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A207324: Sequencer program based on the SJT algorithm (C)

algorithmuscanorj
Dec 28th, 2012
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  1. /*
  2.  * SeaDragon 0.91 - A sequencer program for A207324 at oeis.org
  3.  *
  4.  * 2012 Sept. R.J. Cano <aallggoorriitthhmmuuss@gmail.com>
  5.  *
  6.  * This program was devised and written for documentation purposes and is
  7.  * subject to the terms of use of the On Line Encyclopedia Of Integer Sequences.
  8.  *
  9.  *
  10.  * Changes:
  11.  *
  12.  *  This update has no leaks at all, and  runs a litte bit faster than older versions.
  13.  *
  14.  * About A055998 and the memory leaks present in older versions of this code:
  15.  *
  16.  * The counting of memory blocks leaked by missed calls to free(), a bug already fixed for
  17.  * the present version of this program, behaved as an arithmetical progession documented
  18.  * in oeis.org as the A055998 sequence adding 2 in each one of its terms. Such +2 addition
  19.  * was caused by an implementation mistake of the author. The actual counting is the shown
  20.  * by A055998. Also, the leaks were caused by a forgotten "memory release instruction",
  21.  * omited by the author when translating his pseudocode interpretation of the SJT Algorithm
  22.  * into a C program. There is no design errors neither in the SJT Algorithm nor in the
  23.  * operational interpretation made of it.
  24.  *
  25.  * Hints:
  26.  *
  27.  *  For authors and contributors about C programs:
  28.  *
  29.  *      It is suggested when compiling C programs verify if it's written in an
  30.  *      acceptable way using a command like: "gcc -O2 -W -Wall my_oeis_program.c"
  31.  *
  32.  *  (Thanks to: Joerg Arndt)
  33.  *
  34.  *
  35.  */
  36.  
  37. #include <stdio.h>
  38. #include <stdlib.h>
  39.  
  40. /*---------> non-standard datatype definitions <-----------------------------------------------------------*/
  41.  
  42. typedef struct matrix_linear_stack {
  43.  
  44.   long integer_value;
  45.   struct matrix_linear_stack *arrow;
  46.  
  47. } matrix_linear_stack;
  48.  
  49.  
  50. /*---------> non-standard constant values definition <------------------------------------------------------*/
  51.  
  52.  const long __mode_ZERO = 0;
  53.  const long __mode_EQUAL = 1;
  54.  const long __mode_DETERMINANT = 2;
  55.  const long __TOKEN_TEMPLATE   = 0;
  56.  const long __UNIT    = 1;
  57.  long generator_settings = 0;
  58.  long __config_generator[3][2];
  59.  
  60. /*---------> Suitable globals <-----------------------------------------------------------------------------*/
  61.  
  62. matrix_linear_stack *__the_ring_stckPointerReference_HEAD, *__the_ring_stckPointerReference_TAIL;
  63.  
  64. // About the ring:
  65. // Warning: After calling close__the_ring() a first time, don't call it again before a call to open_the_ring() of course
  66. // for the same parameter list (Else it would have possible harmful and unpredictible consequences).
  67.  
  68. /*---------> non-standards called by main(); <-----------------------------------------------------*/
  69.  
  70. void configure_modes(void);
  71.  
  72. void runSequencer(int, long);
  73.  
  74. /*---------> non-standards called by others; <-----------------------------------------------------*/
  75.  
  76. void finalizer_matrix(matrix_linear_stack **, matrix_linear_stack**);
  77.  
  78. void print_matrix(matrix_linear_stack **);
  79.  
  80. void apply_SteinhausJohnsonTrotterAlgorithm(matrix_linear_stack**, matrix_linear_stack**, long);
  81.  
  82. void mode_matrix_waterfall(void);
  83.  
  84. matrix_linear_stack* generate_square_matrix(matrix_linear_stack**, matrix_linear_stack**, matrix_linear_stack**, matrix_linear_stack**, long);
  85.  
