【php】すべての文字を1回ずつ使って作れる文字列の一覧を作る（順列）
問題
a,b,c,d,e,fの文字をすべて、1回ずつ使って作れる文字列をすべて書き出せ。
（異なるn個のものからr個とって1列に並べる順列の数は？）
解答例
順列ですね。
個数は 
ですね。
以下プログラムで一覧を書き出します。
/**
* 順列作成関数
*
* @param $a 後方に付ける文字の配列
* @param $s 前方の文字列
* @return 文字の組み合わせ結果の配列
*/
function pat($a, $s = '')
{
$r = array();
if (count($a) && is_array($a)) {
//第1引数に文字の配列を渡されたらループして処理
foreach ($a as $k => $v) {
//文字の配列から1文字もらってこちらにくっつけて
$_s = $s . $v;
//もらった1文字を除いた文字の配列を作って
$_a = $a;
unset($_a[$k]);
//再帰呼び出し
$_r = pat($_a, $_s);
//返り値にする変数に結果を追加
$r = array_merge($r, $_r);
}
} else {
//第1引数が空っぽの配列だったら、再帰呼び出しはここでストップ
//返り値はこれだけ
$r[] = $s;
}
return $r;
}
$a = array('a', 'b', 'c', 'd', 'e', 'f');
var_export(pat($a));
実行結果
array ( 0 => 'abcdef', 1 => 'abcdfe', 2 => 'abcedf', 3 => 'abcefd', 4 => 'abcfde', 5 => 'abcfed', 6 => 'abdcef', 7 => 'abdcfe', 8 => 'abdecf', 9 => 'abdefc', 10 => 'abdfce', 11 => 'abdfec', 12 => 'abecdf', 13 => 'abecfd', 14 => 'abedcf', 15 => 'abedfc', 16 => 'abefcd', 17 => 'abefdc', 18 => 'abfcde', 19 => 'abfced', 20 => 'abfdce', 21 => 'abfdec', 22 => 'abfecd', 23 => 'abfedc', 24 => 'acbdef', 25 => 'acbdfe', 26 => 'acbedf', 27 => 'acbefd', 28 => 'acbfde', 29 => 'acbfed', 30 => 'acdbef', 31 => 'acdbfe', 32 => 'acdebf', 33 => 'acdefb', 34 => 'acdfbe', 35 => 'acdfeb', 36 => 'acebdf', 37 => 'acebfd', 38 => 'acedbf', 39 => 'acedfb', 40 => 'acefbd', 41 => 'acefdb', 42 => 'acfbde', 43 => 'acfbed', 44 => 'acfdbe', 45 => 'acfdeb', 46 => 'acfebd', 47 => 'acfedb', 48 => 'adbcef', 49 => 'adbcfe', 50 => 'adbecf', 51 => 'adbefc', 52 => 'adbfce', 53 => 'adbfec', 54 => 'adcbef', 55 => 'adcbfe', 56 => 'adcebf', 57 => 'adcefb', 58 => 'adcfbe', 59 => 'adcfeb', 60 => 'adebcf', 61 => 'adebfc', 62 => 'adecbf', 63 => 'adecfb', 64 => 'adefbc', 65 => 'adefcb', 66 => 'adfbce', 67 => 'adfbec', 68 => 'adfcbe', 69 => 'adfceb', 70 => 'adfebc', 71 => 'adfecb', 72 => 'aebcdf', 73 => 'aebcfd', 74 => 'aebdcf', 75 => 'aebdfc', 76 => 'aebfcd', 77 => 'aebfdc', 78 => 'aecbdf', 79 => 'aecbfd', 80 => 'aecdbf', 81 => 'aecdfb', 82 => 'aecfbd', 83 => 'aecfdb', 84 => 'aedbcf', 85 => 'aedbfc', 86 => 'aedcbf', 87 => 'aedcfb', 88 => 'aedfbc', 89 => 'aedfcb', 90 => 'aefbcd', 91 => 'aefbdc', 92 => 'aefcbd', 93 => 'aefcdb', 94 => 'aefdbc', 95 => 'aefdcb', 96 => 'afbcde', 97 => 'afbced', 98 => 'afbdce', 99 => 'afbdec', 100 => 'afbecd', 101 => 'afbedc', 102 => 'afcbde', 103 => 'afcbed', 104 => 'afcdbe', 105 => 'afcdeb', 106 => 'afcebd', 107 => 'afcedb', 108 => 'afdbce', 109 => 'afdbec', 110 => 'afdcbe', 111 => 'afdceb', 112 => 'afdebc', 113 => 'afdecb', 114 => 'afebcd', 115 => 'afebdc', 116 => 'afecbd', 117 => 'afecdb', 118 => 