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Direct search for diagonal cyclicity squares added
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The new version of latin.c file constructs squares both with horizontal/vertical and main-diagonal/antidiagonal cyclicity. The new datasets with all order-13 and order-17 squares added (the latter in the zip file).
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@ipgmvq
ipgmvq authored Apr 21, 2021
1 parent f8773e7 commit 90f05a1
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Showing 5 changed files with 19,163 additions and 36,850 deletions.
60 changes: 57 additions & 3 deletions latin.c
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,7 @@
#define ORDER_LIMIT 19
#define mod(x, p) (x < 0 ? x % p + p : x % p)


int order = 5;
int * vector;
FILE * output;
Expand Down Expand Up @@ -60,14 +61,27 @@ static void normalize(int position) {
static void hashSquareSraight(int _count) {
for (int row = 0; row < order; ++row)
for (int column = 0; column < order; ++column)
matrices[_count * matrix_size + row * order + column] = (char) mod(column - vector[row], order);
matrices[_count * matrix_size + row * order + column] = (char) mod((column - vector[row]), order);
}


static void hashSquareTranspose(int _count) {
for (int column = 0; column < order; ++column)
for (int row = 0; row < order; ++row)
matrices[_count * matrix_size + column * order + row] = (char) mod(column - vector[row], order);
matrices[_count * matrix_size + column * order + row] = (char) mod((column - vector[row]), order);
}

static void hashSquareMainDiagonal(int _count) {
for (int row = 0; row < order; ++row)
for (int column = 0; column < order; ++column)
matrices[_count * matrix_size + mod((column + row), order) * order + column] = (char) mod((column - vector[row]), order);
}


static void hashSquareAntiDiagonal(int _count) {
for (int column = 0; column < order; ++column)
for (int row = 0; row < order; ++row)
matrices[_count * matrix_size + mod((column + row), order) * order + order - 1 - column] = (char) mod((column - vector[row]), order);
}


Expand All @@ -76,7 +90,11 @@ static void step(int row) {
for (int column = 1; column < order; ++column) {
to_proceed = 1;
for (int row_history = 0; row_history < row; ++row_history)
if (column == vector[row_history] || mod(column - vector[row_history], order) == row - row_history || mod(vector[row_history] - column, order) == row - row_history)
if (
column == vector[row_history] ||
mod((column - vector[row_history]), order) == row - row_history ||
mod((vector[row_history] - column), order) == row - row_history
)
to_proceed = 0;
if (to_proceed) {
vector[row] = column;
Expand All @@ -93,6 +111,36 @@ static void step(int row) {
}



static void step_diagonal(int row) {
int to_proceed;
for (int column = 1; column < order; ++column) {
to_proceed = 1;
for (int row_history = 0; row_history < row; ++row_history)
if (
column == vector[row_history] ||
mod((row + column), order) == mod((row_history + vector[row_history]), order) ||
mod((mod((row + column), order) - mod((row_history + vector[row_history]), order)), order) == mod((column - vector[row_history]), order) ||
mod((- mod((row + column), order) + mod((row_history + vector[row_history]), order)), order) == mod((column - vector[row_history]), order) ||
mod((mod((row + column), order) - mod((row_history + vector[row_history]), order)), order) == mod((- column + vector[row_history]), order) ||
mod((- mod((row + column), order) + mod((row_history + vector[row_history]), order)), order) == mod((- column + vector[row_history]), order)
)
to_proceed = 0;
if (to_proceed) {
vector[row] = column;
if (row + 1 < order)
step_diagonal(row + 1);
else {
if (order <= ORDER_LIMIT) {
hashSquareMainDiagonal(count++);
hashSquareAntiDiagonal(count++);
} else count += 2;
}
}
}
}


