When to use which data structure!

A big question is which data structure to use and in which cases.

First, take a look at what you will be doing with the data items and ask yourself some questions:

do you need random access?
do you perform a lot of insertions? how about deletions?
do you allow duplicates?
are you searching for elements frequently?
does your data need to be ordered?
would you need to traverse the elements?
how big is your data?

these and other questions need to be considered before choosing which data structure to use. it is a good idea to start from the simplest structure to see if it satisfies your criteria. it would be a waste of time to slave over implementing a complicated structure when an array can fulfil all your needs.

//THE PROCESS

start with arrays...
arrays are a suitable structure to use when you know the size you'll need and the number of elements is reasonably small. if fast insertion is needed and you do not need to traverse the elements in a specified order, use an unordered array. however, if you need search to be fast use binary search and an ordered array. this however, will make insertion slower, so if you need fast insertion and fast search, choose another structure. deletion is always slow in any kind of an array, so if you are doing a lot of deletions, array is probably not the best structure for you to use. additionally, if you overestimate or underestimate the size of the array, you will either have to expand the array (make a new bigger array and copy all elements from original array into the new one - costly operation), or you will have wasted memory. the biggest detriment of arrays is that size must be known beforehand, as failure to do so results in slow operations or memory waste. also, deletions are always slow, regardless of whether the array is sorted or not.

when arrays are not good enough, move on to linked lists
if you need a more flexible structure that does not require you to know the size ahead of time, a linked list is a good starting point. unordered linked lists offer constant time insertion (at the end or beginning of the list) since only references are being changed and no items need to be shifted. deletion runs in O(N) time since the element we're deleting needs to be found first. this is still faster than the array because, as with insertion, no items are shifted. searching is slow in the linked list because it can only be linear. remember that binary search is not possible to use with an ordered list since we cannot access elements from the middle of the list. also, if you need random access, use arrays or hash tables; linked lists are not the structure to use since they are built on relationships and every element can only be accessed from the first node.

linked lists still not good enough, move on to binary trees
if you have looked at arrays and linked lists and decided that they are not satisfactory, a binary search tree might be what you need. it provides fast O(logN) time for all operations: search, insertion, and deletion. you can easily find the minimum and maximum value of the data, and traversal in order is possible with the use of recursion. however, trees degrade to O(N) speed when they become unbalanced. if you are sure that data will be inserted in random order, a regular binary tree might be a sufficient solution. otherwise, a red-black tree or 2-3-4 tree that retains balance would be your best choice.

the end of the line: hash tables
as we've seen in the last post, hash tables offer close to O(1) search and insertion. deletion also runs in O(1) time assuming the deleted item is simply replaced with a special flag object that the search and insertion algorithms treat as an empty cell. hash tables are very fast if the load factor is suitable: .5 or .66 for open addressing, and around 1 for separate chaining. beware though, that any sort of traversal of the elements inside the hash table is not possible. we are only able to search, insert, and delete (in the special way described earlier). hash tables are much faster than trees, but can degrade catastrophically when the load factor gets too big. since hash tables are based on arrays, it is important to have a rough idea of how many elements you would be expecting. if you cannot accurately predict the size of your elements beforehand, using the separate chaining method would be a better choice over open addressing in implementing your hash table.

//EXTERNAL STORAGE
i mentioned external storage in the post on b-trees. recall that accessing data on in external storage is much slower than access in main memory, so to increase efficiency while working with external storage we need to minimize the number of disk accesses. this happens if we increase the number of data per node, which can be done with a multi-way tree. this way, we can read in a whole block into main memory, and work from there to search for our key (supposing we are doing insertion). if the block contains 1000 data items, by fitting all these items into a single block we have reduced the number of disk accesses from 1000 to 1. this is the direction of thinking you need to be aware of while working with external storage and deciding which data structure to use.

//ABSTRACT DATA TYPES

stack:                       O(1) insertion, O(1) deletion
queue:                     O(1) insertion, O(1) deletion
priority queue:        O(N) insertion, O(1) deletion

to review, there are three types of ADTs: the stack, the queue, and the priority queue. these are interfaces and can be implemented with either an array or linked list (in the case of a priority queue, a heap can be used). the stack is a last-in-first-out data structure, and offers constant time insertion and deletion. the queue has the same efficiency, except that it is a first-in-first-out structure. priority queue is a sorted queue by priority (from greatest to lowest key) - meaning it is sorted. insertion in a priority queue runs in O(N) time, while removal is still in constant time.

