/// <summary>
/// Gets a linked list containing all the primes less than n.
/// </summary>
/// <param name="n">The upper bound on the primes (all primes must be less than this value).</param>
/// <returns>A linked list containing all the primes less than n.</returns>
private LinkedListCell <int> GetPrimesLessThan(int n)
{
LinkedListCell <int> list = GetNumbersLessThan(n);
for (LinkedListCell <int> p = list; p != null && p.Data * p.Data < n; p = p.Next)
{
RemoveMultiples(p.Data, p);
}
return(list);
}
/// <summary>
/// Gets a linked list of the prime numbers less than the given value.
/// </summary>
/// <param name="n">The upper limit.</param>
/// <returns>A list of the prime numbers less than n.</returns>
public static LinkedListCell <int> GetPrimesLessThan(int n)
{
LinkedListCell <int> list = GetNumbersLessThan(n);
LinkedListCell <int> p = list;
while (p != null && p.Data * p.Data < n)
{
RemoveMultiples(p.Data, p);
p = p.Next;
}
return(list);
}
/// <summary>
/// Forms a linked list containing all prime numbers less than the given value.
/// </summary>
/// <param name="value">The upper limit (exclusive) on the prime numbers to generate.</param>
/// <returns>A linked list containing all the prime numbers less than value.</returns>
private LinkedListCell <int> GetPrimesLessThan(int value)
{
LinkedListCell <int> x = GetNumbersLessThan(value);
LinkedListCell <int> temp = x;
while (temp != null)
{
RemoveMultiples(temp.Data, temp);
temp = temp.Next;
}
return(x);
}
/// <summary>
/// Handles a Click event on the "Find Primes" button.
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void uxFindPrimes_Click(object sender, EventArgs e)
{
LinkedListCell <int> primes = GetPrimesLessThan((int)uxInput.Value);
uxPrimes.BeginUpdate();
uxPrimes.Items.Clear();
for (LinkedListCell <int> p = primes; p != null; p = p.Next)
{
uxPrimes.Items.Add(p.Data);
}
uxPrimes.EndUpdate();
}
/// <summary>
/// Forms a linked list containing all prime numbers less than the given value.
/// </summary>
/// <param name="value">The upper limit (exclusive) on the prime numbers to generate.</param>
/// <returns>A linked list containing all the prime numbers less than value.</returns>
private LinkedListCell <int> GetPrimesLessThan(int value)
{
LinkedListCell <int> tempCell = GetNumbersLessThan(value);
LinkedListCell <int> pointer = tempCell;
while (pointer != null)
{
RemoveMultiples(pointer.Data, pointer);
pointer = pointer.Next;
}
return(tempCell);
}//end GetPrimesLessThan
/// <summary>
/// Gets a linked list of the integers strictly between 1 and n.
/// </summary>
/// <param name="n">The upper limit.</param>
/// <returns>A list of the integers strictly between 1 and n.</returns>
public static LinkedListCell <int> GetNumbersLessThan(int n)
{
LinkedListCell <int> list = null;
for (int i = n - 1; i > 1; i--)
{
LinkedListCell <int> cell = new LinkedListCell <int>();
cell.Data = i;
cell.Next = list;
list = cell;
}
return(list);
}
/// <summary>
/// Returns a linked list beginning at 2 and is less than n
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
private LinkedListCell <int> GetNumbersLessThan(int n)
{
LinkedListCell <int> temp = new LinkedListCell <int>();
for (int i = n - 1; i > 1; i--)
{
LinkedListCell <int> cell = new LinkedListCell <int>();
cell.Data = i;
cell.Next = temp;
temp = cell;
}
return(temp);
}
/// <summary>
/// Gets a linked list containing all the primes less than n.
/// </summary>
/// <param name="n">The upper bound on the primes (all primes must be less than this value).</param>
/// <returns>A linked list containing all the primes less than n.</returns>
private LinkedListCell <int> GetPrimesLessThan(int n)
{
LinkedListCell <int> front = GetNumbersLessThan(n);
LinkedListCell <int> temp = front;
while (temp.Next != null && (temp.Data * temp.Data < n))
{
RemoveMultiples(temp.Data, temp);
temp = temp.Next;
}
return(front);
}
/// <summary>
/// Gets a linked list containing the values 2 through n - 1.
/// </summary>
/// <param name="n">One greater than the largest value to be placed in the list.</param>
/// <returns>A linked list containing the values 2 through n - 1.</returns>
private LinkedListCell <int> GetNumbersLessThan(int n)
{
LinkedListCell <int> front = null;
for (int i = n - 1; i > 1; i--)
{
LinkedListCell <int> temp = new LinkedListCell <int>();
temp.Data = i;
temp.Next = front;
front = temp;
}
return(front);
}
}//end GetPrimesLessThan
/// <summary>
/// Private method GetNumbersLessThan; Returns LinkedListCell<int>;
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
private LinkedListCell <int> GetNumbersLessThan(int n)
{
LinkedListCell <int> numLessThan = null;
for (int i = n - 1; i > 1; i--)
{
LinkedListCell <int> tempCell = new LinkedListCell <int>();
tempCell.Data = i;
tempCell.Next = numLessThan;
numLessThan = tempCell;
} //end for
return(numLessThan);
} //end LinkedListCell
/// <summary>
/// Removes all multiples of the given int from the linked list beginning after the given cell.
/// </summary>
/// <param name="k">The value whose multiples are to be removed.</param>
/// <param name="list">The cell preceding the first cell to examine.</param>
public static void RemoveMultiples(int k, LinkedListCell <int> list)
{
while (list.Next != null)
{
if (list.Next.Data % k == 0)
{
list.Next = list.Next.Next;
}
else
{
list = list.Next;
}
}
}
/// <summary>
/// Removes from the given linked list all cells (except the first) containing
/// values divisible by the given int. The given cell must not be null.
/// </summary>
/// <param name="k">The value whose multiples are to be removed.</param>
/// <param name="list">The cell containing the divisor.</param>
private void RemoveMultiples(int k, LinkedListCell <int> list)
{
LinkedListCell <int> temp = list;
while (temp.Next != null)
{
if (temp.Next.Data % k == 0)
{
temp.Next = temp.Next.Next;
}
else
{
temp = temp.Next;
}
}
}
} //end LinkedListCell
/// <summary>
/// Private method RemoveMultiples; returns null
/// </summary>
/// <param name="k"></param>
/// <param name="list"></param>
private void RemoveMultiples(int k, LinkedListCell <int> list)
{
LinkedListCell <int> pointer = list;
while (pointer.Next != null)
{
if ((pointer.Next.Data % k) == 0)
{
pointer.Next = pointer.Next.Next;
}
else
{
pointer = pointer.Next;
}
} //end while
} //RemoveMultiples