Algorithm to get all possible string combinations from array up to certain length
What is the best algorithm to get all possible string combinations from a given array with a minimum & maximum length value.
Note: This adds complexity since the
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Best and neat way to solve this problem is to use recursive solution, hope in-line comments are good enough to understand the solution:
<?php // Recursive method that print all permutation of a given length // @param $arr input array // @param $arrLen just the length of the above array // @param $size length or size for which we are making all permutation // @param $perArr this is a temporary array to hold the current permutation being created // @param $pos current position of $perArr function printPermutation($arr, $arrLen, $size, $perArr, $pos) { if ($size==$pos) { //if $pos reach $size then we have found one permutation for ($i=0; $i<$size; $i++) print $perArr[$i]; print ("\n"); return; } for ($i=0; $i<$arrLen; $i++) { $perArr[$pos] = $arr[$i]; //put i'th char in current position //The recursive call that move to next position with $pos+1 printPermutation($arr, $arrLen, $size, $perArr, $pos+1); } } //all printPermutation method with 1 - maxLen function showAllPermutation($letters, $maxLen) { $length = count($letters); $perArr = array(); for ($i=1; $i<=$maxLen; $i++) { printPermutation ($letters, $length, $i, $perArr, 0); } } //main $letters = array('a','b','c','1','2','3'); $max_length = 4; showAllPermutation ($letters, $max_length); ?>If you are interested, here is the very big output of the above code: stdout:
a b c 1 2 3 aa ab ac a1 a2 a3 ba bb bc b1 b2 b3 ca cb cc c1 c2 c3 1a 1b 1c 11 12 13 2a 2b 2c 21 22 23 3a 3b 3c 31 32 33 aaa aab aac aa1 aa2 aa3 aba abb abc ab1 ab2 ab3 aca acb acc ac1 ac2 ac3 a1a a1b a1c a11 a12 a13 a2a a2b a2c a21 a22 a23 a3a a3b a3c a31 a32 a33 baa bab bac ba1 ba2 ba3 bba bbb bbc bb1 bb2 bb3 bca bcb bcc bc1 bc2 bc3 b1a b1b b1c b11 b12 b13 b2a b2b b2c b21 b22 b23 b3a b3b b3c b31 b32 b33 caa cab cac ca1 ca2 ca3 cba cbb cbc cb1 cb2 cb3 cca ccb ccc cc1 cc2 cc3 c1a c1b c1c c11 c12 c13 c2a c2b c2c c21 c22 c23 c3a c3b c3c c31 c32 c33 1aa 1ab 1ac 1a1 1a2 1a3 1ba 1bb 1bc 1b1 1b2 1b3 1ca 1cb 1cc 1c1 1c2 1c3 11a 11b 11c 111 112 113 12a 12b 12c 121 122 123 13a 13b 13c 131 132 133 2aa 2ab 2ac 2a1 2a2 2a3 2ba 2bb 2bc 2b1 2b2 2b3 2ca 2cb 2cc 2c1 2c2 2c3 21a 21b 21c 211 212 213 22a 22b 