//A WORD ON SORTS

                     average               worst
bubble:         O(N^2)                same
selection:      O(N^2)                same
insertion:      O(N^2)                same
shellsort:       O(N^3/2)             same
mergesort:    O(NlogN)            same                [note: requires extra memory]
quicksort:     O(NlogN)           O(N^2)

if you need to sort your data, first start with the simple sorts. insertion is the best of the O(N^2) sorts, so if you have a relatively small amount of data this sort will work fine for your needs, and is also easy to implement. if you have roughly 1,000-5,000 items (figures are estimated), insertion sort is probably not good enough and shellsort can be examined next. if you have a large data set, you can finally turn to the more complex sorting algorithms: mergesort and quicksort, which run in fastest O(NlogN) time. mergesort requires twice the amount of space as the original array, so if you are limited on memory this would not be the best choice. quicksort can then be used. however, beware of quicksort's catastrophic degradation to O(N^2) time if the items are not random. the table above summarizes these points.

Compilation stages for a C program

There are four main stages through which a source code passes in order to finally become an executable.

The four stages for a C program to become an executable are the following:

1. Pre-processing
2. Compilation
3. Assembly
4. Linking

In Part-I of this article series, we will discuss the steps that the gcc compiler goes through when a C program source code is compiled into an executable.
Before going any further, lets take a quick look on how to compile and run a ‘C’ code using gcc, using a simple hello world example.

$ vi print.c
#include <stdio.h>
#define STRING "Hello World"
int main(void)
{
/* Using a macro to print 'Hello World'*/
printf(STRING);
return 0;
}

Now, lets run gcc compiler over this source code to create the executable.

$ gcc -Wall print.c -o print

In the above command:

• gcc – Invokes the GNU C compiler
• -Wall – gcc flag that enables all warnings. -W stands for warning, and we are passing “all” to -W.
• print.c – Input C program
• -o print – Instruct C compiler to create the C executable as print. If you don’t specify -o, by default C compiler will create the executable with name a.out

Finally, execute print which will execute the C program and display hello world.

$ ./print
Hello World

Note: When you are working on a big project that contains several C program, use make utility to manage your C program compilation as we discussed earlier.
Now that we have a basic idea about how gcc is used to convert a source code into binary, we’ll review the 4 stages a C program has to go through to become an executable.

1. PRE-PROCESSING

This is the very first stage through which a source code passes. In this stage the following tasks are done:

1. Macro substitution
2. Comments are stripped off
3. Expansion of the included files

To understand preprocessing better, you can compile the above ‘print.c’ program using flag -E, which will print the preprocessed output to stdout.

$ gcc -Wall -E print.c

Even better, you can use flag ‘-save-temps’ as shown below. ‘-save-temps’ flag instructs compiler to store the temporary intermediate files used by the gcc compiler in the current directory.

$ gcc -Wall -save-temps print.c -o print

So when we compile the program print.c with -save-temps flag we get the following intermediate files in the current directory (along with the print executable)

$ ls
print.i
print.s
print.o

The preprocessed output is stored in the temporary file that has the extension .i (i.e ‘print.i’ in this example)
Now, lets open print.i file and view the content.

$ vi print.i
......
......
......
......
# 846 "/usr/include/stdio.h" 3 4
extern FILE *popen (__const char *__command, __const char *__modes) ;
extern int pclose (FILE *__stream);
extern char *ctermid (char *__s) __attribute__ ((__nothrow__));

# 886 "/usr/include/stdio.h" 3 4
extern void flockfile (FILE *__stream) __attribute__ ((__nothrow__));
extern int ftrylockfile (FILE *__stream) __attribute__ ((__nothrow__)) ;
extern void funlockfile (FILE *__stream) __attribute__ ((__nothrow__));

# 916 "/usr/include/stdio.h" 3 4
# 2 "print.c" 2

int main(void)
{
printf("Hello World");
return 0;
}

In the above output, you can see that the source file is now filled with lots and lots of information, but still at the end of it we can see the lines of code written by us. Lets analyze on these lines of code first.

1. The first observation is that the argument to printf() now contains directly the string “Hello World” rather than the macro. In fact the macro definition and usage has completely disappeared. This proves the first task that all the macros are expanded in the preprocessing stage.
2. The second observation is that the comment that we wrote in our original code is not there. This proves that all the comments are stripped off.
3. The third observation is that beside the line ‘#include’ is missing and instead of that we see whole lot of code in its place. So its safe to conclude that stdio.h has been expanded and literally included in our source file. Hence we understand how the compiler is able to see the declaration of printf() function.

