A person from the thirteenth century, named Leonardo Pisano, known as Fibonacci depicted the following problem in his book Liber abaci: In an island two rabbits are placed. Two rabbits can reproduce after they are two months old. First two months there are one pair of rabbits, they reproduce after 2 months and produce another pair. The new born pair does not reproduce until they are 2 months old, the older pair produces another pair on the 4^{th} month. Reproducing like this how many pairs of rabbits would be there in the island after n months, under the condition no rabbits die. The Fibonacci series is where each represents the number of rabbit pairs in the island on month n.

In this post we will see the obvious recursive solution, an iterative solution and a solution with which you can find the n^{th} fibonacci number directly from an equation.

Fibonacci Series

The Fibonacci numbers are shown belows:

From the origin of the Fibonacci numbers and also studying the series it is clear that each number of the series is generated from the addition of the previous two numbers. Initially the first two number of the series are 1 , and that is given. That is the first two months there are 1 pair of rabbit in the island. Continue reading “Generating Fibonacci Numbers”→

This is another quick post about an unfinished (but working) software which I wrote around 8 years ago. It is an Intel 8085 microprocessor simulator, with a text based interface. The objective was to simulate the microprocessor, along with a minimal interface which closely resembles the microprocessor kit with the 7-segment displays, hex keyboard and minimal debugging features.

Quick story

In our undergraduate computer science degree, we had a few subjects on microprocessor architecture. One of the subjects focused on the Intel 8085 microprocessor architecture in great details, Intel 8086 architecture, interfacing, etc. Along with the detailed architecture, we also had to do some assembly code for 8085. It was fun because, we had to use a physical 8085 microprocessor kit with a hex keyboard and just those 7-segment displays.

To write a code in the kit, you need to scan through the memory and enter the values of the assembled code. Who assembles it? We had to do that manually. We would have a table of all the instructions and the hex value for the op-code. More essentially it is very important to know the precise operations for each instruction. What operation it performs, which registers are accessed, what memory locations are accessed and how does it change the flags.

It gets more interesting (sometimes painful) when you first write your code in assembly in a white sheet of physical paper, then you refer the table and convert the assembly code to machine code, basically an entire page of hex values. Next, you get to your 8085 microprocessor kit, start from a memory location and keep on typing these hex values like a maniac. There were 8085 microprocessor kits which had some “debugging” facility, but essentially, if something goes wrong, it was extremely difficult to find, given our skills.

Although we were required to use the physical 8085 microprocessor kit in the exams, but for practice, we used 8085 microprocessor simulators. There are quite a few 8085 microprocessor simulators available. One of them was provided with one of the text books. There were simulators with text interface, some with text and some with nice GUI interfaces. I used one of them, the GNUSim8085. You can find an in depth review of GNUSim8085, which I wrote for OpenSource For You long ago, also posted here: Reviewing the GNUSim8085 (v1.3.7).

I personally did not like most of the simulators or the interfaces. All of them involved a lot of mouse-clicking, which slows you down a lot and does not reflect the actual 8085 trainer kit experience. There were a few which had full keyboard control, but somehow we felt that they were cumbersome. The Intel 8085 trainer kit experience was highly required inorder to timely and correctly finish the tasks given in the examination. The good thing was, I (and a few of my friends) knew exactly what I was looking for. Therefore I tried to make one … (drum roll) … Dirty8085.

In this post, I will quickly show how you can use a debugger to hack poorly written or packaged code. More specifically, how to enter a wrong password but still get access. Before proceeding, I should be clear, that this is just a demonstration, and the programs out there in production (these days) will definitely not vulnerable to this method (if it is, then it is a shitty program). This is to demonstrate how you can change the execution path as you wish.

First I will show a simple code which prompts for a password to be set, then encrypts it using MD5 sum hash and salt and stores the hash in a file. Then it asks for the same password, reads the hash from the stored file and compares if the two entered passwords are same or not. Then I will show how to reverse engineer the executable file and enter the wrong password, but still make it think that we the correct password was entered. Continue reading “Hacking (Reverse engineering): Gaining access with wrong password”→

It’s been a long time since I posted here. Therefore I decided to dig out some quick and straightforward stuffs from my disk which I previously decided should’t be in this blog.

