cfirst lused INDEX ttlast clast lused .

DEFINE VARIABLE ii AS INTEGER NO-UNDO.

DO ii = 1 TO NUM-ENTRIES( cpokemon, " " ):

  CREATE tt.
  ASSIGN
     tt.cname    =  ENTRY( ii, cpokemon, " " )
     tt.cfirst   =  SUBSTRING( tt.cname, 1, 1 )
     tt.clast    =  SUBSTRING( tt.cname, LENGTH( tt.cname ), 1 )
     .

END.

FUNCTION getChain RETURNS INTEGER (

  i_cname     AS CHARACTER,
  i_clast     AS CHARACTER,
  i_ilength   AS INTEGER,
  i_cchain    AS CHARACTER

):

  DEFINE BUFFER tt FOR tt.

  DEFINE VARIABLE lend_of_chain AS LOGICAL     NO-UNDO INITIAL TRUE.

  FOR EACH tt
     WHERE tt.cfirst   =  i_clast
     AND   tt.lused    =  FALSE
     OR    i_clast     =  ""
  :
     lend_of_chain = FALSE.
     tt.lused = TRUE.
     getChain( tt.cname, tt.clast, i_ilength + 1, i_cchain + tt.cname + " " ).
     tt.lused = FALSE.
  END.
  IF lend_of_chain THEN DO:
     FIND tt WHERE tt.cname = ENTRY( 1, i_cchain, " " ).
     IF i_ilength = tt.ilength THEN
        tt.imax = tt.imax + 1.
     ELSE IF i_ilength > tt.ilength THEN
        ASSIGN
           tt.ilength  =  i_ilength
           tt.cchain   =  i_cchain
           tt.imax     =  1
           .
  END.

END FUNCTION. /* getChain */

DEFINE VARIABLE itime AS INTEGER NO-UNDO EXTENT 2. DEFINE VARIABLE lcontinue AS LOGICAL NO-UNDO.

itime[1] = ETIME. getChain( "", "", 0, "" ). itime[2] = ETIME.

FOR EACH tt BY tt.ilength DESCENDING:

  MESSAGE
     "Maximum path length:"  tt.ilength SKIP
     "Paths of that length:" tt.imax SKIP(1)
     "Example path of that length:" tt.cchain SKIP(1)
     "Time taken:" STRING( INTEGER( ( itime[2] - itime[1] ) / 1000 ), "HH:MM:SS" )
  VIEW-AS ALERT-BOX BUTTONS YES-NO TITLE tt.cname UPDATE lcontinue.
  IF lcontinue = FALSE THEN
     STOP.

END.</lang>

Output:

---------------------------
machamp
---------------------------
Maximum path length: 23 
Paths of that length: 1248 

Example path of that length: machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino  

Time taken: 00:40:09
---------------------------
Yes   No   
---------------------------

PicoLisp

<lang PicoLisp>(de pokemonChain (File)

  (let Names (make (in File (while (read) (link @))))
     (for Name Names
        (let C (last (chop Name))
           (set Name
              (filter '((Nm) (pre? C Nm)) Names) ) ) )
     (let Res NIL
        (for Name Names
           (let Lst NIL
              (recur (Name Lst)
                 (if (or (memq Name Lst) (not (val (push 'Lst Name))))
                    (when (> (length Lst) (length Res))
                       (setq Res Lst) )
                    (mapc recurse (val Name) (circ Lst)) ) ) ) )
        (flip Res) ) ) )</lang>

Test:

: (pokemonChain "pokemon.list")
-> (machamp petilil landorus scrafty yamask kricketune emboar registeel loudred
darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking
girafarig gabite exeggcute emolga audino)
: (length @)
-> 23

Python

<lang python>from collections import defaultdict

def order_words(words):

   byfirst = defaultdict(set)
   for word in words:
       byfirst[word[0]].add( word )
   #byfirst = dict(byfirst)
   return byfirst

def linkfirst(byfirst, sofar):

