Problem 2026. Skyscrapers - Puzzle

Created by Richard Zapor

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The Skyscraper puzzle challenge comes from <a href = "http://logicmastersindia.com/home/">Logic Masters India</a> and <a href = "http://www.conceptispuzzles.com/">Games' Concept is Puzzles</a>.Create an NxN matrix where each row and column contains 1:N given the constraints of View_Right, View_Left, View_Down, and View_Up. A View is the number of Skyscrapers visible the given edge location. A Zero value is No Information provided.Input: [vr,vL,vd,vu] vectors of sizes (N,1),(N,1),(1,N),(1,N)Output: M an NxN matrixExample:<pre class="language-matlab">vr=[0 0 3 0 0]';
vL=[3 0 0 1 0]';
vd=[0 0 0 0 0];
vu=[5 2 0 0 0];
</pre><pre class="language-matlab">M
 5 4 2 1 3
 4 5 1 3 2
 3 2 4 5 1
 2 1 3 4 5
 1 3 5 2 4
</pre>Algorithm Discussion:<pre class="language-matlab">1) Create permutations H and V vectors of length N of values 1:N. (N=5) [12345;12354;...54321]
2) Calc Skyscraper count from Left and Right
3) Determine subset of SkyVectors possible for each Row and Column
4) Sort the Qty of 2*N possible solutions
5) Recursion from least to most valid SkyVectors
6) In recursion verify valid overlay or return
</pre>

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