Give the simplest big-Θ for the following functions:
15 n3 + 2 n2 + 2002
Θ( n3 )
3n + n2002 + 2002
Θ( 3n )
1030 n
Θ( n )
15 n log n + 20 n
Θ( n log n )
17 log n
Θ( log n )
17 log2 n
Θ( log n )
17 log2 (n5)
Θ( log n )
Give the simplest big-Θ in terms of
n
for the following nested loops:
for (i=0; i<=n; ++i)
for (j=0; j<10000; ++j)
++sum ;
Θ( n
)
for (i=0; i<=n; ++i)
for (j=0; j<n-10000; ++j)
++sum ;
Θ( n
2 )
for (i=0; i<=n; i=i+3)
++sum ;
Θ( n
)
for (i=0; i<=n; i=i+(n/10000)+1)
++sum ;
Θ( 1 )
for (i=0; i<=n; i=3*i+1)
++sum ;
Θ( log n
)
for (i=0; i<=n; i=10*i)
++sum ;
It's an infinite loop! Therefore, it has no Θ class.
for (i=0; i*i<=n; ++i)
++sum ;
Θ( n
½ )