  86. void initializer_matrix(matrix_linear_stack **, matrix_linear_stack**);
  87.  
  88. matrix_linear_stack* extract_first_nodes(matrix_linear_stack**, matrix_linear_stack**, long);
  89.  
  90. void concat_matrices_node_by_node(matrix_linear_stack**, matrix_linear_stack**, matrix_linear_stack**);
  91.  
  92. /*---------> additional non-standards (some of them called by more than one function); <-----------------------------------------------------*/
  93.  
  94. long only_initialized(matrix_linear_stack**);
  95.  
  96. long absolute_value(long);
  97.  
  98. matrix_linear_stack* insert_new_node(long, matrix_linear_stack**);
  99.  
  100. void close__the_ring(matrix_linear_stack**, matrix_linear_stack**);
  101.  
  102. void open_the_ring(matrix_linear_stack**, matrix_linear_stack**);
  103.  
  104. long LeibnitzLaplaceSignature(long);
  105.  
  106. /*------------------------------------------------------------------------------------------------------------------------------*/
  107.  
  108. int main(void) {
  109.  
  110.   int j, _OScurrentExecutionFeedbackCode = EXIT_SUCCESS;
  111.   long N;
  112.  
  113.   configure_modes(); // Don't change this, it is for initialization.
  114.  
  115.   printf("%s%s","\n\nDemonstration program: ", "\n\n\tShould be run the sequencer only for a particular SJT-array? (1=yes, 0=No) ");  
  116.   scanf("%i", &j);
  117.   getchar();  
  118.   printf("%s","\n\n\tWhich is the upper size? (try first 1-11 on 32-bit machines): ");
  119.   scanf("%li", &N);
  120.   getchar();
  121.  
  122.   runSequencer(j, N);
  123.  
  124.   return _OScurrentExecutionFeedbackCode;
  125.  
  126. }
  127.  
  128. /*------------------------------------------------------------------------------------------------------------------------------*/
  129.  
  130. void configure_modes(void) {
  131.  
  132.   __config_generator[__mode_ZERO][__TOKEN_TEMPLATE] = 0;
  133.   __config_generator[__mode_ZERO][__UNIT]  = 0;
  134.  
  135.   __config_generator[__mode_EQUAL][__TOKEN_TEMPLATE] = 0;
  136.   __config_generator[__mode_EQUAL][__UNIT]  = 1;
  137.  
  138.   __config_generator[__mode_DETERMINANT][__TOKEN_TEMPLATE] = 1;
  139.   __config_generator[__mode_DETERMINANT][__UNIT]  = 0;
  140.  
  141. }
  142.  
  143. /*------------------------------------------------------------------------------------------------------------------------------*/
  144.  
  145. void runSequencer(int just_for_the_Nth_array, long N) {
  146.  
  147.   long k;
  148.  
  149.   matrix_linear_stack *J0_head, *J0_tail;
  150.  
  151.   for (k=(just_for_the_Nth_array ? N : 1);k<=N;k++) {
  152.     apply_SteinhausJohnsonTrotterAlgorithm(&J0_head, &J0_tail, k);
  153.     print_matrix(&J0_head);
  154.     finalizer_matrix(&J0_head, &J0_tail);
  155.   }
  156.  
  157.   printf("\n\n\tSequencer execution completed successfully.\n");    
  158.  
  159. }
  160.  
  161. /*------------------------------------------------------------------------------------------------------------------------------*/
  162.  
  163. void finalizer_matrix(matrix_linear_stack **stckPointerReference_HEAD, matrix_linear_stack **stckPointerReference_TAIL) {
  164.  
  165.   while (*stckPointerReference_HEAD != NULL) {
  166.  
  167.     (*stckPointerReference_TAIL) = (*stckPointerReference_HEAD);
  168.    
  169.     (*stckPointerReference_HEAD) = (*stckPointerReference_HEAD)->arrow;
  170.    
  171.     free( *stckPointerReference_TAIL );
  172.  
  173.   }
  174.  