'afedbc', 119 => 'afedcb', 120 => 'bacdef', 121 => 'bacdfe', 122 => 'bacedf', 123 => 'bacefd', 124 => 'bacfde', 125 => 'bacfed', 126 => 'badcef', 127 => 'badcfe', 128 => 'badecf', 129 => 'badefc', 130 => 'badfce', 131 => 'badfec', 132 => 'baecdf', 133 => 'baecfd', 134 => 'baedcf', 135 => 'baedfc', 136 => 'baefcd', 137 => 'baefdc', 138 => 'bafcde', 139 => 'bafced', 140 => 'bafdce', 141 => 'bafdec', 142 => 'bafecd', 143 => 'bafedc', 144 => 'bcadef', 145 => 'bcadfe', 146 => 'bcaedf', 147 => 'bcaefd', 148 => 'bcafde', 149 => 'bcafed', 150 => 'bcdaef', 151 => 'bcdafe', 152 => 'bcdeaf', 153 => 'bcdefa', 154 => 'bcdfae', 155 => 'bcdfea', 156 => 'bceadf', 157 => 'bceafd', 158 => 'bcedaf', 159 => 'bcedfa', 160 => 'bcefad', 161 => 'bcefda', 162 => 'bcfade', 163 => 'bcfaed', 164 => 'bcfdae', 165 => 'bcfdea', 166 => 'bcfead', 167 => 'bcfeda', 168 => 'bdacef', 169 => 'bdacfe', 170 => 'bdaecf', 171 => 'bdaefc', 172 => 'bdafce', 173 => 'bdafec', 174 => 'bdcaef', 175 => 'bdcafe', 176 => 'bdceaf', 177 => 'bdcefa', 178 => 'bdcfae', 179 => 'bdcfea', 180 => 'bdeacf', 181 => 'bdeafc', 182 => 'bdecaf', 183 => 'bdecfa', 184 => 'bdefac', 185 => 'bdefca', 186 => 'bdface', 187 => 'bdfaec', 188 => 'bdfcae', 189 => 'bdfcea', 190 => 'bdfeac', 191 => 'bdfeca', 192 => 'beacdf', 193 => 'beacfd', 194 => 'beadcf', 195 => 'beadfc', 196 => 'beafcd', 197 => 'beafdc', 198 => 'becadf', 199 => 'becafd', 200 => 'becdaf', 201 => 'becdfa', 202 => 'becfad', 203 => 'becfda', 204 => 'bedacf', 205 => 'bedafc', 206 => 'bedcaf', 207 => 'bedcfa', 208 => 'bedfac', 209 => 'bedfca', 210 => 'befacd', 211 => 'befadc', 212 => 'befcad', 213 => 'befcda', 214 => 'befdac', 215 => 'befdca', 216 => 'bfacde', 217 => 'bfaced', 218 => 'bfadce', 219 => 'bfadec', 220 => 'bfaecd', 221 => 'bfaedc', 222 => 'bfcade', 223 => 'bfcaed', 224 => 'bfcdae', 225 => 'bfcdea', 226 => 'bfcead', 227 => 'bfceda', 228 => 'bfdace', 229 => 'bfdaec', 230 => 'bfdcae', 231 => 'bfdcea', 232 => 'bfdeac', 233 => 'bfdeca', 234 => 'bfeacd', 235 => 'bfeadc', 236 => 'bfecad', 237 => 'bfecda', 238 => 'bfedac', 239 => 'bfedca', 240 => 'cabdef', 241 => 'cabdfe', 242 => 'cabedf', 243 => 'cabefd', 244 => 'cabfde', 245 => 'cabfed', 246 => 'cadbef', 247 => 'cadbfe', 248 => 'cadebf', 249 => 'cadefb', 250 => 'cadfbe', 251 => 'cadfeb', 252 => 'caebdf', 253 => 'caebfd', 254 => 'caedbf', 255 => 'caedfb', 256 => 'caefbd', 257 => 'caefdb', 258 => 'cafbde', 259 => 'cafbed', 260 => 'cafdbe', 261 => 'cafdeb', 262 => 'cafebd', 263 => 'cafedb', 264 => 'cbadef', 265 => 'cbadfe', 266 => 'cbaedf', 267 => 'cbaefd', 268 => 'cbafde', 269 => 'cbafed', 270 => 'cbdaef', 