Problem 2026. Skyscrapers - Puzzle

Created by Richard Zapor

Solve Later

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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>

The Skyscraper puzzle challenge comes from <http://logicmastersindia.com/home/ Logic Masters India> and <http://www.conceptispuzzles.com/ Games' Concept is Puzzles>.

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 matrix

*Example:*

vr=[0 0 3 0 0]';
  vL=[3 0 0 1 0]';
  vd=[0 0 0 0 0];
  vu=[5 2 0 0 0];

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

*Algorithm Discussion:*

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

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Problem 2026. Skyscrapers - Puzzle

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