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## Solution Idea of CS502 Assignment No 1 2019 Fundamental Algorithm Due Date 15-05-2019

** Question 1:**
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.

**p50 Chapter 4**

**Reference:****Question 2:****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 ≥ n0 If g(n) = n

^{2}, find the value of c for which the upper bound cg(n) holds.

**p22 Chapter 1**

**Reference:**Solution of Assignment is Given Below;

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