group__gdsl__perm.html

一个通用的C语言实现的数据结构

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<p>
Convert a linear permutation to its canonical form. 
<p>
Convert the linear permutation P to its canonical form. The resulted canonical permutation is placed into Q without modifying P.<p>
<dl compact><dt><b>Note:</b></dt><dd>Complexity: O( |P| ) </dd></dl>
<dl compact><dt><b>Precondition:</b></dt><dd>P &amp; Q must be valids gdsl_perm_t &amp; |P| == |Q| &amp; P != Q </dd></dl>
<dl compact><dt><b>Parameters:</b></dt><dd>
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    <tr><td valign="top"></td><td valign="top"><em>Q</em>&nbsp;</td><td>The canonical form of P </td></tr>
    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>The linear permutation used to compute its canonical form into Q </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>the canonical form Q of the permutation P. </dd></dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="group__gdsl__perm.html#g648a4fc1929f159a58e3e768fa0396ae">gdsl_perm_canonical_to_linear()</a> </dd></dl>
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<a class="anchor" name="g648a4fc1929f159a58e3e768fa0396ae"></a><!-- doxytag: member="gdsl_perm.h::gdsl_perm_canonical_to_linear" ref="g648a4fc1929f159a58e3e768fa0396ae" args="(gdsl_perm_t Q, const gdsl_perm_t P)" --><p>
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          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a> gdsl_perm_canonical_to_linear           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname" nowrap> <em>Q</em>, </td>
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          <td class="md" nowrap>const <a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname" nowrap> <em>P</em></td>
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          <td class="md">)&nbsp;</td>
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<p>
Convert a canonical permutation to its linear form. 
<p>
Convert the canonical permutation P to its linear form. The resulted linear permutation is placed into Q without modifying P.<p>
<dl compact><dt><b>Note:</b></dt><dd>Complexity: O( |P| ) </dd></dl>
<dl compact><dt><b>Precondition:</b></dt><dd>P &amp; Q must be valids gdsl_perm_t &amp; |P| == |Q| &amp; P != Q </dd></dl>
<dl compact><dt><b>Parameters:</b></dt><dd>
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    <tr><td valign="top"></td><td valign="top"><em>Q</em>&nbsp;</td><td>The linear form of P </td></tr>
    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>The canonical permutation used to compute its linear form into Q </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>the linear form Q of the permutation P. </dd></dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="group__gdsl__perm.html#gd015b546ff3bad397617661869a1fcfb">gdsl_perm_linear_to_canonical()</a> </dd></dl>
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<a class="anchor" name="gefadbcc1a7b7182da1f54f7d10db3d2b"></a><!-- doxytag: member="gdsl_perm.h::gdsl_perm_inverse" ref="gefadbcc1a7b7182da1f54f7d10db3d2b" args="(gdsl_perm_t P)" --><p>
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          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a> gdsl_perm_inverse           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname1" valign="top" nowrap> <em>P</em>          </td>
          <td class="md" valign="top">&nbsp;)&nbsp;</td>
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<p>
Inverse in place a permutation. 
<p>
<dl compact><dt><b>Note:</b></dt><dd>Complexity: O( |P| ) </dd></dl>
<dl compact><dt><b>Precondition:</b></dt><dd>P must be a valid gdsl_perm_t </dd></dl>
<dl compact><dt><b>Parameters:</b></dt><dd>
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    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>The permutation to invert </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>the inverse permutation of P in case of success. <p>
NULL in case of insufficient memory. </dd></dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="group__gdsl__perm.html#g1db013c30cc84b004344fd1269614845">gdsl_perm_reverse()</a> </dd></dl>
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<a class="anchor" name="g1db013c30cc84b004344fd1269614845"></a><!-- doxytag: member="gdsl_perm.h::gdsl_perm_reverse" ref="g1db013c30cc84b004344fd1269614845" args="(gdsl_perm_t P)" --><p>
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          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a> gdsl_perm_reverse           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname1" valign="top" nowrap> <em>P</em>          </td>
          <td class="md" valign="top">&nbsp;)&nbsp;</td>
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<p>
Reverse in place a permutation. 
<p>
<dl compact><dt><b>Note:</b></dt><dd>Complexity: O( |P| / 2 ) </dd></dl>
<dl compact><dt><b>Precondition:</b></dt><dd>P must be a valid gdsl_perm_t </dd></dl>
<dl compact><dt><b>Parameters:</b></dt><dd>
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    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>The permutation to reverse </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>the mirror image of the permutation P </dd></dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="group__gdsl__perm.html#gefadbcc1a7b7182da1f54f7d10db3d2b">gdsl_perm_inverse()</a> </dd></dl>
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<a class="anchor" name="ge98151cfcded6cf6d4a66374db5c4714"></a><!-- doxytag: member="gdsl_perm.h::gdsl_perm_randomize" ref="ge98151cfcded6cf6d4a66374db5c4714" args="(gdsl_perm_t P)" --><p>
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          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a> gdsl_perm_randomize           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname1" valign="top" nowrap> <em>P</em>          </td>
          <td class="md" valign="top">&nbsp;)&nbsp;</td>
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<p>
Randomize a permutation. 
<p>
The permutation P is randomized in an efficient way, using inversions array.<p>
<dl compact><dt><b>Note:</b></dt><dd>Complexity: O( |P| ) </dd></dl>
<dl compact><dt><b>Precondition:</b></dt><dd>P must be a valid gdsl_perm_t </dd></dl>
<dl compact><dt><b>Parameters:</b></dt><dd>
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    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>The permutation to randomize </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>the mirror image ~P of the permutation of P in case of success. <p>
NULL in case of insufficient memory. </dd></dl>
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<a class="anchor" name="gf03dc9a6539bf9dca426858db7f55b51"></a><!-- doxytag: member="gdsl_perm.h::gdsl_perm_apply_on_array" ref="gf03dc9a6539bf9dca426858db7f55b51" args="(gdsl_element_t *V, const gdsl_perm_t P)" --><p>
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          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__types.html#g0e2b9d7fb5ca9e6d50100e5d9e4bcae7">gdsl_element_t</a>* gdsl_perm_apply_on_array           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="group__gdsl__types.html#g0e2b9d7fb5ca9e6d50100e5d9e4bcae7">gdsl_element_t</a> *&nbsp;</td>
          <td class="mdname" nowrap> <em>V</em>, </td>
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          <td class="md"></td>
          <td class="md" nowrap>const <a class="el" href="group__gdsl__perm.html#gd6fc9c69f61c5703242070522910bea8">gdsl_perm_t</a>&nbsp;</td>
          <td class="mdname" nowrap> <em>P</em></td>
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          <td class="md">)&nbsp;</td>
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