CS502 Fundamentals of Algorithms Assignment No 01 Spring 2019 Solution & Discussion Due Date: 15-05-2019
Question No 01: (Marks: 10)
The following algorithm (procedure) is computing the multiplication of two squared matrices. A[][] and B[][] are two squared matrices, Mul[][] is a square matrix which store the multiplication of A[][] and B[][]. As the matrices are squared so, “n” would be the number of columns or rows. You are required to calculate the worst case time complexity {T(n)} of this algorithm.
1 Matrix_Multiplication (A[][], B[][],Mul[][], int n)
2 Sum = 0
3 for (int i to n)
4 for (int j to n)
5 for (int k to n)
6 Sum = Sum + A[i][k] * B[k][j];
7 Mul[i][j] = Sum;
Note: Make sure that the alignment of each step/line is important in the algorithm, because it may indicate you that the loops are nested or in sequence.
Question No. 02 (Marks 10)
Consider the following function f(n) which represent the time complexity of an algorithm.
f(n) = 2n^{2} + 4n + 7
As per the definition of Big O, we have, 0 ≤ f(n) ≤ cg(n) , where c >0 and n ≥ n_{0}
If g(n) = n^{2} , find the value of c for which the upper bound cg(n) holds.
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For any query about the assignment, contact at CS502@vu.edu.pk
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