I have posted multiple trie and dictionary search based programs in C, C++ and Perl before Jumble Work Solver and Jumble Work Solver Again. This time (again!) it’s about a trie. Although this time there was a specific requirement from a group who needed to implement a trie based word distance counting for bangla language, therefore Unicode support. This was supposed to be modified more and plugged into a spelling correction for scanned OCR text in the Bengali language.

Initially I suggested that a ternary tree would be more appropriate as the memory cost for standard trie (not compressed) would be huge. Although, finally the decision was to go with plain and simple trie. I know it is mad, but this is what it is :D.

Also, before going into the implementation, I should note that there is an efficient implementation of Radix Tree present in libcprops library. Though which we won’t be using for this one. I would recommend you people to have a look into this library if you already haven’t seen it yet.

Let’s say, we have a word “hello” and a node with an array of pointers of length 26 representing each character of the English language, each of which indicates that if the i^{th} character follows the character represented by this node. Therefore for this example “hello”, the head node’s array of pointers will have the location 7 pointing to another node, which will have the 4th location of the pointer pointing to another node, whose pointer array’s 11 th location will point to another node and so on. Note here the indexing starts from zero. When the word ends, then the next pointer can be pointed to a special terminal marker node, which can be common to all, and the node is marked as a terminal node. This is essential as a valid word can be a substring of another valid word, in which case the shorter would need to be decided. When another new word like “help” comes in, we will follow the same path upto “hel” created by the word “hello”, and as we find there are no pointer for “p” pointing to any node, a new node will be created as explained before. Continue reading “A wide character trie implementation”→

It’s been a long time I have done any activity in this blog. I was going through some old stuffs and thought to post something. Today I will post a generic implementation for Fisher-Yates Shuffle.

Although you can get the Fisher-Yates algorithm from wiki, still I am briefly explaining it.

Let us assume that there is a array arr of length n. We need to find a uniformly random permutation of the elements of the array. One of the variations of the algorithm is as follows.

arr is an array of length n, where indexing starts from 0
i=n-1
while i>0
{
r = generate a random number between 0 and i (both inclusive)
swap the array elements arr[r] and arr[i]
i = i - 1
}
arr is now uniformly permuted

The problem statement is, an long array is given with n elements, we need to find all the pairs of numbers in this long array which have a constant difference k. I will post three methods. The first method is the brute force method and has a runtime complexity O (n^{2}), the next method has runtime complexity O (n*log (n)), and the last one will have the runtime complexity O (n).

I have already posted a jumbled word solver written in C language, although what I posted is actually become old, as I have changed some of the things in the code. I will update the post with this (hope to update!) with the new changes, but before it I would like to post the the same stuff in other languages and with different datastructure. Recently I am learning Perl and brushing up C++, therefore I will post jumble word solver written in C++ and Perl in this post. Continue reading “Jumble word solver again”→

There are two strings. We need to find if one string is a rotation of the other. If yes then how many places it was rotated. The solution is pretty straightforward. I will describe two ways in this post. Continue reading “Check if a string is rotation of another”→

The puzzle is to implement basic queue operations with using only basic stack operations. That is, a stack object is given, we need construct a wrapper for the queue functions, insert, remove, which will only use the stack object as its storage, and naturally will have to use the stack operations. I have already posted the opposite task in the post Implement stack using a queue

This can be done using two stack objects. We call these the first stack and the second stack. Although either the insert or the remove complexity will no more be O(1).

I have discussed the process gradually. I added the last solution when it clicked in my mind while reviewing this post.

We had assignments to print “*”s in different formation in undergraduate class, which I never liked as they were pointless. Now I got a somewhat justifiable application, plot histogram in terminal. In the last post Generating random numbers from Normal distribution in C I posted the C code to generate random numbers from the Normal distribution using the Polar method. In this post I am posting a simple code to plot the histogram of generated random numbers from this or any other distribution. Let me first post the code and then explain what is going on. Continue reading “Plot histogram in terminal”→