22c 221 222 223 23a 23b 23c 231 232 233 3aa 3ab 3ac 3a1 3a2 3a3 3ba 3bb 3bc 3b1 3b2 3b3 3ca 3cb 3cc 3c1 3c2 3c3 31a 31b 31c 311 312 313 32a 32b 32c 321 322 323 33a 33b 33c 331 332 333 aaaa aaab aaac aaa1 aaa2 aaa3 aaba aabb aabc aab1 aab2 aab3 aaca aacb aacc aac1 aac2 aac3 aa1a aa1b aa1c aa11 aa12 aa13 aa2a aa2b aa2c aa21 aa22 aa23 aa3a aa3b aa3c aa31 aa32 aa33 abaa abab abac aba1 aba2 aba3 abba abbb abbc abb1 abb2 abb3 abca abcb abcc abc1 abc2 abc3 ab1a ab1b ab1c ab11 ab12 ab13 ab2a ab2b ab2c ab21 ab22 ab23 ab3a ab3b ab3c ab31 ab32 ab33 acaa acab acac aca1 aca2 aca3 acba acbb acbc acb1 acb2 acb3 acca accb accc acc1 acc2 acc3 ac1a ac1b ac1c ac11 ac12 ac13 ac2a ac2b ac2c ac21 ac22 ac23 ac3a ac3b ac3c ac31 ac32 ac33 a1aa a1ab a1ac a1a1 a1a2 a1a3 a1ba a1bb a1bc a1b1 a1b2 a1b3 a1ca a1cb a1cc a1c1 a1c2 a1c3 a11a a11b a11c a111 a112 a113 a12a a12b a12c a121 a122 a123 a13a a13b a13c a131 a132 a133 a2aa a2ab a2ac a2a1 a2a2 a2a3 a2ba a2bb a2bc a2b1 a2b2 a2b3 a2ca a2cb a2cc a2c1 a2c2 a2c3 a21a a21b a21c a211 a212 a213 a22a a22b a22c a221 a222 a223 a23a a23b a23c a231 a232 a233 a3aa a3ab a3ac a3a1 a3a2 a3a3 a3ba a3bb a3bc a3b1 a3b2 a3b3 a3ca a3cb a3cc a3c1 a3c2 a3c3 a31a a31b a31c a311 a312 a313 a32a a32b a32c a321 a322 a323 a33a a33b a33c a331 a332 a333 baaa baab baac baa1 baa2 baa3 baba babb babc bab1 bab2 bab3 baca bacb bacc bac1 bac2 bac3 ba1a ba1b ba1c ba11 ba12 ba13 ba2a ba2b ba2c ba21 ba22 ba23 ba3a ba3b ba3c ba31 ba32 ba33 bbaa bbab bbac bba1 bba2 bba3 bbba bbbb bbbc bbb1 bbb2 bbb3 bbca bbcb bbcc bbc1 bbc2 bbc3 bb1a bb1b bb1c bb11 bb12 bb13 bb2a bb2b bb2c bb21 bb22 bb23 bb3a bb3b bb3c bb31 bb32 bb33 bcaa bcab bcac bca1 bca2 bca3 bcba bcbb bcbc bcb1 bcb2 bcb3 bcca bccb bccc bcc1 bcc2 bcc3 bc1a bc1b bc1c bc11 bc12 bc13 bc2a bc2b bc2c bc21 bc22 bc23 bc3a bc3b bc3c bc31 bc32 bc33 b1aa b1ab b1ac b1a1 b1a2 b1a3 b1ba b1bb b1bc b1b1 b1b2 b1b3 b1ca b1cb b1cc b1c1 b1c2 b1c3 b11a b11b b11c b111 b112 b113 b12a b12b b12c b121 b122 b123 b13a b13b b13c b131 b132 b133 b2aa b2ab b2ac b2a1 b2a2 b2a3 b2ba b2bb b2bc b2b1 b2b2 b2b3 b2ca b2cb b2cc b2c1 b2c2 b2c3 b21a b21b b21c b211 b212 b213 b22a b22b b22c b221 b222 b223 b23a b23b b23c b231 b232 b233 b3aa b3ab b3ac b3a1 b3a2 b3a3 b3ba b3bb b3bc b3b1 b3b2 b3b3 b3ca b3cb b3cc b3c1 b3c2 b3c3 b31a b31b b31c b311 b312 b313 b32a b32b b32c b321 b322 b323 b33a b33b b33c b331 b332 b333 caaa caab caac caa1 caa2 caa3 caba cabb cabc cab1 cab2 cab3 caca cacb cacc cac1 cac2 cac3 