Birthday Paradox

This amount of code just print out the probability that at least two persons in a room have the same birthday. This was code in Python.

p=1.0
for x in range(1,42):
  if x == 1:
    print "   N P(%)"
  print "  %2d %2.2f%%" % (x,100*(1-p))
  p = (365-x)*p/365

The output is:

   N P(%)
   1 0.00%
   2 0.27%
   3 0.82%
   4 1.64%
   5 2.71%
   6 4.05%
   7 5.62%
   8 7.43%
   9 9.46%
  10 11.69%
  11 14.11%
  12 16.70%
  13 19.44%
  14 22.31%
  15 25.29%
  16 28.36%
  17 31.50%
  18 34.69%
  19 37.91%
  20 41.14%
  21 44.37%
  22 47.57%
  23 50.73%
  24 53.83%
  25 56.87%
  26 59.82%
  27 62.69%
  28 65.45%
  29 68.10%
  30 70.63%
  31 73.05%
  32 75.33%
  33 77.50%
  34 79.53%
  35 81.44%
  36 83.22%
  37 84.87%
  38 86.41%
  39 87.82%
  40 89.12%
  41 90.32%

Makefile of resource shared among distributed process

Sometimes you need to start a batch process from several machines. One possible scenario may have a common resource, such as a library, that need to be built, and is placed in a common directory. If no care is taken, all process may start to build and write at the same file, causing corruption.

For such scenarios, a special Makefile need to handle multiple access to the resource. The target employs lockfile command to create a lock variable and prevent other process to start the compilation. Once the lock is acquired, the makefile calls itself recursively, now with a flag (called PROTECTED) set. The rule will be checked again, but now it will actually build the library or file, if it not updated.

If it was updated, it won't compile again. This happen when a process check the file need to be built, but other process already get the lock. Once the lock is released, it won't need to build the process again.

The sample Makefile showed bellow try to build the out out_file from the source_file (what a lack of creativity!).

# This makefile that generate one resouce in paralellal mode.
# the out_file is the target. First, the makefile verify if it
# is running protected, by consulting a PROTECTED variable.
# If not, it will create a lock file, and call itself with
# protected flag on, once it aquired the lock. As it call the 
# Makefile again, the rule will be checked if the resource 
# has already been created. So, the shared resource between
# process running the makefile will only be created once!
#
MAKEFILE=./Makefile

ifeq ($(PROTECTED),YES)
else
all: out_file
 @echo "Makefile $(MAKE_NUM) done!"
endif


out_file: source_file
ifeq ($(PROTECTED),YES)
 @echo "Creating out_file"
 @rm -f out_file
 @sleep 3
 @touch out_file
else
 @lockfile make.lock
 @echo "Enter Critical Section"
 @$(MAKE) -f $(MAKEFILE)  PROTECTED=YES 
 @echo "Leave Critical Section"
 @rm -f make.lock
endif

Perl and Unicode

#!/usr/bin/env perl
#
use strict;
use charnames ':full';
use utf8;

# First, let's print the source code.
open THIS, $0;
print $_ while (<THIS>);

# Get the vector elements sum. We use the Sigma greek letter.
sub Σ
{
    my ($accum) = shift;
    
    foreach(@_)
    {
      $accum += $_;  
    }
    return $accum;
}

# My Day is done!
# But Gauss would do it better!
# We can see that perl allows any
# Alphabet caracter to be used, but any symbol
# is reserverd. This is the case of integral symbols
# ∫, ∬, ∭, ∮, ∯, ∰, ∳, ∲. and even the Summantion sign ∑
# Note that this is not the greek sigma letter. Perl is smart, hum?

my @Ϯ = 1 .. 100; 
my $ΔU = Σ @Ϯ;  # Σ is not ∑. (Sigma and summantion sign).

print "The Summation from one to a handred is $ΔU.\n";

# Energy Funcion Ψ. 
# It goes from ± a radius around
# the center.
sub Ψ
{
    my ($α,$β,$γ) = @_[0..2];
    return  $α**2 + $β**2 + $γ**2;
}



# My runic letter Gar
my $ᚸ = Ψ(2.3, 234.0, 23.4);

# Listing day in Japanese, from Sunday to Saturday
my @Ա = qw/㈰ ㈪ ㈫ ㈬ ㈭ ㈮ ㈯/;

# A dictionary.
my %Ծ = 
(
    "㈰" => ["Sun", "Sunday"],
    "㈪"  => ["Moon", "Monday"],
    "㈫ " => ["Fire", "Tuesday"],
    "㈬"  => ["Water", "Wednesday"],
    "㈭"  => ["Wood", "Thursday"],
    "㈮"  => ["Metal", "Friday"],
    "㈯"  => ["Earth", "Saturday"],
);


# Now, lets print the sign for Astrological sign.

my $signs = join ", ", map { chr(ord("♈") + $_ - 1) } 1..12;

print "This is a list with the signs $signs.\n";

foreach my $Ʃ (@Ա)
{
    print "$Ʃ is the Japanese symbol for $Ծ{$Ʃ}->[0] element, also  $Ծ{$Ʃ}->[1] week\'s day.\n";
}

String character permutation.