  175.     (*stckPointerReference_TAIL) = NULL;
  176.  
  177. }
  178.  
  179. /*------------------------------------------------------------------------------------------------------------------------------*/
  180.  
  181. void print_matrix(matrix_linear_stack **stckPointerReference_HEAD) {
  182.  
  183.   matrix_linear_stack* focus= *stckPointerReference_HEAD;
  184.  
  185.   if ( NULL == focus ) {
  186.  
  187.     printf(" Not initialized! ");
  188.  
  189.   } else {
  190.  
  191.     if ( -1 == (focus->integer_value) ) {
  192.  
  193.       focus = (*stckPointerReference_HEAD)->arrow;
  194.  
  195.       if ( NULL == focus ) {
  196.  
  197.     printf(" initialized but empty. ");
  198.  
  199.       } else {;}
  200.  
  201.     } else {
  202.  
  203.     }
  204.  
  205.     while ( NULL != focus ) {
  206.  
  207.       printf("\n%li", (focus->integer_value) );
  208.  
  209.       focus = focus->arrow;
  210.     }
  211.  
  212.   }
  213.  
  214. }
  215.  
  216. /*------------------------------------------------------------------------------------------------------------------------------*/
  217.  
  218. void apply_SteinhausJohnsonTrotterAlgorithm(matrix_linear_stack **J_head, matrix_linear_stack **J_tail, long _SIZE) {
  219.  
  220.   matrix_linear_stack *JJ_head;
  221.   matrix_linear_stack *JJ_tail;
  222.   matrix_linear_stack *P_head;
  223.   matrix_linear_stack *P_tail;
  224.   matrix_linear_stack *Q_head;
  225.   matrix_linear_stack *Q_tail;
  226.  
  227.   long diagonal;
  228.  
  229.   long _CASE = 1;
  230.  
  231.   mode_matrix_waterfall();
  232.  
  233.   initializer_matrix(J_head, J_tail);
  234.   insert_new_node(1, J_tail);
  235.  
  236.   while (_CASE < _SIZE) {
  237.  
  238.     _CASE++;
  239.     diagonal = -1;
  240.     initializer_matrix(&JJ_head, &JJ_tail);
  241.  
  242.     while ( !only_initialized(J_head) ) {
  243.  
  244.       P_head = extract_first_nodes(J_head, &P_tail, (_CASE-1)) ;
  245.       generate_square_matrix(&P_head, &P_tail, &Q_head, &Q_tail, _CASE*diagonal);
  246.       concat_matrices_node_by_node(&JJ_tail, &Q_head, &Q_tail);
  247.       finalizer_matrix(&P_head, &P_tail);
  248.  
  249.       diagonal *= -1;
  250.  
  251.     }
  252.  
  253.     finalizer_matrix(J_head, J_tail);
  254.     *J_head = JJ_head;
  255.     *J_tail   = JJ_tail;
  256.     JJ_head = NULL;
  257.     JJ_tail   = NULL;
  258.  
  259.   }
  260.  
  261. }
  262.  
  263. /*------------------------------------------------------------------------------------------------------------------------------*/
  264.  
  265. void  mode_matrix_waterfall(void) {
  266.  
  267.   generator_settings = __mode_DETERMINANT;
  268.  
  269. }
  270.  
  271. /*------------------------------------------------------------------------------------------------------------------------------*/
  272.  
  273. matrix_linear_stack* generate_square_matrix(matrix_linear_stack **baseRef_head, matrix_linear_stack **baseRef_tail, matrix_linear_stack **ref_answer_head, matrix_linear_stack **ref_answer_tail, long TOKEN_TEMPLATE) {
  274.  
  275.   long counting_L = 1;
  276.   long counting_X = 1;
  277.   long counting_Y = 1;
  278.   long matrix_size = absolute_value(TOKEN_TEMPLATE);
  279.   long newValuetobeIncluded;
  280.  