ca1a ca1b ca1c ca11 ca12 ca13 ca2a ca2b ca2c ca21 ca22 ca23 ca3a ca3b ca3c ca31 ca32 ca33 cbaa cbab cbac cba1 cba2 cba3 cbba cbbb cbbc cbb1 cbb2 cbb3 cbca cbcb cbcc cbc1 cbc2 cbc3 cb1a cb1b cb1c cb11 cb12 cb13 cb2a cb2b cb2c cb21 cb22 cb23 cb3a cb3b cb3c cb31 cb32 cb33 ccaa ccab ccac cca1 cca2 cca3 ccba ccbb ccbc ccb1 ccb2 ccb3 ccca cccb cccc ccc1 ccc2 ccc3 cc1a cc1b cc1c cc11 cc12 cc13 cc2a cc2b cc2c cc21 cc22 cc23 cc3a cc3b cc3c cc31 cc32 cc33 c1aa c1ab c1ac c1a1 c1a2 c1a3 c1ba c1bb c1bc c1b1 c1b2 c1b3 c1ca c1cb c1cc c1c1 c1c2 c1c3 c11a c11b c11c c111 c112 c113 c12a c12b c12c c121 c122 c123 c13a c13b c13c c131 c132 c133 c2aa c2ab c2ac c2a1 c2a2 c2a3 c2ba c2bb c2bc c2b1 c2b2 c2b3 c2ca c2cb c2cc c2c1 c2c2 c2c3 c21a c21b c21c c211 c212 c213 c22a c22b c22c c221 c222 c223 c23a c23b c23c c231 c232 c233 c3aa c3ab c3ac c3a1 c3a2 c3a3 c3ba c3bb c3bc c3b1 c3b2 c3b3 c3ca c3cb c3cc c3c1 c3c2 c3c3 c31a c31b c31c c311 c312 c313 c32a c32b c32c c321 c322 c323 c33a c33b c33c c331 c332 c333 1aaa 1aab 1aac 1aa1 1aa2 1aa3 1aba 1abb 1abc 1ab1 1ab2 1ab3 1aca 1acb 1acc 1ac1 1ac2 1ac3 1a1a 1a1b 1a1c 1a11 1a12 1a13 1a2a 1a2b 1a2c 1a21 1a22 1a23 1a3a 1a3b 1a3c 1a31 1a32 1a33 1baa 1bab 1bac 1ba1 1ba2 1ba3 1bba 1bbb 1bbc 1bb1 1bb2 1bb3 1bca 1bcb 1bcc 1bc1 1bc2 1bc3 1b1a 1b1b 1b1c 1b11 1b12 1b13 1b2a 1b2b 1b2c 1b21 1b22 1b23 1b3a 1b3b 1b3c 1b31 1b32 1b33 1caa 1cab 1cac 1ca1 1ca2 1ca3 1cba 1cbb 1cbc 1cb1 1cb2 1cb3 1cca 1ccb 1ccc 1cc1 1cc2 1cc3 1c1a 1c1b 1c1c 1c11 1c12 1c13 1c2a 1c2b 1c2c 1c21 1c22 1c23 1c3a 1c3b 1c3c 1c31 1c32 1c33 11aa 11ab 11ac 11a1 11a2 11a3 11ba 11bb 11bc 11b1 11b2 11b3 11ca 11cb 11cc 11c1 11c2 11c3 111a 111b 111c 1111 1112 1113 112a 112b 112c 1121 1122 1123 113a 113b 113c 1131 1132 1133 12aa 12ab 12ac 12a1 12a2 12a3 12ba 12bb 12bc 12b1 12b2 12b3 12ca 12cb 12cc 12c1 12c2 12c3 121a 121b 121c 1211 1212 1213 122a 122b 122c 1221 1222 1223 123a 123b 123c 1231 1232 1233 13aa 13ab 13ac 13a1 13a2 13a3 13ba 13bb 13bc 13b1 13b2 13b3 13ca 13cb 13cc 13c1 13c2 13c3 131a 131b 131c 1311 1312 1313 132a 132b 132c 1321 1322 1323 133a 133b 133c 1331 1332 1333 2aaa 2aab 2aac 2aa1 2aa2 2aa3 2aba 2abb 2abc 2ab1 2ab2 2ab3 2aca 2acb 2acc 2ac1 2ac2 2ac3 2a1a 2a1b 2a1c 2a11 2a12 2a13 2a2a 2a2b 2a2c 2a21 2a22 2a23 2a3a 2a3b 2a3c 2a31 2a32 2a33 2baa 2bab 2bac 2ba1 2ba2 2ba3 2bba 2bbb 2bbc 2bb1 2bb2 2bb3 2bca 2bcb 2bcc 2bc1 2bc2 2bc3 2b1a 2b1b 2b1c 2b11 2b12 2b13 2b2a 2b2b 2b2c 2b21 2b22 2b23 2b3a 2b3b 2b3c 2b31 2b32 2b33 2caa 