4. (25 points) consider the following procedure that performs multiplication of two upper triangular matrices a[1: : n][1: : n] and b[1: : n][1: : n]. matrix multiply(a[1: : n][1: : n], b[1: : n][1: : n]) cost times 1. for i 1 to n c1 2. for j i to n c2 3. ci j 0 c3 4. for k i to j c4 5. ci j ci j +aik bk j c5 6. return c c6 as the product c[1: : n][1: : n] is also upper triangular, we assume that we do not have to be concerned with the strictly lower triangular entries of the matrix. (a) fill in for each line of instruction, the number of times the instruction is executed. (b) derive the expression for the running time of matrix multiply in terms of n and ci. what is the complexity of the algorithm using the big-o notation?

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Assume the existence of a bankaccount class. define a derived class, savingsaccount that contains two instance variables: the first a double, named interestrate, and the second an integer named interesttype. the value of the interesttype variable can be 1 for simple interest and 2 for compound interest. there is also a constructor that accepts two parameters: a double that is used to initialize the interestrate variable, and a string that you may assume will contain either "simple", or "compound", and which should be used to initialize the interesttype variable appropriately. there should also be a pair of functions getinterestrate and getinteresttype that return the values of the corresponding data members (as double and int respectively).

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