  281.   matrix_linear_stack* BASE_head = *baseRef_head;
  282.   matrix_linear_stack* BASE_tail = *baseRef_tail;
  283.  
  284.   close__the_ring(&BASE_head, &BASE_tail);
  285.  
  286.   initializer_matrix(ref_answer_head, ref_answer_tail);
  287.  
  288.   matrix_size = absolute_value(TOKEN_TEMPLATE);
  289.  
  290.   while (counting_L <= (matrix_size*matrix_size)) {
  291.  
  292.     if (BASE_head->integer_value == -1) { BASE_head = BASE_head->arrow; }
  293.  
  294.     newValuetobeIncluded = (TOKEN_TEMPLATE < 0) ? ( ( counting_X + counting_Y == (matrix_size+1) ) ? (matrix_size*__config_generator[generator_settings][__TOKEN_TEMPLATE] + __config_generator[generator_settings][__UNIT]) : (0) ) : ( (counting_X - counting_Y == 0) ? (matrix_size*__config_generator[generator_settings][__TOKEN_TEMPLATE] + __config_generator[generator_settings][__UNIT]) : (0) );
  295.  
  296.     if ( ( 0 == newValuetobeIncluded ) && ( __mode_ZERO != generator_settings) ) {
  297.  
  298.       newValuetobeIncluded+= (BASE_head->integer_value);
  299.       BASE_head = BASE_head->arrow;
  300.  
  301.     }
  302.  
  303.     insert_new_node(newValuetobeIncluded, ref_answer_tail);
  304.  
  305.     counting_L++;
  306.     counting_X++;
  307.     if (counting_X > matrix_size) {
  308.       counting_X = 1;
  309.       counting_Y++;
  310.     }
  311.   }
  312.  
  313.   open_the_ring(&BASE_head, &BASE_tail);
  314.  
  315.   return (*ref_answer_head);
  316. }
  317.  
  318. /*----------------------------------------------------------------------------------------------------------------------(OJO)---*/
  319.  
  320. void initializer_matrix(matrix_linear_stack **stckPointerReference_HEAD, matrix_linear_stack **stckPointerReference_TAIL) {
  321.  
  322.   (*stckPointerReference_HEAD) = NULL;
  323.   (*stckPointerReference_TAIL) = insert_new_node( -1, stckPointerReference_HEAD );
  324.  
  325. }
  326.  
  327. /*------------------------------------------------------------------------------------------------------------------------------*/
  328.  
  329. matrix_linear_stack* extract_first_nodes(matrix_linear_stack** refSource, matrix_linear_stack** refRemainderTail, long extractions) {
  330.  
  331.   matrix_linear_stack* newRefSource= *refSource;
  332.   matrix_linear_stack* answer= (*refSource)->arrow;
  333.   matrix_linear_stack* cursor= (*refSource);
  334.   long steps= (0 == extractions) ? 1 : extractions;
  335.   long counter=0;
  336.   while (counter < steps) {
  337.     cursor= cursor->arrow;
  338.     counter++;
  339.   }
  340.   newRefSource->arrow= cursor->arrow;
  341.   cursor->arrow= NULL;
  342.   (*refRemainderTail)= cursor;
  343.   *refSource = newRefSource;
  344.  
  345.   return answer;
  346.  
  347. }
  348.  
  349. /*------------------------------------------------------------------------------------------------------------------------------*/
  350.  
  351. void concat_matrices_node_by_node(matrix_linear_stack **operand_left_tail, matrix_linear_stack **operand_right_head, matrix_linear_stack **operand_right_tail) {
  352.  
  353.   matrix_linear_stack *slayer = *operand_right_head;
  354.   *operand_right_head = NULL;
  355.   (*operand_left_tail)->arrow = slayer->arrow;
  356.   slayer->arrow               = NULL;
  357.   free(slayer);
  358.   *operand_left_tail          = *operand_right_tail;
  359.   *operand_right_tail         = NULL;
  360.  
  361. }
  362.  
  363. /*------------------------------------------------------------------------------------------------------------------------------*/
  364.  