2cab 2cac 2ca1 2ca2 2ca3 2cba 2cbb 2cbc 2cb1 2cb2 2cb3 2cca 2ccb 2ccc 2cc1 2cc2 2cc3 2c1a 2c1b 2c1c 2c11 2c12 2c13 2c2a 2c2b 2c2c 2c21 2c22 2c23 2c3a 2c3b 2c3c 2c31 2c32 2c33 21aa 21ab 21ac 21a1 21a2 21a3 21ba 21bb 21bc 21b1 21b2 21b3 21ca 21cb 21cc 21c1 21c2 21c3 211a 211b 211c 2111 2112 2113 212a 212b 212c 2121 2122 2123 213a 213b 213c 2131 2132 2133 22aa 22ab 22ac 22a1 22a2 22a3 22ba 22bb 22bc 22b1 22b2 22b3 22ca 22cb 22cc 22c1 22c2 22c3 221a 221b 221c 2211 2212 2213 222a 222b 222c 2221 2222 2223 223a 223b 223c 2231 2232 2233 23aa 23ab 23ac 23a1 23a2 23a3 23ba 23bb 23bc 23b1 23b2 23b3 23ca 23cb 23cc 23c1 23c2 23c3 231a 231b 231c 2311 2312 2313 232a 232b 232c 2321 2322 2323 233a 233b 233c 2331 2332 2333 3aaa 3aab 3aac 3aa1 3aa2 3aa3 3aba 3abb 3abc 3ab1 3ab2 3ab3 3aca 3acb 3acc 3ac1 3ac2 3ac3 3a1a 3a1b 3a1c 3a11 3a12 3a13 3a2a 3a2b 3a2c 3a21 3a22 3a23 3a3a 3a3b 3a3c 3a31 3a32 3a33 3baa 3bab 3bac 3ba1 3ba2 3ba3 3bba 3bbb 3bbc 3bb1 3bb2 3bb3 3bca 3bcb 3bcc 3bc1 3bc2 3bc3 3b1a 3b1b 3b1c 3b11 3b12 3b13 3b2a 3b2b 3b2c 3b21 3b22 3b23 3b3a 3b3b 3b3c 3b31 3b32 3b33 3caa 3cab 3cac 3ca1 3ca2 3ca3 3cba 3cbb 3cbc 3cb1 3cb2 3cb3 3cca 3ccb 3ccc 3cc1 3cc2 3cc3 3c1a 3c1b 3c1c 3c11 3c12 3c13 3c2a 3c2b 3c2c 3c21 3c22 3c23 3c3a 3c3b 3c3c 3c31 3c32 3c33 31aa 31ab 31ac 31a1 31a2 31a3 31ba 31bb 31bc 31b1 31b2 31b3 31ca 31cb 31cc 31c1 31c2 31c3 311a 311b 311c 3111 3112 3113 312a 312b 312c 3121 3122 3123 313a 313b 313c 3131 3132 3133 32aa 32ab 32ac 32a1 32a2 32a3 32ba 32bb 32bc 32b1 32b2 32b3 32ca 32cb 32cc 32c1 32c2 32c3 321a 321b 321c 3211 3212 3213 322a 322b 322c 3221 3222 3223 323a 323b 323c 3231 3232 3233 33aa 33ab 33ac 33a1 33a2 33a3 33ba 33bb 33bc 33b1 33b2 33b3 33ca 33cb 33cc 33c1 33c2 33c3 331a 331b 331c 3311 3312 3313 332a 332b 332c 3321 3322 3323 333a 333b 333c 3331 3332 3333讨论(0) -
This is a different language, but is this the results that you are looking for in the end?
>>> import itertools >>> def my_combinations(string, max_length): for repeat in range(1, max_length + 1): for result in itertools.product(string, repeat=repeat): yield ''.join(result) >>> print(*my_combinations('abc123', 4), sep='\n') a b c 1 2 3 aa ab ac a1 a2 a3 ba bb bc b1 b2 b3 ca cb cc c1 c2 c3 1a 1b 1c 11 12 13 2a 2b 2c 21 22 23 3a 3b 3c 31 32 33 aaa aab aac aa1 aa2 aa3 aba abb abc ab1 ab2 ab3 aca acb acc ac1 ac2 ac3 a1a a1b a1c a11 a12 a13 a2a a2b a2c a21 a22 a23 a3a a3b a3c a31 a32 a33 baa bab bac ba1 ba2 ba3 bba bbb bbc bb1 bb2 