271 => 'cbdafe', 272 => 'cbdeaf', 273 => 'cbdefa', 274 => 'cbdfae', 275 => 'cbdfea', 276 => 'cbeadf', 277 => 'cbeafd', 278 => 'cbedaf', 279 => 'cbedfa', 280 => 'cbefad', 281 => 'cbefda', 282 => 'cbfade', 283 => 'cbfaed', 284 => 'cbfdae', 285 => 'cbfdea', 286 => 'cbfead', 287 => 'cbfeda', 288 => 'cdabef', 289 => 'cdabfe', 290 => 'cdaebf', 291 => 'cdaefb', 292 => 'cdafbe', 293 => 'cdafeb', 294 => 'cdbaef', 295 => 'cdbafe', 296 => 'cdbeaf', 297 => 'cdbefa', 298 => 'cdbfae', 299 => 'cdbfea', 300 => 'cdeabf', 301 => 'cdeafb', 302 => 'cdebaf', 303 => 'cdebfa', 304 => 'cdefab', 305 => 'cdefba', 306 => 'cdfabe', 307 => 'cdfaeb', 308 => 'cdfbae', 309 => 'cdfbea', 310 => 'cdfeab', 311 => 'cdfeba', 312 => 'ceabdf', 313 => 'ceabfd', 314 => 'ceadbf', 315 => 'ceadfb', 316 => 'ceafbd', 317 => 'ceafdb', 318 => 'cebadf', 319 => 'cebafd', 320 => 'cebdaf', 321 => 'cebdfa', 322 => 'cebfad', 323 => 'cebfda', 324 => 'cedabf', 325 => 'cedafb', 326 => 'cedbaf', 327 => 'cedbfa', 328 => 'cedfab', 329 => 'cedfba', 330 => 'cefabd', 331 => 'cefadb', 332 => 'cefbad', 333 => 'cefbda', 334 => 'cefdab', 335 => 'cefdba', 336 => 'cfabde', 337 => 'cfabed', 338 => 'cfadbe', 339 => 'cfadeb', 340 => 'cfaebd', 341 => 'cfaedb', 342 => 'cfbade', 343 => 'cfbaed', 344 => 'cfbdae', 345 => 'cfbdea', 346 => 'cfbead', 347 => 'cfbeda', 348 => 'cfdabe', 349 => 'cfdaeb', 350 => 'cfdbae', 351 => 'cfdbea', 352 => 'cfdeab', 353 => 'cfdeba', 354 => 'cfeabd', 355 => 'cfeadb', 356 => 'cfebad', 357 => 'cfebda', 358 => 'cfedab', 359 => 'cfedba', 360 => 'dabcef', 361 => 'dabcfe', 362 => 'dabecf', 363 => 'dabefc', 364 => 'dabfce', 365 => 'dabfec', 366 => 'dacbef', 367 => 'dacbfe', 368 => 'dacebf', 369 => 'dacefb', 370 => 'dacfbe', 371 => 'dacfeb', 372 => 'daebcf', 373 => 'daebfc', 374 => 'daecbf', 375 => 'daecfb', 376 => 'daefbc', 377 => 'daefcb', 378 => 'dafbce', 379 => 'dafbec', 380 => 'dafcbe', 381 => 'dafceb', 382 => 'dafebc', 383 => 'dafecb', 384 => 'dbacef', 385 => 'dbacfe', 386 => 'dbaecf', 387 => 'dbaefc', 388 => 'dbafce', 389 => 'dbafec', 390 => 'dbcaef', 391 => 'dbcafe', 392 => 'dbceaf', 393 => 'dbcefa', 394 => 'dbcfae', 395 => 'dbcfea', 396 => 'dbeacf', 397 => 'dbeafc', 398 => 'dbecaf', 399 => 'dbecfa', 400 => 'dbefac', 401 => 'dbefca', 402 => 'dbface', 403 => 'dbfaec', 404 => 'dbfcae', 405 => 'dbfcea', 406 => 'dbfeac', 407 => 'dbfeca', 408 => 'dcabef', 409 => 'dcabfe', 410 => 'dcaebf', 411 => 'dcaefb', 412 => 'dcafbe', 413 => 'dcafeb', 414 => 'dcbaef', 415 => 'dcbafe', 416 => 'dcbeaf', 417 => 'dcbefa', 418 => 'dcbfae', 419 => 'dcbfea', 420 => 'dceabf', 421 => 'dceafb', 422 => 'dcebaf', 423 => 