Write a program that reads an arbitrary number of columns of numbers from a file and fills in a matrix with these numbers until you reach to the end of file.

• Your code should also print out succesfully read number of lines and columns.

Read in a column of real numbers from a file. Sort the numbers and write the sorted numbers in a different file.

• You cannot use a sorting algorithm from any package.

• No shortcuts, you MUST write your own!

Multiply two 30-digit numbers not using simple multiplication or math functions or libraries. This field is called "number crunching" but you should solve the problem in a simple way explained below. Numbers should not start with zero.

Hint (the simplest way):

n1="123456789012345678901234567890"

n2="234567890123456789012345678901"

• Split each of these two numbers (strings n1 and n2) into two arrays (Note that naturally each character of strings can be accessed: n1[0] = '1')

• Cross process each digit from these two arrays (i.e two numbers) accordingly.

• Note that in your code only perform multiplication of single digit numbers e.g 9 x 9 = 81

• You are not allowed to use powers of 10 in your calculation loop.

• You have to leave the result as string (in case of example below: '1476')

123

x 12

-----

246 : 3x2=6 (1's), 2x2=4 (10's), 2x1=2 (100's)

+123 : 1x3=3 (10's), 1x2=2 (100's), 1x3=3 (1000's)

-----

1476

The color coding of images on a screen is done in a pixel-by-pixel fashion. One way to code the color is to get the RGB (red-blue-green) code of the image pixel-by-pixel and use an algorithm to convert it to grayscale.

• Write a code that does this conversion.

• In order for this project to be complete, you must find a way to visualize both the color and the grayscale images.

• You can use any python library to read & write the image file (eg matplotlib). However, you cannot use library's own conversion functions.

Random numbers are used very often in various branches of scientific computing. For instance, the Monte Carlo method aims to find the lowest energy configuration of a system by means of taking steps along random directions and testing whether each step causes an energy drop. Achieving truly random numbers, however, is a challenging task. For this reason, most computer languages provide functions that generate pseudorandom numbers, which are a sequence of numbers that simulate a true random sequence but are generated deterministically following a well-defined algorithm. There are several random number generator algorithms but one of the simplest ones is the middle-square method. Write a Python code, which generates a sequence of random numbers, each of 4 digits. Here are the steps to follow :

• Start with a long integer, N. Take this to be the current time in milliseconds. (Hint : You can use the time module.)

• Take the last four digits of N. This will potentially be your seed number, which initiates the sequence of random numbers.

• Check if there are any zeros anywhere in the seed. If there are, create a new seed by means of finding the current time in milliseconds and taking the last four digits. When you get a four digit number that doesn't have any zeros in it, this will be your seed.

• The reason why we are avoiding zeros is that their presence ruins the randomness of the sequence to be generated.

• Take the seed and take its square.

• Take the middle four digits; this is your new seed.

• Take the new seed and take its square, take the middle four digits; this is your new seed.

• Continue in this manner and collect the first 500 numbers in your sequence in an array.

• Plot a histogram of these numbers and see whether they are really randomly distributed.

Read two columns of data from a file. Take the first column as X and second column as Y axis. Display the data so that X axis runs/flows down and the number on the Y axis is scaled to fit in horizontal 80 characters of ’*’ (depending on the maximum value of the axis)

Hint:

• Make a subroutine for the function i.e. give a number (x) it returns value of this function at that point (y).

• Now in a 2D array, arranged according to your canvas size, locate this point P(x,y) according to your scale on x and y axes.

• Note that project’s key point is arranging the scales of the axis on the canvas.

• Corresponding string graphics is given below/right.

Example:

6| **

5| **

4| **

3| **

2|**

1|

+----------

1 2 3 4

Remember the game "hangman" where the computer grabs a word from a dictionary and plays a guessing game with the user. By entering one letter at a time, the user must guess the word before the man hangs. There is no set "correct" way to do this. Get creative!