   \
   For all words matching last char of last word in sofar as FIRST char and not in sofar,
   return longest chain as sofar + chain
   

   assert sofar
   chmatch = sofar[-1][-1]
   options = byfirst[chmatch] - set(sofar)
   #print('  linkfirst options: %r %r' % (chmatch, options))
   if not options:
       return sofar
   else:
       alternatives = ( linkfirst(byfirst, list(sofar) + [word])
                        for word in options )
       mx = max( alternatives, key=len )
       #input('linkfirst: %r' % mx)
       return mx

def llfl(words):

   byfirst = order_words(words)
   return max( (linkfirst(byfirst, [word]) for word in words), key=len )

if __name__ == '__main__':

   pokemon = audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon

cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask

   pokemon = pokemon.strip().lower().split()
   pokemon = sorted(set(pokemon))    
   l = llfl(pokemon)
   for i in range(0, len(l), 8): print(' '.join(l[i:i+8]))
   print(len(l))</lang>

Sample output

audino bagon baltoy banette bidoof braviary bronzor carracosta
charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute
gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent
23

Alternative version

Adapted from the D version. This uses Psyco. <lang python>import psyco

nsolutions = 0

def search(sequences, ord_minc, curr_word, current_path,

          current_path_len, longest_path):
   global nsolutions

   current_path[current_path_len] = curr_word
   current_path_len += 1

   if current_path_len == len(longest_path):
       nsolutions += 1
   elif current_path_len > len(longest_path):
       nsolutions = 1
       longest_path[:] = current_path[:current_path_len]

   # recursive search
   last_char_index = ord(curr_word[-1]) - ord_minc
   if last_char_index >= 0 and last_char_index < len(sequences):
       for pair in sequences[last_char_index]:
           if not pair[1]:
               pair[1] = True
               search(sequences, ord_minc, pair[0], current_path,
                      current_path_len, longest_path)
               pair[1] = False

def find_longest_chain(words):

   ord_minc = ord(min(word[0] for word in words))
   ord_maxc = ord(max(word[0] for word in words))
   sequences = [[] for _ in xrange(ord_maxc - ord_minc + 1)]
   for word in words:
       sequences[ord(word[0]) - ord_minc].append([word, False])

   current_path = [None] * len(words)
   longest_path = []

   # try each item as possible start
   for seq in sequences:
       for pair in seq:
           pair[1] = True
           search(sequences, ord_minc, pair[0],
                  current_path, 0, longest_path)
           pair[1] = False

   return longest_path

def main():

   global nsolutions

   pokemon = """audino bagon baltoy banette bidoof braviary

bronzor carracosta charmeleon cresselia croagunk darmanitan deino emboar emolga exeggcute gabite girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask""".lower().split()

   # remove duplicates
   pokemon = sorted(set(pokemon))

   sol = find_longest_chain(pokemon)
   print "Maximum path length:", len(sol)
   print "Paths of that length:", nsolutions
   print "Example path of that length:"
   for i in xrange(0, len(sol), 7):
       print " ", " ".join(sol[i : i+7])

psyco.full() main()</lang> Output:

Maximum path length: 23
Paths of that length: 1248
Example path of that length:
  machamp petilil landorus scrafty yamask kricketune emboar
  registeel loudred darmanitan nosepass simisear relicanth heatmor
  rufflet trapinch haxorus seaking girafarig gabite exeggcute
  emolga audino

Run time: about 0.44 seconds with Psyco and Python 2.6.6.