When I searched print.i file, I found, The function printf is declared as:

extern int printf (__const char *__restrict __format, ...);

The keyword ‘extern’ tells that the function printf() is not defined here. It is external to this file. We will later see how gcc gets to the definition of printf().
You can use gdb to debug your c programs. Now that we have a decent understanding on what happens during the preprocessing stage. let us move on to the next stage.

2. COMPILING

After the compiler is done with the pre-processor stage. The next step is to take print.i as input, compile it and produce an intermediate compiled output. The output file for this stage is ‘print.s’. The output present in print.s is assembly level instructions.
Open the print.s file in an editor and view the content.

$ vi print.s
.file "print.c"
.section .rodata
.LC0:
.string "Hello World"
.text
.globl main
.type main, @function
main:
.LFB0:
.cfi_startproc
pushq %rbp
.cfi_def_cfa_offset 16
movq %rsp, %rbp
.cfi_offset 6, -16
.cfi_def_cfa_register 6
movl $.LC0, %eax
movq %rax, %rdi
movl $0, %eax
call printf
movl $0, %eax
leave
ret
.cfi_endproc
.LFE0:
.size main, .-main
.ident "GCC: (Ubuntu 4.4.3-4ubuntu5) 4.4.3"
.section .note.GNU-stack,"",@progbits

Though I am not much into assembly level programming but a quick look concludes that this assembly level output is in some form of instructions which the assembler can understand and convert it into machine level language.

3. ASSEMBLY

At this stage the print.s file is taken as an input and an intermediate file print.o is produced. This file is also known as the object file.
This file is produced by the assembler that understands and converts a ‘.s’ file with assembly instructions into a ‘.o’ object file which contains machine level instructions. At this stage only the existing code is converted into machine language, the function calls like printf() are not resolved.
Since the output of this stage is a machine level file (print.o). So we cannot view the content of it. If you still try to open the print.o and view it, you’ll see something that is totally not readable.

$ vi print.o
^?ELF^B^A^A^@^@^@^@^@^@^@^@^@^A^@>^@^A^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@0^
^@UH<89>å¸^@^@^@^@H<89>ǸHello World^@^@GCC: (Ubuntu 4.4.3-4ubuntu5) 4.4.3^@^
T^@^@^@^@^@^@^@^AzR^@^Ax^P^A^[^L^G^H<90>^A^@^@^\^@^@]^@^@^@^@A^N^PC<86>^B^M^F
^@^@^@^@^@^@^@^@.symtab^@.strtab^@.shstrtab^@.rela.text^@.data^@.bss^@.rodata
^@.comment^@.note.GNU-stack^@.rela.eh_frame^@^@^@^@^@^@^@^@^@^@^@^
...
...
…

The only thing we can explain by looking at the print.o file is about the string ELF.
ELF stands for executable and linkable format.
This is a relatively new format for machine level object files and executable that are produced by gcc. Prior to this, a format known as a.out was used. ELF is said to be more sophisticated format than a.out (We might dig deeper into the ELF format in some other future article).
Note: If you compile your code without specifying the name of the output file, the output file produced has name ‘a.out’ but the format now have changed to ELF. It is just that the default executable file name remains the same.

4. LINKING

This is the final stage at which all the linking of function calls with their definitions are done. As discussed earlier, till this stage gcc doesn’t know about the definition of functions like printf(). Until the compiler knows exactly where all of these functions are implemented, it simply uses a place-holder for the function call. It is at this stage, the definition of printf() is resolved and the actual address of the function printf() is plugged in.
The linker comes into action at this stage and does this task.
The linker also does some extra work; it combines some extra code to our program that is required when the program starts and when the program ends. For example, there is code which is standard for setting up the running environment like passing command line arguments, passing environment variables to every program. Similarly some standard code that is required to return the return value of the program to the system.
The above tasks of the compiler can be verified by a small experiment. Since now we already know that the linker converts .o file (print.o) to an executable file (print).
So if we compare the file sizes of both the print.o and print file, we’ll see the difference.

$ size print.o
   text    data     bss     dec     hex filename
     97       0       0      97      61 print.o 

$ size print
   text    data     bss     dec     hex filename
   1181     520      16    1717     6b5 print

Through the size command we get a rough idea about how the size of the output file increases from an object file to an executable file. This is all because of that extra standard code that linker combines with our program.

C Program Compilation Steps

You compile c program and get executables. Have you ever wondered what happens during compilation process and how c program gets converted to executable?
In this module we will learn what are the stages involved in c program compilation using gcc on Linux.
Normally C program building process involves four stages to get executable (.exe)

1. Preprocessing 
2. Compilation
3. Assembly 
4. Linking  

The following Figure shows the steps involved in the process of building the C program starting from the preprocessing until the loading of the executable image into the memory for program running.

