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Library Methodsand

RecursionInstructor: Mainak Chaudhuri

mainakc@cse.iitk.ac.in

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Announcements• Lab tests next week• You will get 90 minutes to solve two

problems• In the remaining 90 minutes your

work will be graded with the tutors’ inputs

• Syllabus same as mid-term I

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Math library• Math.sqrt (x)

– Takes double, returns double

• Math.pow (x, n)– Takes two doubles, returns double

• Math.sin (x)– Takes double, returns double

• Math.cos (x)– Takes double, returns double

• Check out online Math library and other libraries

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Roots of a quadraticclass QuadraticSolver { public static void main (String arg[]) { double a=1.0, b=-2.0, c=1.0; double r1, r2;

r1 = (-b+Math.sqrt(b*b-4*a*c))/(2*a);

r2 = (-b-Math.sqrt(b*b-4*a*c))/(2*a); System.out.println(“Roots are: ” + r1

+ “, ” + r2); }}

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Velocity on inclined plane

class velocityExample{ public static void main(String arg[]){ double theta=Math.PI/3.0; double g=9.81; double x=10; double velocity; velocity =

Math.sqrt(2*g*Math.sin(theta)*x); System.out.println(“Final velocity: ” +

velocity + “ m/s”); } }

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Error in eπ

class errorE{ public static void main(String arg[]){ double x = Math.PI; double approx, error;

approx = 1 + x + x*x/2 + Math.pow(x, 3)/6 + Math.pow(x, 4)/24;

error = Math.exp(x) – approx; System.out.println(“Error up to fourth

power: ” + error); }

}

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Sum of vectorsclass vectorSum{ public static void main(String arg[]){ double v1 = 10.0; double v2 = 21.2; double angle = 120; // In degrees double resultant;

resultant = Math.sqrt(v1*v1 + v2*v2 - 2*v1*v2*Math.cos(angle*Math.PI/180.0));

System.out.println(“Resultant of ” + v1 + “ and ” + v2 + “ at ” + angle + “ degrees is ” + resultant);

}}

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Which one is bigger?class whichOneIsBigger{ public static void main(String arg[]){ double x = Math.PI; double y = Math.E; double difference;

difference = Math.exp(x) – Math.pow(x, y);

System.out.println(“Difference: ” + difference);

}

}

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Adiabatic expansionclass Adiabatic{ public static void main(String arg[]){ double P1 = 10; double P2 = 15.6; double V1 = 100; double V2; double gamma = 1.66;

V2 = V1*Math.pow((P1/P2), 1.0/gamma); System.out.println(“New volume: ” + V2); }}

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Recursion• Recursion is a process of calling the same

method from the method body: self-reference

class recurExample { public static void main (String arg[]) { f (10); }

public static void f (int n) { System.out.println(n); if (n > 0) { f(n-1); } }}

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Recursionclass AnotherExample { public static void main (String arg[]) { f (10); }

public static void f (int n) { System.out.println(n); if (n > 0) { f(n-1); } System.out.println(n); }}

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Recurrence relations• Recursive methods can be used to

compute recurrence relations easily• Sum of the first n natural numbers

satisfies the following recurrenceS(n) = S(n-1) + n for n > 1; S(1) = 1

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Sum of first n numbersclass SumOfNumbers { public static void main (String arg[]) { int n = 10; System.out.println(“Sum of the first ” + n

+ “ natural numbers is ” + Sum(n)); } public static int Sum(int n) { if (n == 1) return 1; // initial condition return (Sum(n-1) + n); }}

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Fibonacci series• A second order recurrence

Fn = Fn-1 + Fn-2 for n > 2; F1 = F2 = 1class Fibonacci { public static void main (String arg[]) { int n = 10; System.out.println(n + “th Fibonacci

number is ” + Fibonacci(n)); }

public static int Fibonacci (int n) { if ((1==n) || (2==n)) return 1; return (Fibonacci(n-1) + Fibonacci(n-2)); } // Try to compute the total number of} // method calls