/* Actual powerset generation function
* Returns a PowersetList object containing each possible subset
* possible to generate from the given set
*/
static PowersetList PowerSet(SetList S)
{
/* How many values do we have in original set?
* This will affect length of powerset
* We create an array with this length to hold values from the set
* which simplifies our algorithm later
*/
int len = size(S);
int[] vals = new int[len];
int counter = 0;
SetNode node = S.first;
/* Iterate through values in set,
* adding each to the array
*/
while (node != null) {
vals[counter++] = node.data;
node = node.next;
}
/* At this point, vals[] contains all our set values.
* We set up our list container class, and our first node.
* Even if there are no values in given set, we still want the empty set {}
* so we set that as our first subset.
*/
PowersetList powerset = new PowersetList();
PowersetNode prev_node = new PowersetNode();
prev_node.data = new SetList();
powerset.first = prev_node;
/* Calculate power-set length using 2^N where N = number of values.
* Math.Pow isn't C-Core so we created a simple power function for this
*/
int n = pow(2, len);
/* Our empty set {} is at location 0, so we start the loop at 1
* then loop through until we have n values.
*/
for (int x = 1; x < n; x++) {
/* Set up this sub-set's containers */
PowersetNode New_Node = new PowersetNode();
New_Node.data = new SetList();
/* Now iterate through each value in our vals[] array */
for (int i = 0; i < len; i++) {
/* If it should be in this subset, then we add it to the current subset.
* This is done by using the bitwise operators & and << to check if
* the binary conversion of x AND 1 << i is greater than 0. */
if ((x & (1 << i)) > 0) {
add(ref New_Node.data, vals[i]);
}
}
/* Finally, add our completed subset to the previous node's next
*/
prev_node.next = New_Node;
prev_node = prev_node.next;
}
return powerset;
}
/*
* Task 2 - Powerset Functions
* Implemented using a nested linked list data structure
*/
/*
* Print: Prints the powerset in a user-readable format.
* Overrides standard print function for powersets only.
*/
static void print(PowersetList S)
{
Console.Write("{ ");
PowersetNode node = S.first;
/* Loop through each node, printing it's value */
while (node != null) {
print_subset(node.data);
Console.Write(", ");
node = node.next;
}
Console.WriteLine(" }");
}
static void Main()
{
//variable declaration
SetList S = new SetList();
Console.Write("Set S: ");
print(S);
Console.WriteLine();
//checks whether the list is empty (should be "true")
System.Console.WriteLine("is_empty(S): " + is_empty(S));
Console.WriteLine();
add(ref S, 1);
add(ref S, 2);
add(ref S, 3);
add(ref S, 4);
add(ref S, 5);
add(ref S, 6);
add(ref S, 7);
add(ref S, 19);
System.Console.Write("After adding " + size(S) + " values to set S: ");
print(S);
Console.WriteLine();
System.Console.WriteLine("Size of S: " + size(S));
Console.WriteLine();
System.Console.WriteLine("is_empty(S): " + is_empty(S));
Console.WriteLine();
SetList T = new SetList();
add(ref T, 1);
add(ref T, 2);
add(ref T, 4);
add(ref T, 5);
add(ref T, 8);
System.Console.Write("Set T: ");
print(T);
Console.WriteLine();
System.Console.WriteLine("Size of T: " + size(T));
Console.WriteLine();
Console.WriteLine("Is 3 in set T? " + is_element_of(3, T));
Console.WriteLine();
Console.Write("Set S after removing some elements:");
remove(ref S, 1);
remove(ref S, 4);
remove(ref S, 6);
print(S);
Console.WriteLine();
Console.WriteLine("Is 7 in set S? " + is_element_of(7, S));
Console.WriteLine();
Console.WriteLine("X = copy_set(S). Set X:");
SetList X = copy_set(S);
print(X);
Console.WriteLine();
Console.WriteLine("Is S a subset of T? " + is_subset(S, T));
Console.WriteLine();
Console.WriteLine("union(S, T): ");
print(union(S, T));
Console.WriteLine("intersection(S, T): ");
print(intersection(S, T));
Console.WriteLine("difference(S, T): ");
print(difference(S, T));
Console.WriteLine("difference(T, S): ");
print(difference(T, S));
Console.WriteLine("symmetricDifference(S, T): ");
print(symmetricDifference(S, T));
SetList Y = new SetList();
PowersetList test = new PowersetList();
Console.Write("Powerset({}): ");
PowersetList PS = new PowersetList();
PS = PowerSet(Y);
print(PS);
add(ref Y, 1);
add(ref Y, 2);
add(ref Y, 3);
add(ref Y, 4);
add(ref Y, 5);
add(ref Y, 6);
Console.Write("Powerset({1,2,3,4,5,6}): ");
print(PowerSet(Y));
Console.ReadLine();
}