bb3 bca bcb bcc bc1 bc2 bc3 b1a b1b b1c b11 b12 b13 b2a b2b b2c b21 b22 b23 b3a b3b b3c b31 b32 b33 caa cab cac ca1 ca2 ca3 cba cbb cbc cb1 cb2 cb3 cca ccb ccc cc1 cc2 cc3 c1a c1b c1c c11 c12 c13 c2a c2b c2c c21 c22 c23 c3a c3b c3c c31 c32 c33 1aa 1ab 1ac 1a1 1a2 1a3 1ba 1bb 1bc 1b1 1b2 1b3 1ca 1cb 1cc 1c1 1c2 1c3 11a 11b 11c 111 112 113 12a 12b 12c 121 122 123 13a 13b 13c 131 132 133 2aa 2ab 2ac 2a1 2a2 2a3 2ba 2bb 2bc 2b1 2b2 2b3 2ca 2cb 2cc 2c1 2c2 2c3 21a 21b 21c 211 212 213 22a 22b 22c 221 222 223 23a 23b 23c 231 232 233 3aa 3ab 3ac 3a1 3a2 3a3 3ba 3bb 3bc 3b1 3b2 3b3 3ca 3cb 3cc 3c1 3c2 3c3 31a 31b 31c 311 312 313 32a 32b 32c 321 322 323 33a 33b 33c 331 332 333 aaaa aaab aaac aaa1 aaa2 aaa3 aaba aabb aabc aab1 aab2 aab3 aaca aacb aacc aac1 aac2 aac3 aa1a aa1b aa1c aa11 aa12 aa13 aa2a aa2b aa2c aa21 aa22 aa23 aa3a aa3b aa3c aa31 aa32 aa33 abaa abab abac aba1 aba2 aba3 abba abbb abbc abb1 abb2 abb3 abca abcb abcc abc1 abc2 abc3 ab1a ab1b ab1c ab11 ab12 ab13 ab2a ab2b ab2c ab21 ab22 ab23 ab3a ab3b ab3c ab31 ab32 ab33 acaa acab acac aca1 aca2 aca3 acba acbb acbc acb1 acb2 acb3 acca accb accc acc1 acc2 acc3 ac1a ac1b ac1c ac11 ac12 ac13 ac2a ac2b ac2c ac21 ac22 ac23 ac3a ac3b ac3c ac31 ac32 ac33 a1aa a1ab a1ac a1a1 a1a2 a1a3 a1ba a1bb a1bc a1b1 a1b2 a1b3 a1ca a1cb a1cc a1c1 a1c2 a1c3 a11a a11b a11c a111 a112 a113 a12a a12b a12c a121 a122 a123 a13a a13b a13c a131 a132 a133 a2aa a2ab a2ac a2a1 a2a2 a2a3 a2ba a2bb a2bc a2b1 a2b2 a2b3 a2ca a2cb a2cc a2c1 a2c2 a2c3 a21a a21b a21c a211 a212 a213 a22a a22b a22c a221 a222 a223 a23a a23b a23c a231 a232 a233 a3aa a3ab a3ac a3a1 a3a2 a3a3 a3ba a3bb a3bc a3b1 a3b2 a3b3 a3ca a3cb a3cc a3c1 a3c2 a3c3 a31a a31b a31c a311 a312 a313 a32a a32b a32c a321 a322 a323 a33a a33b a33c a331 a332 a333 baaa baab baac baa1 baa2 baa3 baba babb babc bab1 bab2 bab3 baca bacb bacc bac1 bac2 bac3 ba1a ba1b ba1c ba11 ba12 ba13 ba2a ba2b ba2c ba21 ba22 ba23 ba3a ba3b ba3c ba31 ba32 ba33 bbaa bbab bbac bba1 bba2 bba3 bbba bbbb bbbc bbb1 bbb2 bbb3 bbca bbcb bbcc bbc1 bbc2 bbc3 bb1a bb1b bb1c bb11 bb12 bb13 bb2a bb2b bb2c bb21 bb22 bb23 bb3a bb3b bb3c bb31 bb32 bb33 bcaa bcab bcac bca1 bca2 bca3 bcba bcbb bcbc bcb1 bcb2 bcb3 bcca bccb bccc bcc1 bcc2 bcc3 bc1a bc1b bc1c bc11 bc12 bc13 bc2a bc2b bc2c bc21 bc22 bc23 bc3a bc3b bc3c bc31 bc32 bc33 b1aa b1ab b1ac b1a1 b1a2 b1a3 b1ba b1bb b1bc b1b1 b1b2 b1b3 b1ca b1cb b1cc b1c1 b1c2 b1c3 b11a b11b b11c b111 b112 b113 b12a b12b b12c