Have a look at the Big-O complexity chart:
A function has an order, it can be for example
- constant (O(c)),
- logarithmic (O(log n)),
- linear (O(n)),
- linearithmic (O(n log n)),
- quadratic (O(n^2)),
- cubic (O(n^3)),
- exponential (O(c^n)),
- factorial (O(n!)).
This can make a very significant difference, as exemplified in the following code:
using System;
using System.IO;
class Program
{
static int factorial(int n)
{
if (n == 0)
return 1;
else
return checked(factorial(n - 1) * n);
}
static void Main()
{
Console.WriteLine(int.MaxValue);
int x = int.MaxValue;
int y = x + 1;
Console.WriteLine(y);
try
{
y = checked(x + 1);
}
catch (System.OverflowException)
{
Console.WriteLine("An overflow exception was thrown.");
}
int count0 = 0;
int n0 = 3;
try
{
while (true)
{
count0++;
n0 = checked(n0 +1 );
}
}
catch (System.OverflowException)
{
Console.WriteLine("An overflow exception was thrown after " + count0 + " iterations.");
// An overflow exception was thrown after 2147483645 iterations.
}
int count1 = 0;
int n1 = 3;
try
{
while (true)
{
count1++;
n1 = checked(n1 * n1);
}
}
catch (System.OverflowException)
{
Console.WriteLine("An overflow exception was thrown after " + count1 + " iterations.");
// An overflow exception was thrown after 5 iterations.
}
int count2 = 0;
int n2 = 3;
try
{
while (true)
{
count2++;
n2 = factorial(n2);
}
}
catch (System.OverflowException)
{
Console.WriteLine("An overflow exception was thrown after " + count2 + " iterations.");
// An overflow exception was thrown after 3 iterations.
}
int count3 = 0;
int n3 = 100;
try
{
while (true)
{
count3++;
n3 = checked(n3 * (int)Math.Log(n3, 2));
}
}
catch (System.OverflowException)
{
Console.WriteLine("An overflow exception was thrown after " + count3 + " iterations.");
// An overflow exception was thrown after 7 iterations.
}
}
}