Problem 2324. GJam 2014 Rd 1c: Train Cars

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/3004486/dashboard#s=p1">GJam 2014 Rd 1c: Reordering Train Cars</a>.Determine number of sequences for set of strings under the constraint that all same characters must be contiguous.Input: s, string of N space separated string segments of letters [a..z]. 1&lt;=N&lt;=10. Total letters &lt;=100.Output: val, number of possible sequencesExample: Small Case<pre class="language-matlab">ab bbbc cd Val=1 as only abbbbccd can be created
aa aa bc c Val=4 aa gives 2 positions, aa'aa''bcc,aa''aa'bcc, bcccaa'aa'',bcccaa''aa'
abc bcd Val=0 as c is internal and thus can not connect to c of abc
</pre>Theory: (Spoilers)A methodical approach implements the following checks: No internal equals any Start/End. Note aaa has no internal. Verify each string has no non-contiguous letters. Verify no two strings have same start or end except where start==end as in bbbb. Val is N! if there are N cc strings. Each string segment is considered a unique piece when counting. Reduce the strings of type aa until there is only one and increase Val by N!. With remaining strings merge to S strings. Val is then scaled by S!. Key merging issue is that ab ba may look mergeable to aa but in actuality it creates abba - invalid and baab -invalid thus Val=0. Creation of full length string and then a final validity check resolves this issue.Additional GJam solutions can be found at <a href = "http://go-hero.net/jam">Example GJam Matlab solutions</a>. Select Find Solutions, change Language to Matlab. The Test Suite, at the bottom, contains a full GJam Matlab solution. No Valid Matlab solutions were submitted during the contest.

This Challenge is derived from <http://code.google.com/codejam/contest/3004486/dashboard#s=p1 GJam 2014 Rd 1c: Reordering Train Cars>.

Determine number of sequences for set of strings under the constraint that all same characters must be contiguous.

*Input:* s, string of N space separated string segments of letters [a..z]. 1<=N<=10. Total letters <=100.

*Output:* val, number of possible sequences

*Example:*  Small Case

ab bbbc cd Val=1 as only abbbbccd can be created
  aa aa bc c Val=4 aa gives 2 positions, aa'aa''bcc,aa''aa'bcc, bcccaa'aa'',bcccaa''aa'
  abc bcd    Val=0 as c is internal and thus can not connect to c of abc

*Theory:* (Spoilers)

A methodical approach implements the following checks: No internal equals any Start/End. Note aaa has no internal. Verify each string has no non-contiguous letters. Verify no two strings have same start or end except where start==end as in bbbb. Val is N! if there are N cc strings. Each string segment is considered a unique piece when counting. Reduce the strings of type aa until there is only one and increase Val by N!. With remaining strings merge to S strings. Val is then scaled by S!. Key merging issue is that ab ba may look mergeable to aa but in actuality it creates abba - invalid and baab -invalid thus Val=0. Creation of full length string and then a final validity check resolves this issue.

Additional GJam solutions can be found at <http://go-hero.net/jam Example GJam Matlab solutions>. Select Find Solutions, change Language to Matlab. The Test Suite, at the bottom, contains a full GJam Matlab solution. No Valid Matlab solutions were submitted during the contest.

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Problem 2324. GJam 2014 Rd 1c: Train Cars

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