b121 b122 b123 b13a b13b b13c b131 b132 b133 b2aa b2ab b2ac b2a1 b2a2 b2a3 b2ba b2bb b2bc b2b1 b2b2 b2b3 b2ca b2cb b2cc b2c1 b2c2 b2c3 b21a b21b b21c b211 b212 b213 b22a b22b b22c b221 b222 b223 b23a b23b b23c b231 b232 b233 b3aa b3ab b3ac b3a1 b3a2 b3a3 b3ba b3bb b3bc b3b1 b3b2 b3b3 b3ca b3cb b3cc b3c1 b3c2 b3c3 b31a b31b b31c b311 b312 b313 b32a b32b b32c b321 b322 b323 b33a b33b b33c b331 b332 b333 caaa caab caac caa1 caa2 caa3 caba cabb cabc cab1 cab2 cab3 caca cacb cacc cac1 cac2 cac3 ca1a ca1b ca1c ca11 ca12 ca13 ca2a ca2b ca2c ca21 ca22 ca23 ca3a ca3b ca3c ca31 ca32 ca33 cbaa cbab cbac cba1 cba2 cba3 cbba cbbb cbbc cbb1 cbb2 cbb3 cbca cbcb cbcc cbc1 cbc2 cbc3 cb1a cb1b cb1c cb11 cb12 cb13 cb2a cb2b cb2c cb21 cb22 cb23 cb3a cb3b cb3c cb31 cb32 cb33 ccaa ccab ccac cca1 cca2 cca3 ccba ccbb ccbc ccb1 ccb2 ccb3 ccca cccb cccc ccc1 ccc2 ccc3 cc1a cc1b cc1c cc11 cc12 cc13 cc2a cc2b cc2c cc21 cc22 cc23 cc3a cc3b cc3c cc31 cc32 cc33 c1aa c1ab c1ac c1a1 c1a2 c1a3 c1ba c1bb c1bc c1b1 c1b2 c1b3 c1ca c1cb c1cc c1c1 c1c2 c1c3 c11a c11b c11c c111 c112 c113 c12a c12b c12c c121 c122 c123 c13a c13b c13c c131 c132 c133 c2aa c2ab c2ac c2a1 c2a2 c2a3 c2ba c2bb c2bc c2b1 c2b2 c2b3 c2ca c2cb c2cc c2c1 c2c2 c2c3 c21a c21b c21c c211 c212 c213 c22a c22b c22c c221 c222 c223 c23a c23b c23c c231 c232 c233 c3aa c3ab c3ac c3a1 c3a2 c3a3 c3ba c3bb c3bc c3b1 c3b2 c3b3 c3ca c3cb c3cc c3c1 c3c2 c3c3 c31a c31b c31c c311 c312 c313 c32a c32b c32c c321 c322 c323 c33a c33b c33c c331 c332 c333 1aaa 1aab 1aac 1aa1 1aa2 1aa3 1aba 1abb 1abc 1ab1 1ab2 1ab3 1aca 1acb 1acc 1ac1 1ac2 1ac3 1a1a 1a1b 1a1c 1a11 1a12 1a13 1a2a 1a2b 1a2c 1a21 1a22 1a23 1a3a 1a3b 1a3c 1a31 1a32 1a33 1baa 1bab 1bac 1ba1 1ba2 1ba3 1bba 1bbb 1bbc 1bb1 1bb2 1bb3 1bca 1bcb 1bcc 1bc1 1bc2 1bc3 1b1a 1b1b 1b1c 1b11 1b12 1b13 1b2a 1b2b 1b2c 1b21 1b22 1b23 1b3a 1b3b 1b3c 1b31 1b32 1b33 1caa 1cab 1cac 1ca1 1ca2 1ca3 1cba 1cbb 1cbc 1cb1 1cb2 1cb3 1cca 1ccb 1ccc 1cc1 1cc2 1cc3 1c1a 1c1b 1c1c 1c11 1c12 1c13 1c2a 1c2b 1c2c 1c21 1c22 1c23 1c3a 1c3b 1c3c 1c31 1c32 1c33 11aa 11ab 11ac 11a1 11a2 11a3 11ba 11bb 11bc 11b1 11b2 11b3 11ca 11cb 11cc 11c1 11c2 11c3 111a 111b 111c 1111 1112 1113 112a 112b 112c 1121 1122 1123 113a 113b 113c 1131 1132 1133 12aa 12ab 12ac 12a1 12a2 12a3 12ba 12bb 12bc 12b1 12b2 12b3 12ca 12cb 12cc 12c1 12c2 12c3 121a 121b 121c 1211 1212 1213 122a 122b 122c 1221 1222 1223 123a 123b 123c 1231 1232 1233 13aa 13ab 13ac 13a1 13a2 13a3 13ba 13bb 13bc 13b1 