TopCoder Statistics - Problem Statement

Problem Statement

It is possible to number all the words that could be formed from a specified alphabet. One way to do it is to put the words in order based on length, with words of common length ordered alphabetically. Using this scheme, if we use the alphabet consisting of just the 3 letters 'a', 'b', and 'c' then the words are numbered:

   1:a 2:b 3:c 4:aa 5:ab 6:ac 7:ba 8:bb   etc.

There are an infinite number of possible words, but each has its own positive number.

We want to be able to find the word that corresponds to any given number. Create a class WordNumber that contains a method theWord that is given alpha, the number of letters in the alphabet, and n, the number of a word. It returns the String that is the word corresponding to n.

The alphabet to be used is the first alpha letters of the normal lowercase alphabet, with their usual alphabetical ordering.

Definition

Class:: WordNumber
Method:: theWord
Parameters:: int, int
Returns:: String
Method signature:: String theWord(int alpha, int n)
(be sure your method is public)

Constraints

alpha will be between 2 and 26, inclusive.
n will be between 1 and 2,000,000,000, inclusive.

Examples

3

5

Returns: "ab"

See the table above.
3

13

Returns: "aaa"

Extending the table above, we find that word 12 is "cc" so the next word, word 13, must be the first 3 letter word.
26

2000000000

Returns: "flhomvx"
15

1

Returns: "a"
26

456

Returns: "qn"
2

13

Returns: "bba"
2

14

Returns: "bbb"
2

15

Returns: "aaaa"
2

9

Returns: "aba"
25

15625

Returns: "xxy"
25

15626

Returns: "xya"
17

1999999999

Returns: "dnnjadcm"
4

13652

Returns: "bdddddd"
4

13651

Returns: "bdddddc"
20

20

Returns: "t"
20

21

Returns: "aa"
20

22

Returns: "ab"
20

40

Returns: "at"
20

41

Returns: "ba"
26

1987654321

Returns: "fkgocac"
2

7

Returns: "aaa"
18

1700430165

Returns: "bmqpdqdi"
6

1879066806

Returns: "dffbdbecaaff"
19

1833149783

Returns: "asrfgrdj"
17

1674669406

Returns: "dafgnona"
17

462567884

Returns: "abbmemoi"
5

816519128

Returns: "cacbeaaeebdec"
24

1660558457

Returns: "hpmaiwq"
15

14662179

Returns: "addieci"
22

40352794

Returns: "greokt"
20

1999886706

Returns: "akdsepof"
7

1681133903

Returns: "efddbbedgaa"
2

586596412

Returns: "aaababbbbabbabbaaaaaaaabbbbab"
10

1999927401

Returns: "aiiiibgcja"
20

1304372648

Returns: "tglfklh"
14

1558323530

Returns: "njmffbch"
2

2000000000

Returns: "bbabbbaabbababbaababaaaaaaaaab"
25

2000000000

Returns: "hdsxxxy"
26

1

Returns: "a"
2

1999999999

Returns: "bbabbbaabbababbaababaaaaaaaaaa"
22

1999999973

Returns: "qnanogo"
26

2000000000

Returns: "flhomvx"
26

1234000000

Returns: "cyviitl"
3

82

Returns: "bbca"
2

5

Returns: "ba"
2

25

Returns: "baba"
3

6

Returns: "ac"
3

3

Returns: "c"
3

565645454

Returns: "ccbccacbcacbabcabb"
2

26

Returns: "babb"
26

26

Returns: "z"
2

2000000000

Returns: "bbabbbaabbababbaababaaaaaaaaab"
2

20000000

Returns: "aabbaaabaababbabaaaaaaab"
2

8

Returns: "aab"
2

2000000

Returns: "bbbabaaaabaabaaaaaab"
2

1073741822

Returns: "bbbbbbbbbbbbbbbbbbbbbbbbbbbbb"
2

16

Returns: "aaab"
3

9

Returns: "bc"
25

24

Returns: "x"
22

113379904

Returns: "uuuuuv"
23

2000000000

Returns: "mkpuagq"
26

700

Returns: "zx"

Statistics

Problem Statement for "WordNumber"

Problem Statement

Definition

Constraints

Examples