Compilation with gcc with different options

-E            Preprocess only; do not compile, assemble or link
-S            Compile only; do not assemble or link
-c            Compile and assemble, but do not link
-o  <file>  Place the output into <file>

 We will use below hello.c program to expain all the 4 phases

#include<stdio.h>        //Line 1 #define MAX_AGE  21   //Line 2 int main() {  printf( "Maximum age : %d ",MAX_AGE); //Line 5 }

1. Preprocessing

This is the very first stage through which a source code passes. In this stage the following tasks are done:

1. Macro substitution
2. Comments are stripped off
3. Expansion of the included files

To understand preprocessing better, you can compile the above ‘hello.c’ program using flag –E with gcc. This will generate the preprocessed hello.i
Example:
>gcc  -E hello.c  -o hello.i
//hello.i file content

# 1 "hello.c" # 1 "<built-in>" # 1 "<command-line>" # 1 "hello.c" # 1 "/usr/include/stdio.h" 1 3 4 # 28 "/usr/include/stdio.h" 3 4 ………… ………… Truncated some text… ……… ……… extern void funlockfile (FILE *__stream) __attribute__ ((__nothrow__)); # 918 "/usr/include/stdio.h" 3 4   # 2 "hello.c" 2   int main() {  printf( "Maximum age : %d ",21); }

In above code (hello.i) you can see macros are substituted with its value (MA_AGE with 21 in printf statement), comments are stripped off (//Line 1, //Line 2 and //Line 5)and libraries are expanded(<stdio.h>)

2. Compilation

Compilation is the second pass. It takes the output of the preprocessor (hello.i) and generates assembler source code (hello.s)
> gcc -S hello.i  -o hello.s
//hello.s file content

.file   "hello.c"         .section        .rodata .LC0:         .string "Maximum age : %d "         .text .globl main         .type   main, @function main: .LFB0:         .cfi_startproc         pushq   %rbp         .cfi_def_cfa_offset 16         movq    %rsp, %rbp         .cfi_offset 6, -16         .cfi_def_cfa_register 6         movl    $.LC0, %eax         movl    $21, %esi         movq    %rax, %rdi         movl    $0, %eax         call    printf         leave         .cfi_def_cfa 7, 8         ret         .cfi_endproc .LFE0:         .size   main, .-main         .ident  "GCC: (GNU) 4.4.2 20091027 (Red Hat 4.4.2-7)"         .section        .note.GNU-stack,"",@progbits

Above code is assembly code which assembler can understand and generate machine code.

3. Assembly

Assembly is the third stage of compilation. It takes the assembly source code (hello.s) and produces an assembly listing with offsets. The assembler output is stored in an object file (hello.o)
>gcc -c hello.s -o hello.o
Since the output of this stage is a machine level file (hello.o). So we cannot view the content of it. If you still try to open the hello.o and view it, you’ll see something that is totally not readable
//hello.o file content

^?ELF^B^A^A^@^@^@^@^@^@^@^@^@^A^@>^@^A^@^@^@^@^@^@^@^@^@^@^@^@^ @^@^@^@^@^@^@@^A^@^@^@^@^@^@^@^@^@^@@^@^@^@^@^@@^@^M^@^@UH<89>å¸ ^@^@^@^@¾^U^@^@^@H<89>ç¸^@^@^@^@è^@^@^@^@éã^@^@^@Maximum age :%d  ^@^@GCC:GNU)4.4.220091027(RedHat4.4.2-7)^@^@^T^@^@^@^@^@^@^@^AzR^ @^Ax^P^A^[^L^G^H<90>^A^@^@^\^@^@^@^\^@^@^@^@^@^@^@^]^@^@^@^@A^N^PC <86>^B^M^FX^L^G^H^@^@^@^@.symtab^@.strtab^@.shstrtab^@.rela.text^@ .data^@.bss^@.rodata^@.comment^@.note.GNU-stack^@.rela.eh_frame^@ ^@^@^@^@^@^@^@^@^@^@^

By looking at above code only thing we can explain is ELF (executable and linkable format). This is a relatively new format for machine level object files and executable that are produced by gcc.

4. Linking  

Linking is the final stage of compilation. It takes one or more object files or libraries as input and combines them to produce a single executable file (hello.exe). In doing so, it resolves references to external symbols, assigns final addresses to procedures/functions and variables, and revises code and data to reflect new addresses (a process called relocation).
> gcc hello.o -o hello
./hello
Maximum age : 21

Now you know c program compilation steps (Preprocessing, Compiling, Assembly, and Linking). There is lot more things to explain in liking phase.