Mysteries and Beauty of Fractals

Its really amazing to know know how a simple equation z_n+1 = z_n² + c can create patterns which are so intricate, so vivid and so beautiful. The set defined by above equation is know as Mandelbrot set and it represents a set of points denoted by c in a complex plane for which z_n+1 remains always bounded starting with  z₀ = 0. 

Going Native - Talk by Bjarne Stroustrup on C++11

"The world runs on C and C++". And hearing from the master himself about it is so enlightening. His emphasis on simple and clean code, explanation of new C++ 11 features and crisp examples to showcase them will encourage many to take a fresh view at the language.  The examples on type rich programming and move constructor are very interesting and that is something I look forward to use. The STL example on vector breaks my conventional understanding of the STL libraries, though I am a avid user of STL libraries myself, I always had a concern that they may not be fast. But thanks to his explanation my belief in STL is vindicated.
This presentation is quite long(Around 90 Mins) so preferably watch it at your leisure and get enlightened..

TSP Simulator based on Simulated Annealing Technique

Traveling Salesman Problem is one of the very interesting topics among algorithm enthusiast. The problem definition is very simple. Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? It is an NP hard problem with no polynomial time algorithm known till date. It finds several important real life application such as routing and floor planning of Integrated Circuits, Mechanical Arm sequencing etc.
More regarding this interesting problem can by found on Wikipedia(TSP).
Simulated Annealing algorithm is a generic probabilistic metaheuristic technique for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. Simulated Annealing can be used for solving several optimization problems. TSP is one of them.

A Sudoku Solver

For quite sometime Sudoku has become a one of the most enjoyable pass time for many people and they are visible every where. We are having daily Sudoku in newspaper, several online website where we can play Sudoku and several apps for hand held devices on android and Apple app store.  In principle I knew how to solve a Sudoku and have tried several of them as well. But I wanted to code my thought process for a computer to do the job for me. Hence I ended up writing my own Sudoku solver.

The solver employs back tracking algorithm to solve a given Sudoku. Moreover if the Sudoku is not a valid one or if it cannot be solved then this programs reports that as well and exits. The idea of sharing this post is to let the users understand how a back tracking algorithm works and how it can be put in code using a stack. The pseudo code for the algorithm is as below:

Ten Assertions Puzzle

Fill in the blanks with numbers so that all the statements are true.

Number of occurrences of the digit 0 in this puzzle is  _____.
Number of occurrences of the digit 1 in this puzzle is  _____.

Number of occurrences of the digit 2 in this puzzle is  _____.

Number of occurrences of the digit 3 in this puzzle is  _____.

Number of occurrences of the digit 4 in this puzzle is  _____.

Number of occurrences of the digit 5 in this puzzle is  _____.

Number of occurrences of the digit 6 in this puzzle is  _____.

Number of occurrences of the digit 7 in this puzzle is  _____.

Number of occurrences of the digit 8 in this puzzle is  _____.

Number of occurrences of the digit 9 in this puzzle is  _____.