  365. long  only_initialized(matrix_linear_stack** stckPointerReference_HEAD) {
  366.  
  367.  
  368.  
  369.   if ( 0 != ( NULL != stckPointerReference_HEAD ) ) {
  370.     if ( 0 != ( NULL != *stckPointerReference_HEAD ) ) {
  371.       if ( 0 != ( NULL == (*stckPointerReference_HEAD)->arrow ) ) {
  372.     if ( -1 == (*stckPointerReference_HEAD)->integer_value ) {
  373.       return 1;
  374.     }
  375.       }
  376.     }
  377.   }
  378.  
  379.   return 0;
  380.  
  381. }
  382.  
  383. /*------------------------------------------------------------------------------------------------------------------------------*/
  384.  
  385. long absolute_value(long argument) {
  386.  
  387.   return ( argument * LeibnitzLaplaceSignature(argument) );
  388.  
  389. }
  390.  
  391. /*------------------------------------------------------------------------------------------------------------------------------*/
  392.  
  393. matrix_linear_stack* insert_new_node(long value_assigned, matrix_linear_stack **stckPointerReference_TAIL) {
  394.  
  395.   matrix_linear_stack *focus;
  396.   matrix_linear_stack *inserto = (matrix_linear_stack *)( malloc( sizeof( matrix_linear_stack ) ) );
  397.  
  398.   matrix_linear_stack *answer_ref = inserto;
  399.   inserto->integer_value  = value_assigned;
  400.   inserto->arrow = NULL;
  401.  
  402.   if (( NULL == (*stckPointerReference_TAIL) ) && (-1 == value_assigned)) {
  403.  
  404.     (*stckPointerReference_TAIL) = inserto;
  405.  
  406.   } else if ( NULL != (*stckPointerReference_TAIL) ) {
  407.  
  408.       focus = (*stckPointerReference_TAIL);
  409.       while ( NULL != focus->arrow ) { focus = focus->arrow; }
  410.       focus->arrow = inserto;
  411.       if ( focus == (*stckPointerReference_TAIL) ) { (*stckPointerReference_TAIL) = inserto; }
  412.  
  413.   }
  414.  
  415.   return answer_ref;
  416. }
  417.  
  418. /*------------------------------------------------------------------------------------------------------------------------------*/
  419.  
  420. void close__the_ring(matrix_linear_stack** stckPointerReference_HEAD, matrix_linear_stack** stckPointerReference_TAIL) {
  421.  
  422.   __the_ring_stckPointerReference_HEAD = *stckPointerReference_HEAD;
  423.   __the_ring_stckPointerReference_TAIL   = *stckPointerReference_TAIL;
  424.   (*stckPointerReference_TAIL)->arrow = *stckPointerReference_HEAD;
  425.  
  426. }
  427.  
  428. /*------------------------------------------------------------------------------------------------------------------------------*/
  429.  
  430. void open_the_ring(matrix_linear_stack** stckPointerReference_HEAD, matrix_linear_stack** stckPointerReference_TAIL) {
  431.  
  432.   (*stckPointerReference_HEAD)       = __the_ring_stckPointerReference_HEAD;
  433.   (*stckPointerReference_TAIL)         = __the_ring_stckPointerReference_TAIL;
  434.   (*stckPointerReference_TAIL)->arrow = NULL;
  435.  
  436. }
  437.  
  438. /*------------------------------------------------------------------------------------------------------------------------------*/
  439.  
  440. long LeibnitzLaplaceSignature(long argument) {
  441.  
  442.   long answer;
  443.  
  444.   answer = (argument < 0) ? (-1) : (1) ;
  445.  
  446.   return answer;
  447.  
  448. }
  449.  
  450. /*
  451.  *
  452.  *      << If people do not believe that mathematics is simple, it is only because
  453.  *          they do not realize how complicated life is. >>
  454.  *
  455.  *                  --John von Neumann
  456.  *
  457.  */
  458.  
  459. // The end.
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