Problem 42805. GJam 2016 Rd1A: Rank and File (small)

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/4304486/dashboard#s=p1">GJam Rd1A 2016 Rank and File</a>. This is the small case with max N=10The GJam story is a matrix H(NxN) which has every row and column increasing. Each row and column is recorded on strips. The strips get scrambled and one gets incinerated. The goal is to reconstruct the missing increasing vector strip.Input: [M], matrix of size [2*N-1,N] of all rows and columns of H except oneOutput: [V], the missing vector of H not included in MExamples: [M] [V]<pre class="language-matlab">[1 2 3;2 3 5;3 5 6;2 3 4;1 2 3] [3 4 6] 
[22 222;2 22;2 22][22 222] 
</pre>GJam 2016 Rd1A Matlab results show three qualifiers for Rd2.Theory: With max N=10 it is possible to brute force the 50 puzzles. Persistent may be useful with the usage of nchoosek which may be the critical path. <a href = "https://www.go-hero.net/jam/16/solutions/1/2/MATLAB">GJam Rank_file solutions</a>. Writing the general solution for N=50 is better for the contest. The min corner or the max corner will always be available. Evolving solution, no guessing, is possible. OR one can observe an inherent mathematical result to create a 1-line solution.

This Challenge is derived from <http://code.google.com/codejam/contest/4304486/dashboard#s=p1 GJam Rd1A 2016 Rank and File>. This is the small case with max N=10

The GJam story is a matrix H(NxN) which has every row and column increasing. Each row and column is recorded on strips. The strips get scrambled and one gets incinerated. The goal is to reconstruct the missing increasing vector strip.

*Input:* [M], matrix of size [2*N-1,N] of all rows and columns of H except one

*Output:* [V], the missing vector of H not included in M

*Examples:* [M] [V]

[1 2 3;2 3 5;3 5 6;2 3 4;1 2 3] [3 4 6] 
  [22 222;2 22;2 22][22 222] 
 
GJam 2016 Rd1A Matlab results show three qualifiers for Rd2.

*Theory:* With max N=10 it is possible to brute force the 50 puzzles. Persistent may be useful with the usage of nchoosek which may be the critical path. <https://www.go-hero.net/jam/16/solutions/1/2/MATLAB GJam Rank_file solutions>. Writing the general solution for N=50 is better for the contest. The min corner or the max corner will always be available. Evolving solution, no guessing, is possible. OR one can observe an inherent mathematical result to create a 1-line solution.

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Last Solution submitted on Oct 15, 2020

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Rafael S.T. Vieira on 15 Oct 2020

A better description for this problem can be found at http://joonprogramming.blogspot.com/2016/04/google-code-jam-qualification-round-1a_17.html We have to find an NXN matrix, without repeating numbers at any row or column that must be ordered. And we have 2*N-1 strips of scrambled numbers, which can be rows or columns. The problem is to find what the missing strip is (notice that a NXN matrix has 2*N strips).

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