int main(int argc, char * argv[]) {
time_t t0 = time(0);
char file_name[51] = "semi_cyclic_pandiagonal_latin_squares_order_5.txt";
Expand All @@ -118,6 +166,12 @@ int main(int argc, char * argv[]) {
vector[1] = i;
step(2);
}
for (int i = 1; i < order - 1; ++i) {
if (i != 6) {
vector[1] = i;
step_diagonal(2);
}
}
int countNonEqual = 0;
if (order <= ORDER_LIMIT) {
for (int i = 0; i < count; ++i) normalize(i);
Expand Down
30 changes: 16 additions & 14 deletions latin_square_cyclicity_check.html
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Original file line number Diff line number Diff line change
Expand Up @@ -14279,7 +14279,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs ">
<div class="jp-Cell-inputWrapper">
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[1]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[6]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
Expand All @@ -14294,7 +14294,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs ">
<div class="jp-Cell-inputWrapper">
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[2]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[19]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">pandiagonal</span><span class="p">(</span><span class="n">matrix</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
Expand All @@ -14303,14 +14303,14 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
<span class="n">matrix_</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">matrix_</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">mod</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">order</span><span class="p">)</span> <span class="o">+</span> <span class="n">i</span><span class="p">,</span> <span class="n">order</span><span class="p">)]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">order</span><span class="p">):</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">matrix_</span><span class="p">[:,</span><span class="n">i</span><span class="p">])</span><span class="o">.</span><span class="n">size</span> <span class="o">&lt;</span> <span class="n">order</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">matrix_</span><span class="p">[:,</span><span class="n">i</span><span class="p">])</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>
<span class="c1">#print(np.unique(matrix_[:,i]).size)</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="n">matrix_</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">order</span><span class="p">):</span>
<span class="n">matrix_</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">matrix_</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">mod</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">order</span><span class="p">)</span> <span class="o">-</span> <span class="n">i</span><span class="p">,</span> <span class="n">order</span><span class="p">)]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">order</span><span class="p">):</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">matrix_</span><span class="p">[:,</span><span class="n">i</span><span class="p">])</span><span class="o">.</span><span class="n">size</span> <span class="o">&lt;</span> <span class="n">order</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">matrix_</span><span class="p">[:,</span><span class="n">i</span><span class="p">])</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>
<span class="c1">#print(np.unique(matrix_[:,i]).size)</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">return</span> <span class="kc">True</span>

Expand Down Expand Up @@ -14350,7 +14350,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
<span class="k">break</span>


<span class="n">not_antidiagonal</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">not_main_diagonal</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">main_diag</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">for</span> <span class="n">column</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">order</span><span class="p">):</span>
<span class="n">main_diag</span><span class="p">[:,</span><span class="n">column</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="n">main_diag</span><span class="p">[:,</span><span class="n">column</span><span class="p">],</span> <span class="n">column</span><span class="p">)</span>
Expand All @@ -14360,10 +14360,10 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
<span class="k">if</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="n">main_diag</span><span class="p">[</span><span class="n">row</span><span class="p">],</span> <span class="n">shift</span><span class="p">)</span> <span class="o">==</span> <span class="n">main_diag</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">all</span><span class="p">():</span>
<span class="n">shift_answer</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">shift_answer</span><span class="p">:</span>
<span class="n">not_antidiagonal</span> <span class="o">=</span> <span class="kc">False</span>
<span class="n">not_main_diagonal</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">break</span>

<span class="n">not_main_diagonal</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">not_antidiagonal</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">anti_diag</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">for</span> <span class="n">column</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">order</span><span class="p">):</span>
<span class="n">anti_diag</span><span class="p">[:,</span><span class="n">column</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="n">anti_diag</span><span class="p">[:,</span><span class="n">column</span><span class="p">],</span> <span class="o">-</span><span class="n">column</span><span class="p">)</span>
Expand All @@ -14373,7 +14373,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
<span class="k">if</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="n">anti_diag</span><span class="p">[</span><span class="n">row</span><span class="p">],</span> <span class="n">shift</span><span class="p">)</span> <span class="o">==</span> <span class="n">anti_diag</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">all</span><span class="p">():</span>
<span class="n">shift_answer</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">shift_answer</span><span class="p">:</span>
<span class="n">not_main_diagonal</span> <span class="o">=</span> <span class="kc">False</span>
<span class="n">not_antidiagonal</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">break</span>

<span class="k">return</span> <span class="p">(</span><span class="n">not_horizontal</span><span class="p">,</span> <span class="n">not_vertical</span><span class="p">,</span> <span class="n">not_main_diagonal</span><span class="p">,</span> <span class="n">not_antidiagonal</span><span class="p">)</span>
Expand All @@ -14389,7 +14389,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell ">
<div class="jp-Cell-inputWrapper">
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[3]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[25]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">squares</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
Expand All @@ -14398,7 +14398,7 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an

<span class="n">order</span> <span class="o">=</span> <span class="kc">None</span>

<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="s1">&#39;semi_cyclic_pandiagonal_latin_squares_order_17.txt&#39;</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="s1">&#39;semi_cyclic_pandiagonal_latin_squares_order_13.txt&#39;</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">f</span><span class="o">.</span><span class="n">readlines</span><span class="p">():</span>
<span class="k">if</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">():</span>
<span class="k">if</span> <span class="n">order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
Expand Down Expand Up @@ -14459,10 +14459,12 @@ <h3 id="Please-be-warned-that-the-script-is-sensitive-to-the-newline-symbols-(an

<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain">
<pre>There are 0 non-pandiagonal squares in the dataset
16538 sqaures were read
8262 squares are cyclic in a horizontal direction
8262 squares are cyclic in a vertical direction
14 squares are cyclic in all four directions
1362 sqaures were read
338 squares are cyclic in a horizontal direction
338 squares are cyclic in a main-diagonal direction
338 squares are cyclic in a vertical direction
338 squares are cyclic in a antidiagonal direction
10 squares are cyclic in all four directions
</pre>
</div>
</div>
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