More about Big-O
1) Find the following limits at infinity:
a)
124
32
lim
23
4
xxx
xx
x
b)
1
lim
23
5
xxx
xx
x
c)
4
23
32
124
lim xx
xxx
x
d)
3
23
3
1
lim xx
xxx
x
e)
)2)(72(
)1)(43(
lim
xx
xx
x
f)
x
x
x
1
lim
2
2) Find the order of complexity of:
a)
1
23
xxx
b)
1)ln(
3
xex
x
c)
xx )ln(
d)
2
3
4)ln( xxx
e)
)2)(72(
)1)(43(
xx
xx
3.) Find the order of complexity for the following Java functions. If there are best-case, worst-case
scenarios, assume the worst.
public static void printArray(int[] X)
{
for (int i = 0; i < X.length; i++)
{
System.out.println("X[" + i + "] = " + X[i]);
}
}
public static boolean isIncreasing(int[] A)
{
for (int i = 0; i < A.length-1; i++)
{
if (A[i] > A[i+1])
return false;
}
return true;
}
private static void swap(int[] X, int pos1, int pos2)
{
int tmp = X[pos1];
X[pos1] = X[pos2];
X[pos2] = tmp;
}
