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Project Euler Problem 72 in MATLAB

admin — Fri, 19 Jun 2009 21:49:48 +0000

Show Problem 72
This code took about 30 minutes to run on my computer. I tried to implement the same logic in Java; however, it took hours to get an answer.However, an efficient Java solution with prime sieving is HERE.(Runs under 1 seconds). Here is the logic the totient function of a number gives how many reduced fractions a number has if it is included. Actually, the totient function gives the number of integers coprime with the input.[given n=p1^e1*p2^e2...pk^ek,(p stands for prime factor) totient(n)=n(1-1/p1)(1-1/p2)...(1-1/pk)]So if a number is not coprime with the input it means that the fraction formed with those two numbers has already been presented before. Thus, we do not count those numbers. Unfortunatelly, the answer is out of range of integer in Matlab. In Matlab there is no natural implementation of big integers as in java so I had to download and install an m file from Matlab Snack Bar Working with big integers decreases the speed but it was the only solution I could find.

Here is the code in MATLAB

^?View Code MATLAB

 sum = bigint('0');
for i = 2:1000000
    f = factor(i);
    hey = i;
    b = unique(f);
 
    for j = 1:length(b)
        hey=hey*(b(j)-1)/b(j);
 
    end
    am =bigint(int2str(hey));
    sum=plus(sum,am);
 
    fprintf('i = %g\n', i);
end
display( sum);

Hope this helps.

Quadratic Equation Solver in MATLAB

admin — Fri, 28 Nov 2008 23:46:07 +0000

This algorithm finds the roots of a quadratic equation in the form ax^2 + bx + c = 0.It tests for several conditions:
-If a = 0 and b = 0, then the equation reduces to c = 0. If this condition occurs we call the equation degenarete.
-If a = 0 and b ~= 0, the equation reduces to bx + c = 0 with single root at -c/b.
-If a ~= 0 and c = 0, the equation reduces to ax^2 + bx = 0. There are two roots, 0 and -b/a.
-If none apply we use the famous equation to find roots. Roots are either complex or real depending on the discriminant.

^?View Code MATLAB

%Quadratic Equation Solver in MATLAB
array=input('Specify the coefficients of the quadratic as a row array "[a,b,c]":');
a=array(1);
b=array(2);
c=array(3);
 
if (a==0) && (b==0)
    fprintf('The equation is degenerate');
end
 
if (a==0) && (b~=0)
    fprintf('There is a single root at %g.\n', -c/b);
end
 
if (a~=0) && (c==0)
    fprintf('There are two real roots at 0 and %g.\n', -b/a);
end
 
if (a~=0) && (c~=0)
    root1=(-b+sqrt(b*b-4*a*c)/(2*a));
    root2=(-b-sqrt(b*b-4*a*c)/(2*a));
    if isreal(root1)
        fprintf('There are two real roots at %g and %g.\n.', root1, root2);
    else
        fprintf('The roots are complex:\n');
        fprintf('           ');
        disp(root1);
        fprintf('       and ');
        disp(root2);
    end
end

Guessing Game in MATLAB

admin — Fri, 28 Nov 2008 23:23:13 +0000

This algorithm creates a guessing program in MATLAB. First, it randomly picks an integer in range 1 to 10. Then, the user should guess the number as soon as possible. A counter keeps track of number of guesses made.

^?View Code MATLAB

% This is a guessing game
counter=0;
real_number=rand(1);
real_number=10*real_number;
number=ceil(real_number);
 
fprintf('I am thinking a number between 1 and 10.\n');
guess=input('Guess a number: ');
 
while guess~= number
     counter = counter + 1;
     if guess>number
          fprintf('Your guess is too high!\n');
          guess=input('Guess another number: ');
     else
          fprintf('Your guess is too low!\n');
          guess=input('Guess another number: ');
     end
end
 
counter= counter + 1;
fprintf('Congratulations! You guessed the correct number in %g shots. \n', counter);

Programming in MATLAB

admin — Fri, 28 Nov 2008 23:13:05 +0000

Matlab stands for matrix laboratory. It is a numerical computing environment and a programming language. Created by The MathWorks company, it allows easy matrix manipulation, plotting functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages.

MATLAB

MATLAB R2008a version download links:

Password: www.updatesofts.com

Note: Please refer to install file in crack folder for installation. You also need a Daemon Tools Lite like program to mount the CD image.