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### Write a C++ program that opens a connectivity matrixand Calculatesthe Google PageRank algorithm (search it online what it is) for the web described bythe connectivity matrix.

INSTRUCTIONS TO CANDIDATES

Write a C++ program that opens a connectivity matrix and Calculates the Google PageRank algorithm (search it online what it is) for the web described by the connectivity matrix.

The connectivity matrix will be in a plaintext file called connectivity.txt.

It will be square, and composed entirely of space-separated 0s and 1s (this is an example):

0 1 1 0

1 0 1 0

1 1 0 0

0 0 0 0

Your program must print the result to cout like this (Output):-

Page A: 31.75%

Page B: 31.75%

Page C: 31.75%

Page D: 4.76%

You must create matrix.cpp,  pagerank.cpp (calculates google pagerank algorithm) and main.cpp (should be short). with following requirements: -

• The matrix stores doubles. Implement a default constructorwhich initializes a square 1 x 1 matrix that contains a 0.0.

• Implement a constructorthat accepts a positive integer n and creates a square n x n matrix that contains 0.0s. Throw an exception if the integer passed to the constructor is zero or negative.

• Implement a constructor that accepts two positive integers r and c and creates a matrix with r rows and c columns that contains 0.0s. Throw an exception if either integer passed to the constructor is zero or negative.

• Implement a constructorthat accepts a one-dimensional array/vector of double. If you use an array, it might be helpful to also pass in the size of the array to indicate the number of elements in the array. The size of the array/double must have an integer square root, i.e., the size of the array/double must be 1, or 4, or 9, or 16, etc. Create a square matrix of size 1 x 1, or 2 x 2, or 3 x 3, or 4 x 4, etc., and populate it using the values from the array/double. If the size of the array/double does not have an integer square root, throw an exception.

• Implement a 3-parameter Setterthat accepts two integers representing row and column and a double representing new value for specified location. Throw an exception if integers are negative or too large.

• Implement a 2-parameter Getterthat accepts two integers representing row and column and returns value in the matrix from specified location. Throw an exception if the integers are negative or too large.

• Implement a functioncalled clear which sets all values in the matrix to 0.0.

• Implement a destructorcalled ~matrix.

• Implement an overloaded insertion operatorso we can print the matrix to std::cout or other streams.

• Implement ==and != operators. The equality operators must check if the matrices are same size and contain the same values in the same locations.

• Implement unary incrementand decrement operators. You will need a prefix and a postfix version of each. The operators should (respectively) increment or decrement each value in the matrix by 1.0.

• Implement the assignment operatorusing the copy-and-swap algorithm introduced in class.

• Overload operator +=,operator +, operator - =, and operator - .These will only work if the matrices are the same size otherwise throw an exception. Do not overload operator / or operator/=

• Overload operator*and operator*= . For operator* and operator*= , be careful. You will need to remember that for 2 matrices a and b, the product matrix c is possibly a different size. If matrix a is 1 x 4 and matrix b is 4 x 3, the size of the product matrix c will be 1 x 3. If the number of columns of the first operand is not equal to the number of rows of the second operand, throw an exception.

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