'dcebfa', 424 => 'dcefab', 425 => 'dcefba', 426 => 'dcfabe', 427 => 'dcfaeb', 428 => 'dcfbae', 429 => 'dcfbea', 430 => 'dcfeab', 431 => 'dcfeba', 432 => 'deabcf', 433 => 'deabfc', 434 => 'deacbf', 435 => 'deacfb', 436 => 'deafbc', 437 => 'deafcb', 438 => 'debacf', 439 => 'debafc', 440 => 'debcaf', 441 => 'debcfa', 442 => 'debfac', 443 => 'debfca', 444 => 'decabf', 445 => 'decafb', 446 => 'decbaf', 447 => 'decbfa', 448 => 'decfab', 449 => 'decfba', 450 => 'defabc', 451 => 'defacb', 452 => 'defbac', 453 => 'defbca', 454 => 'defcab', 455 => 'defcba', 456 => 'dfabce', 457 => 'dfabec', 458 => 'dfacbe', 459 => 'dfaceb', 460 => 'dfaebc', 461 => 'dfaecb', 462 => 'dfbace', 463 => 'dfbaec', 464 => 'dfbcae', 465 => 'dfbcea', 466 => 'dfbeac', 467 => 'dfbeca', 468 => 'dfcabe', 469 => 'dfcaeb', 470 => 'dfcbae', 471 => 'dfcbea', 472 => 'dfceab', 473 => 'dfceba', 474 => 'dfeabc', 475 => 'dfeacb', 476 => 'dfebac', 477 => 'dfebca', 478 => 'dfecab', 479 => 'dfecba', 480 => 'eabcdf', 481 => 'eabcfd', 482 => 'eabdcf', 483 => 'eabdfc', 484 => 'eabfcd', 485 => 'eabfdc', 486 => 'eacbdf', 487 => 'eacbfd', 488 => 'eacdbf', 489 => 'eacdfb', 490 => 'eacfbd', 491 => 'eacfdb', 492 => 'eadbcf', 493 => 'eadbfc', 494 => 'eadcbf', 495 => 'eadcfb', 496 => 'eadfbc', 497 => 'eadfcb', 498 => 'eafbcd', 499 => 'eafbdc', 500 => 'eafcbd', 501 => 'eafcdb', 502 => 'eafdbc', 503 => 'eafdcb', 504 => 'ebacdf', 505 => 'ebacfd', 506 => 'ebadcf', 507 => 'ebadfc', 508 => 'ebafcd', 509 => 'ebafdc', 510 => 'ebcadf', 511 => 'ebcafd', 512 => 'ebcdaf', 513 => 'ebcdfa', 514 => 'ebcfad', 515 => 'ebcfda', 516 => 'ebdacf', 517 => 'ebdafc', 518 => 'ebdcaf', 519 => 'ebdcfa', 520 => 'ebdfac', 521 => 'ebdfca', 522 => 'ebfacd', 523 => 'ebfadc', 524 => 'ebfcad', 525 => 'ebfcda', 526 => 'ebfdac', 527 => 'ebfdca', 528 => 'ecabdf', 529 => 'ecabfd', 530 => 'ecadbf', 531 => 'ecadfb', 532 => 'ecafbd', 533 => 'ecafdb', 534 => 'ecbadf', 535 => 'ecbafd', 536 => 'ecbdaf', 537 => 'ecbdfa', 538 => 'ecbfad', 539 => 'ecbfda', 540 => 'ecdabf', 541 => 'ecdafb', 542 => 'ecdbaf', 543 => 'ecdbfa', 544 => 'ecdfab', 545 => 'ecdfba', 546 => 'ecfabd', 547 => 'ecfadb', 548 => 'ecfbad', 549 => 'ecfbda', 550 => 'ecfdab', 551 => 'ecfdba', 552 => 'edabcf', 553 => 'edabfc', 554 => 'edacbf', 555 => 'edacfb', 556 => 'edafbc', 557 => 'edafcb', 558 => 'edbacf', 559 => 'edbafc', 560 => 'edbcaf', 561 => 'edbcfa', 562 => 'edbfac', 563 => 'edbfca', 564 => 'edcabf', 565 => 'edcafb', 566 => 'edcbaf', 567 => 'edcbfa', 568 => 'edcfab', 569 => 'edcfba', 570 => 'edfabc', 571 => 'edfacb', 572 => 'edfbac', 573 => 'edfbca', 574 => 'edfcab', 575 => 'edfcba', 