# Run Time Analysis Provide the

1. Run Time Analysis

Provide the tightest big-Oh bound on the run time for each of the following methods.

1.

{

if( n <= 1 )

time++;

else

{

for(int i=0; i<n; i++)

time++;

}

}

1.

void nerfHerder(int n)

{

if( n <= 1 )

time++;

else

{

for(int i=0; i<n; i++)

time++;

nerfHerder(n-1);

}

}

1.

void squire(int n)

{

if( n <= 1 )

time++;

else

{

squire(n/2);

squire(n/2);

for(int i=0; i<n; i++)

for(int j=i; j<n; j++)

time++;

squire(n/2);

squire(n/2);

squire(n/2);

squire(n/2);

squire(n/2);

squire(n/2);

}

}

1.

void jedi(int n)

{

if( n <= 147 )

time += 54;

else

{

for(int i=0; i<n/2; i++)

time++;

jedi(n/3);

for(int i=0; i<13*n; i++)

time++;

jedi((2*n)/3);

}

}

1.

void strass(int n)

{

if( n<=1 )

time++;

else

{

strass(n/2);

strass(n/2);

strass(n/2);

for(int i=0; i<n; i++)

for(int j=i; j<n; j++)

time++;

strass(n/2);

for(int i=n/2; i<n; i++);

time ++;

strass(n/2);

strass(n/2);

strass(n/2);

}

}

1.

void sithLord(int n)

{

if( n <= 200 )

time += 700;

else

{

sithLord((7*n)/10);

for(int i=0; i<n; i++)

time++;

sithLord(n/5);

for(int i=0; i<130*n; i+=10)

time++;

}

}

1.

void hanoi(int n)

{

if( n==1 )

time++;

else

{

hanoi(n-1);

time++;

hanoi(n-1);

}

}

1.

int fib(int n)

{

if( n==0 )

return 0;

else if( n==1 )

return 1;

else

{

return fib(n-1) + fib(n-2);

}

}

1.

int pow(double x, int n)

{

if( n==0 )

return 1;

else

{

double halfpower = pow(x,n/2);

if( n % 2 == 0 )

{

return halfpower*halfpower;

}

else

{

return halfpower*halfpower*x;

}

}

}

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