13b2 13b3 13ca 13cb 13cc 13c1 13c2 13c3 131a 131b 131c 1311 1312 1313 132a 132b 132c 1321 1322 1323 133a 133b 133c 1331 1332 1333 2aaa 2aab 2aac 2aa1 2aa2 2aa3 2aba 2abb 2abc 2ab1 2ab2 2ab3 2aca 2acb 2acc 2ac1 2ac2 2ac3 2a1a 2a1b 2a1c 2a11 2a12 2a13 2a2a 2a2b 2a2c 2a21 2a22 2a23 2a3a 2a3b 2a3c 2a31 2a32 2a33 2baa 2bab 2bac 2ba1 2ba2 2ba3 2bba 2bbb 2bbc 2bb1 2bb2 2bb3 2bca 2bcb 2bcc 2bc1 2bc2 2bc3 2b1a 2b1b 2b1c 2b11 2b12 2b13 2b2a 2b2b 2b2c 2b21 2b22 2b23 2b3a 2b3b 2b3c 2b31 2b32 2b33 2caa 2cab 2cac 2ca1 2ca2 2ca3 2cba 2cbb 2cbc 2cb1 2cb2 2cb3 2cca 2ccb 2ccc 2cc1 2cc2 2cc3 2c1a 2c1b 2c1c 2c11 2c12 2c13 2c2a 2c2b 2c2c 2c21 2c22 2c23 2c3a 2c3b 2c3c 2c31 2c32 2c33 21aa 21ab 21ac 21a1 21a2 21a3 21ba 21bb 21bc 21b1 21b2 21b3 21ca 21cb 21cc 21c1 21c2 21c3 211a 211b 211c 2111 2112 2113 212a 212b 212c 2121 2122 2123 213a 213b 213c 2131 2132 2133 22aa 22ab 22ac 22a1 22a2 22a3 22ba 22bb 22bc 22b1 22b2 22b3 22ca 22cb 22cc 22c1 22c2 22c3 221a 221b 221c 2211 2212 2213 222a 222b 222c 2221 2222 2223 223a 223b 223c 2231 2232 2233 23aa 23ab 23ac 23a1 23a2 23a3 23ba 23bb 23bc 23b1 23b2 23b3 23ca 23cb 23cc 23c1 23c2 23c3 231a 231b 231c 2311 2312 2313 232a 232b 232c 2321 2322 2323 233a 233b 233c 2331 2332 2333 3aaa 3aab 3aac 3aa1 3aa2 3aa3 3aba 3abb 3abc 3ab1 3ab2 3ab3 3aca 3acb 3acc 3ac1 3ac2 3ac3 3a1a 3a1b 3a1c 3a11 3a12 3a13 3a2a 3a2b 3a2c 3a21 3a22 3a23 3a3a 3a3b 3a3c 3a31 3a32 3a33 3baa 3bab 3bac 3ba1 3ba2 3ba3 3bba 3bbb 3bbc 3bb1 3bb2 3bb3 3bca 3bcb 3bcc 3bc1 3bc2 3bc3 3b1a 3b1b 3b1c 3b11 3b12 3b13 3b2a 3b2b 3b2c 3b21 3b22 3b23 3b3a 3b3b 3b3c 3b31 3b32 3b33 3caa 3cab 3cac 3ca1 3ca2 3ca3 3cba 3cbb 3cbc 3cb1 3cb2 3cb3 3cca 3ccb 3ccc 3cc1 3cc2 3cc3 3c1a 3c1b 3c1c 3c11 3c12 3c13 3c2a 3c2b 3c2c 3c21 3c22 3c23 3c3a 3c3b 3c3c 3c31 3c32 3c33 31aa 31ab 31ac 31a1 31a2 31a3 31ba 31bb 31bc 31b1 31b2 31b3 31ca 31cb 31cc 31c1 31c2 31c3 311a 311b 311c 3111 3112 3113 312a 312b 312c 3121 3122 3123 313a 313b 313c 3131 3132 3133 32aa 32ab 32ac 32a1 32a2 32a3 32ba 32bb 32bc 32b1 32b2 32b3 32ca 32cb 32cc 32c1 32c2 32c3 321a 321b 321c 3211 3212 3213 322a 322b 322c 3221 3222 3223 323a 323b 323c 3231 3232 3233 33aa 33ab 33ac 33a1 33a2 33a3 33ba 33bb 33bc 33b1 33b2 33b3 33ca 33cb 33cc 33c1 33c2 33c3 331a 331b 331c 3311 3312 3313 332a 332b 332c 3321 3322 3323 333a 333b 333c 3331 3332 3333 >>>讨论(0) -
Accumulative set product for k times with a set S which is empty initially will produce all permutations up to k-long, with n = |S| ..