576 => 'efabcd', 577 => 'efabdc', 578 => 'efacbd', 579 => 'efacdb', 580 => 'efadbc', 581 => 'efadcb', 582 => 'efbacd', 583 => 'efbadc', 584 => 'efbcad', 585 => 'efbcda', 586 => 'efbdac', 587 => 'efbdca', 588 => 'efcabd', 589 => 'efcadb', 590 => 'efcbad', 591 => 'efcbda', 592 => 'efcdab', 593 => 'efcdba', 594 => 'efdabc', 595 => 'efdacb', 596 => 'efdbac', 597 => 'efdbca', 598 => 'efdcab', 599 => 'efdcba', 600 => 'fabcde', 601 => 'fabced', 602 => 'fabdce', 603 => 'fabdec', 604 => 'fabecd', 605 => 'fabedc', 606 => 'facbde', 607 => 'facbed', 608 => 'facdbe', 609 => 'facdeb', 610 => 'facebd', 611 => 'facedb', 612 => 'fadbce', 613 => 'fadbec', 614 => 'fadcbe', 615 => 'fadceb', 616 => 'fadebc', 617 => 'fadecb', 618 => 'faebcd', 619 => 'faebdc', 620 => 'faecbd', 621 => 'faecdb', 622 => 'faedbc', 623 => 'faedcb', 624 => 'fbacde', 625 => 'fbaced', 626 => 'fbadce', 627 => 'fbadec', 628 => 'fbaecd', 629 => 'fbaedc', 630 => 'fbcade', 631 => 'fbcaed', 632 => 'fbcdae', 633 => 'fbcdea', 634 => 'fbcead', 635 => 'fbceda', 636 => 'fbdace', 637 => 'fbdaec', 638 => 'fbdcae', 639 => 'fbdcea', 640 => 'fbdeac', 641 => 'fbdeca', 642 => 'fbeacd', 643 => 'fbeadc', 644 => 'fbecad', 645 => 'fbecda', 646 => 'fbedac', 647 => 'fbedca', 648 => 'fcabde', 649 => 'fcabed', 650 => 'fcadbe', 651 => 'fcadeb', 652 => 'fcaebd', 653 => 'fcaedb', 654 => 'fcbade', 655 => 'fcbaed', 656 => 'fcbdae', 657 => 'fcbdea', 658 => 'fcbead', 659 => 'fcbeda', 660 => 'fcdabe', 661 => 'fcdaeb', 662 => 'fcdbae', 663 => 'fcdbea', 664 => 'fcdeab', 665 => 'fcdeba', 666 => 'fceabd', 667 => 'fceadb', 668 => 'fcebad', 669 => 'fcebda', 670 => 'fcedab', 671 => 'fcedba', 672 => 'fdabce', 673 => 'fdabec', 674 => 'fdacbe', 675 => 'fdaceb', 676 => 'fdaebc', 677 => 'fdaecb', 678 => 'fdbace', 679 => 'fdbaec', 680 => 'fdbcae', 681 => 'fdbcea', 682 => 'fdbeac', 683 => 'fdbeca', 684 => 'fdcabe', 685 => 'fdcaeb', 686 => 'fdcbae', 687 => 'fdcbea', 688 => 'fdceab', 689 => 'fdceba', 690 => 'fdeabc', 691 => 'fdeacb', 692 => 'fdebac', 693 => 'fdebca', 694 => 'fdecab', 695 => 'fdecba', 696 => 'feabcd', 697 => 'feabdc', 698 => 'feacbd', 699 => 'feacdb', 700 => 'feadbc', 701 => 'feadcb', 702 => 'febacd', 703 => 'febadc', 704 => 'febcad', 705 => 'febcda', 706 => 'febdac', 707 => 'febdca', 708 => 'fecabd', 709 => 'fecadb', 710 => 'fecbad', 711 => 'fecbda', 712 => 'fecdab', 713 => 'fecdba', 714 => 'fedabc', 715 => 'fedacb', 716 => 'fedbac', 717 => 'fedbca', 718 => 'fedcab', 719 => 'fedcba', )
注意
文字数が9文字、10文字を越えたあたりから、件数が何十万件、何百万件となり、劇的に遅くなっていくと思います。
メモリ上で単純な総当りをしていますが、文字数注意です。
5文字の組合せを作りたいのですが、桁数を指定する場合はどうすれば良いのでしょうか。
よろしくお願いいたします。