Title:
“Program Assignment 1:
Analyzing Program Performance”
Points:
100 points – 60pts for coded portion, 40 points for written analysis
Due Date:
Wednesday September 25, 2002
Objectives:
(1) To reinforce the concepts underlying the asymptotic analysis of a program’s
performance behavior.
(2) Begin to program in Java.
Description:
Create a Java program that produces the necessary data to determine the asymptotic
behavior of three different algorithms that perform operations on matrices.
Do this according to the
steps shown below.
1.
Create 2 randomly filled matrices (see below for the details).
You will need to experiment
with the sizes of the two matrices so that you get nonzero execution times – see below.
Start with 25 x 25 square matrices and work upwards until each algorithm gives a nonzero
execution time for a given size of the matrices.
2.
Determine the execution time required to run each of the algorithms given below on 5
different size matrices where each size gives a nonzero execution time.
Thus you will
generate at total of fifteen different timing values, five for each algorithm.
Note: while your
program must correctly compute the values for these three matrix operations, you do not
need to include this in your output, although you should verify that the algorithms are
executing properly.
(See below for more details on matrix operations.)
Algorithm #1 – Matrix Addition
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
A[i][j] = B[i][j] + C[i][j];
Algorithm #2 – Matrix Multiplication
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
for (k = A[i][j] = 0; k < n; k++)
A[i][j] += B[i][k] * C[k][j];
Algorithm #3 – Matrix Transposition
for (i = 0; i < n1; i++)
for (j = i+1; j < n; j++){
temp = A[i][j];
A[i][j] = A[j][i];
A[j][i] = temp;
}
3.
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 Summer '09
 Computer Science, Multiplication, Big O notation, Analysis of algorithms, Asymptotic analysis

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