Ruby

<lang ruby>def add_name(seq)

 last_letter = seq[-1][-1]
 potentials = $first.include?(last_letter) ? ($first[last_letter] - seq) : []
 if potentials.empty?
   $sequences << seq
 else
   potentials.each {|name| add_name(seq + [name])}
 end

end

names = %w{

 audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
 cresselia croagunk darmanitan deino emboar emolga exeggcute gabite
 girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan
 kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine
 nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2
 porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking
 sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko
 tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask

} $first = names.group_by {|name| name[0]} $sequences = []

names.each {|name| add_name [name]}

max = $sequences.max_by {|seq| seq.length}.length max_seqs = $sequences.select {|seq| seq.length == max}

puts "there are #{$sequences.length} possible sequences" puts "the longest is #{max} names long" puts "there are #{max_seqs.length} such sequences. one is:" max_seqs.last.each_with_index {|name, idx| puts " %2d %s" % [idx+1, name]}</lang> outputs

there are 2076396 possible sequences
the longest is 23 names long
there are 1248 such sequences. one is:
   1 machamp
   2 pinsir
   3 rufflet
   4 trapinch
   5 heatmor
   6 remoraid
   7 darmanitan
   8 nosepass
   9 starly
  10 yamask
  11 kricketune
  12 exeggcute
  13 emboar
  14 relicanth
  15 haxorus
  16 simisear
  17 registeel
  18 landorus
  19 seaking
  20 girafarig
  21 gabite
  22 emolga
  23 audino

Tcl

<lang tcl>proc search {path arcs} {

   set solutions {}
   set c [string index [lindex $path end] end]
   set i -1
   foreach arc $arcs {

incr i if {[string index $arc 0] ne $c} continue set soln [search [concat $path [list $arc]] [lreplace $arcs $i $i]] lappend solutions [list [llength $soln] $soln]

   }
   if {[llength $solutions]} {

return [lindex [lsort -integer -decreasing -index 0 $solutions] 0 1]

   } else {

return $path

   }

} proc firstlast names {

   set solutions {}
   set i -1
   foreach initial $names {

incr i set soln [search [list $initial] [lreplace $names $i $i]] lappend solutions [list [llength $soln] $soln]

   }
   return [lindex [lsort -integer -decreasing -index 0 $solutions] 0 1]

}

set names {

   audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
   cresselia croagunk darmanitan deino emboar emolga exeggcute gabite
   girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff
   kangaskhan kricketune landorus ledyba loudred lumineon lunatone machamp
   magnezone mamoswine nosepass petilil pidgeotto pikachu pinsir poliwrath
   poochyena porygon2 porygonz registeel relicanth remoraid rufflet sableye
   scolipede scrafty seaking sealeo silcoon simisear snivy snorlax spoink
   starly tirtouga trapinch treecko tyrogue vigoroth vulpix wailord wartortle
   whismur wingull yamask

} set path [firstlast $names] puts "Path (length: [llength $path]): $path"</lang> Output:

Path (length 23): machamp petilil landorus scrafty yamask kricketune emboar registeel loudred darmanitan nosepass simisear relicanth heatmor rufflet trapinch haxorus seaking girafarig gabite exeggcute emolga audino

Ursala

<lang Ursala>#import std

mon =

~&*~ sep` mat` -[

  audino bagon baltoy banette bidoof braviary bronzor carracosta charmeleon
  cresselia croagunk darmanitan deino emboar emolga exeggcute gabite
  girafarig gulpin haxorus heatmor heatran ivysaur jellicent jumpluff kangaskhan
  kricketune landorus ledyba loudred lumineon lunatone machamp magnezone mamoswine
  nosepass petilil pidgeotto pikachu pinsir poliwrath poochyena porygon2
  porygonz registeel relicanth remoraid rufflet sableye scolipede scrafty seaking
  sealeo silcoon simisear snivy snorlax spoink starly tirtouga trapinch treecko
  tyrogue vigoroth vulpix wailord wartortle whismur wingull yamask]-

poke = @iiDrzhK16rlXOASK24PiX ~&llrHiFPrYX^=rxS^|\~&iNCS *=+ ~&rlwNrlCQ^*D/~&+ @h

1. show+

example = ~&h poke mon</lang>output:

machamp
petilil
landorus
scrafty
yamask
kricketune
emboar
registeel
loudred
darmanitan
nosepass
simisear
relicanth
heatmor
rufflet
trapinch
haxorus
seaking
girafarig
gabite
exeggcute
emolga
audino