1. Electrical and Computer Engineering Department SUNY – New Paltz
Computer Simulation
“Lecture 4”
Electrical and Computer Engineering Department
SUNY – New Paltz
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2. Developing algorithms
·       structure plan (pseudo- code)
·        systematic procedure or algorithm
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3. What is an Algorithm?
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output"
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4. Solving Quadratic Equation
Structure plans
Solving Quadratic Equation
ax2 + bx + c = 0
Input data
Second Order(a=0)?
If not x=-c/b
Is (b2-4ca)<0
If yes then complex roots
Otherwise x1,2 = (± b + √b2 − 4ac)/(2a)
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5. Pseudo Code Input data Second Order(a=0)? If not x=-c/b
Start
Input data (a, b, c)
If a = 0 then
If b = 0 then
If c = 0 then
Display ‘Solution indeterminate’
else
Display ‘There is no solution’
x = −c/b
Display x (only one root: equation is linear)
else if b2 < 4ac then
Display ‘Complex roots’
else if b2 = 4ac then
x = −b/(2a)
Display x (equal roots)
x1 = (−b + √b2 − 4ac)/(2a)
x2 = (−b − √b2 − 4ac)/(2a)
Display x1, x2
Stop.
Input data
Second Order(a=0)?
If not x=-c/b
Is (b2-4ca)<0
If yes then complex roots
Otherwise x1,2 = (± b + √b2 − 4ac)/(2a)
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6. MATLAB CODE(2) SUNY-New Paltz a = input('Enter a :');
Start
Input data (a, b, c)
If a = 0 then
If b = 0 then
If c = 0 then
Display ‘Solution indeterminate’
else
Display ‘There is no solution’
x = −c/b
Display x (only one root: equation is linear)
else if b2 < 4ac then
Display ‘Complex roots’
else if b2 = 4ac then
x = −b/(2a)
Display x (equal roots)
x1 = (−b + √b2 − 4ac)/(2a)
x2 = (−b − √b2 − 4ac)/(2a)
Display x1, x2
Stop.
a = input('Enter a :');
b = input('Enter b :');
c = input('Enter c :');
if a == 0
if b == 0
if c == 0
display( 'Solution indeterminate!');
else
display('There is no solution');
end
x==-c/b;
display(['only one root: equation is linear, x=', num2str(x)]);
else if b*b < 4*a*c
display('Complex roots')
else if b*b == 4*a*c
x = -b/(2*a)
display(['equal roots, x1=x2=',num2str(x)]);
x1 = (-b + sqrt(b*b - 4*a*c))/(2*a);
x2 = (-b - sqrt(b*b - 4*a*c))/(2*a);
display (['distinct roots x1=', num2str(x1),' x2=', num2str(x2)]);
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7. SOLUTION INDETERMINATE!
Flow Chart N Y
START
a = 0 ?
b = 0
x=-c/b
b2 – 4ac>0?
x1,2 =(±b+sqrt(b2 – 4ac))/2a
c = 0
Input coefficients Y Y
SOLUTION INDETERMINATE!
COMPLEX SOLUTIONS!
THERE IS NO SOLUTION!
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8. SOLUTION INDETERMINATE!
MATLAB CODE(3) N Y
START
INPUT COEFFICIENTS
a = 0 ?
b = 0
THERE IS NO SOLUTION!
x=-c/b
b2 – 4ac>0
x1,2 =(±b+sqrt(b2 – 4ac))/2a
COMPLEX SOLUTIONS!
c = 0
SOLUTION INDETERMINATE!
a = input('Enter a :');
b = input('Enter b :');
c = input('Enter c :');
if a == 0
if b == 0
if c == 0
display( 'Solution indeterminate!');
else
display('There is no solution');
end
x==-c/b;
display(['only one root: equation is linear, x=', num2str(x)]);
else if b*b < 4*a*c
display('Complex roots')
else if b*b == 4*a*c
x = -b/(2*a)
display(['equal roots, x1=x2=',num2str(x)]);
x1 = (-b + sqrt(b*b - 4*a*c))/(2*a);
x2 = (-b - sqrt(b*b - 4*a*c))/(2*a);
display (['distinct roots x1=', num2str(x1),' x2=', num2str(x2)]); N Y Y
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9. Components of Flowchart
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10. Example of a Flowchart
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11. Example of a Flowchart
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12. Exercise Write a flow chart that implements the following algorithm:
A single die is rolled
If it is even, print “Even Roll!”
If it is odd, print “Odd Roll”
Modify the process to roll indefinitely!
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13. Exercise
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14. Exercise Write a flow chart that implements the following algorithm:
Set vector V=[ 2, 5, -1, 6, 0]
Initialize variable maximum myMax = 2
Search through the vector and compare all the elements of the vector to find the maximum of the vector.
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