 
/* 
 * File:   heap.c
 * Author: cassius
 *
 * Created on 19 de Novembro de 2006, 22:27
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>



static void print_recursive(char* str, int pos, int length)
{
    int k;
    char first, current;
    
    if(pos >= (length-1) )
        fprintf(stdout, "%s ", str);
    else 
    {
        first = str[pos];
    
        for(k = pos; k < length; k++) 
        {
            /* swap chars */
            current = str[k];
            str[pos] = current;
            str[k] = first;
        
            print_recursive(str, pos + 1, length);
            /* swap it back. */
            str[k] = current;
        }
        str[pos] = first;
    }
}

void print(char* str) 
{
    int len = strlen(str);
    
    print_recursive(str, 0, len);
    fprintf(stdout, ".\n");
}


/*
 * 
 */
int
main(int argc, char** argv) {
    char max_str[100];
    fprintf(stdout, "Please, digite a word.\n");
    
    fscanf(stdin, "%s ", max_str);
    
    print(max_str);
    fprintf(stdout, "Exiting ...");
    
    return (EXIT_SUCCESS);
}

ANSI C Conditional operator grammar analysis.

A friend I meet at C language lists send me a question about compiling problems with
the conditional operator.

These lines:
int main(){
int a = 10 , b ;
a >= 5 ? b =100: b=200;
}

Did not compile or give a warning, depending on the compiler, of course. But with a little change:


int main(){
int a = 10 , b ;
a >= 5 ? b =100: (b=200);
}

The warnings/erros stoped. The question is why?

Well, before start, I change the code a little ...

int main(){
int a = 10 , b ;
a >= 5
? b =100
: b=200;
}

... and a compile it again (with lcc-wi32). The error where related to the last assignment.

By that time, I was aware that I would need to search for the grammar definition of this operator. In the absence of a ANSI C spec, I search the "The ANSI C Language", Kernighan & Ritchie, whose had an Appendix with ANSI C grammar and comments.

Section A.7.16 the grammar defines the conditional operator as:

conditional-expression:
logical-OR-expression
logical-OR-expression ? expression : conditional-expression

Hum, the third argument is not an expression. It is in fact, redefined as a conditional expression. Probably, in order to allow chained use. Following the definitions, the parser will end to an primary-expression. The primary expression will the resolve, as the a is an identifier.

The compiler will evaluate this as an conditional expression:
a >= 5 ? b =100: b
And, will encounter the assignment and will interpreter this as an attempt to change
the conditional-expression result. Witch is invalid of course. Or, something like that:

(a >= 5 ? b =100: b) = 200;

I tried it in my compiler, and it returned the same error.

Okay, but and about the second try? Why it works? Simple: As the parenthesis are around, it will force the expression b = 200 to be evaluated first.


About the C grammar, you can find it also at the internet at the site http://www.lysator.liu.se/c/ANSI-C-grammar-y.html#conditional-expression, as a YACC grammar definition file. Starting from the beginning of the conditional expression, we have:

conditional_expression -> logical_or_expression -> logical_and_expression -> inclusive_or_expression -> exclusive_or_expression -> and_expression -> equality_expression -> relational_expression -> shift_expression -> additive_expression -> multiplicative_expression -> cast_expression -> unary_expression -> postfix_expression -> primary_expression and finally the IDENTIFIER. At the example give above, it will be the 'b'.

Scrambling a sorted array.

/* 
 * File:   newmain.c
 * Author: cassius
 *
 * Created on 15 de Novembro de 2006, 13:22
 */

#include <stdio.h>
#include <stdlib.h>

const char ptr[] ="string";

typedef struct
{
const char *c;
int i;
}test_struct;

test_struct s={ptr,10};


/* Only to take control of it */
#define DEFAULT_ARRAY_SIZE 10
#define MAX_ARRAY_PERMITED_SIZE 1024

/*
 * 
 */
int
main(int argc, char** argv) {
    int *array = NULL;
    int k = 0;
    int length = DEFAULT_ARRAY_SIZE;
    int arg_pos = 1;
    double n;
    
    /* If you want to force the same resoults, use -seed num to set a seed
     to the pseudo random sequence.
     */
    while(arg_pos < argc) {
        if( (strcmp(argv[arg_pos],"--seed") == 0) && (argc - arg_pos >= 2 ) ) {
            int seed;
            
            arg_pos++;
            seed = atoi(argv[arg_pos]);
            srand(seed);
        } else if( (strcmp(argv[arg_pos],"--length") == 0) && (argc - arg_pos >= 2 ) ) {
            int user_length;
            arg_pos++;
            user_length = atoi(argv[arg_pos]);
            if( (user_length < 1) || (user_length > MAX_ARRAY_PERMITED_SIZE ) )
                fprintf(stdout, "Invalid length. Assuming default value of %d.\n",length);
            else
                length = user_length;
           
        }
        arg_pos++; /* bypass argment name or last args processed */
    }
    
    /* Suppouse we use only 100 positons, for now */
    array = (int*)malloc(sizeof(int)*length);
    
    if(array == NULL)
    {
        fprintf(stderr, "No memory could be allocated. Exiting... ");
        return (EXIT_FAILURE);
    }
    
    for(k = 0; k < length; k++ )
        array[k] = k;
    
    /* Now, scramble the array. The process is simple. The k variable points to 
    the end of the array. We choose randomically between all positions bellow
    k. This position must be swapped with k. And the process goes on until
    the the start of the array.
    Warning: Although */
     
    
    for(k = (length-1); k > 0;k-- )
    {
        int temp_int = array[k];
        int old_pos = rand() % k;
        
        array[k] = array[old_pos];
        array[old_pos] = temp_int;
    }
    
    /* Print the array. */
    
    fprintf(stdout, "[");
    for(k = 0; k < length; k++)
    {
        char term = k == (length -1) ? ']' : ',';
        
        fprintf(stdout, "%d%c",array[k],term);
    }
    fprintf(stdout, "\n");

    return (EXIT_SUCCESS);
}