Time: O(kn^2)
Space: O(kn^2)
// Enumerate all permutations, PHP // by Khaled A Khunaifer, 25/3/2013 function setProduct($a, $b) { $arr = array(); foreach ($a as $s) { foreach ($b as $t) { $arr[] = $s . $t; } } return $arr; } function enumerate ($arrary, $maxLen) { $enumeration = array(); for (var $i = 1; $i <= $maxLen; $i++) { $enumeration += setProduct($enumeration, $array); } }讨论(0) -
One thing that is for sure is that what ever the algo use for this , the best time complexity for generation of all the numbers is around O((n^m+1)/(n-1)) (Assuming that you are not using any paralleled programming . ) . (Where n is size of array , m is max length .)
For which any of the above stated algo suits better .
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Solution
function combinationsByLenth($arr, $len) { $combinations = []; $select = array_fill(0, $len, 0); $selectCount = count($select); $arrCount = count($arr); $possibleCombinations = pow($arrCount, $selectCount); while ($possibleCombinations-- > 0) { $combination = ''; foreach ($select as $index) { $combination .= $arr[$index]; } $combinations[] = $combination; for ($i = $selectCount - 1; $i >= 0; $i--) { if ($select[$i] !== ($arrCount - 1)) { $select[$i]++; break; } else { $select[$i] = 0; } } } return $combinations; } function combinationsByMinMax($arr, $min, $max) { $combinations = []; for ($i = $min; $i <= $max; $i++) { $combinations = array_merge($combinations, combinationsByLenth($arr, $i)); } return $combinations; } print_r(combinationsByMinMax($arr, 1, 5));Output
Array ( [0] => a [1] => b [2] => c [3] => 1 [4] => 2 [5] => 3 [6] => aa [7] => ab [8] => ac [9] => a1 ... [9320] => 3332c [9321] => 33321 [9322] => 33322 [9323] => 33323 [9324] => 3333a [9325] => 3333b [9326] => 3333c [9327] => 33331 [9328] => 33332 [9329] => 33333 )Rationale
- Avoid recursive solutions for this type of problem in PHP (note, I like recursion in languages optimized to handle it better) to avoid stack issues as the length grows.
- Break the function up into two separate functions, one that implements min and max length, and one that gets the possible combinations for a specific length to promote reuse and clarity.
- Limit function calls within the 2 functions as much as possible to enhance performance (this algorithm gets heavy fast!)
How I Developed This Solution
I started out with a function that handled the specific case of combinations of length 5, refactored to generalize the algorithm, refactored to generalize the algorithm, etc. I've put up a quick gist so you can see the iterations to get to this working version as a case study of how to approach building this type of algorithm:
https://gist.github.com/AdamJonR/5278480
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I'd go with recursive solution.
"Guess" what is the first element, and recurse on the following elements.
Repeat for all possible guesses.pseudo code:
findCombinations(array, candidate, length): //base clause: if (candidate.length == length): return for each i from 0to array.length: //i is the next char to add candidate.append(array[i]) //print the candidate, since it is a unique permutation smaller then length: print candidate //recursively find permutations for the remianing elements findCombinations(array,candidate,length) //clean up candidate.removeLasElement()Java Code:
private static void findCombinations(char[] array, StringBuilder candidate, int length) { //base clause: if (candidate.length() == length) return; for (int i = 0; i < array.length; i++) { //i is the next char to add candidate.append(array[i]); //print the candidate, since it is a unique permutation smaller then length: System.out.println(candidate); //recursively find permutations for the remianing elements findCombinations(array,candidate,length); //clean up candidate.deleteCharAt(candidate.length()-1); } } public static void findCombinations(char[] array,int length) { findCombinations(array, new StringBuilder(), length); }Invoking:
char[] arr = "abcde".toCharArray(); findCombinations(arr, 3);results in:
a aa aaa aab aac aad aae ab aba abb abc abd abe ac aca acb acc acd ace ad ada adb adc add ade ae aea aeb aec aed aee b ba baa bab bac bad bae bb bba bbb bbc bbd bbe bc bca bcb bcc bcd bce bd bda bdb bdc bdd bde be bea beb bec bed bee c ca caa cab cac cad cae cb cba cbb cbc cbd cbe cc cca ccb ccc ccd cce cd cda cdb cdc cdd cde ce cea ceb cec ced cee d da daa dab dac dad dae db dba dbb dbc dbd dbe dc dca dcb dcc dcd dce dd dda ddb ddc ffffd dde de dea deb dec ded dee e ea eaa eab eac ead eae eb eba ebb ebc ebd ebe ec eca ecb ecc ecd ece ed eda edb edc edd ede ee eea eeb eec eed eee讨论(0)
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