Generate subsets of size K

1
Generate subsets of size K

• public static getKSubsets(int n, int k)
• boolean subset new booleann // subseti
  indicates if (i1) is in the subset, i 1, 2n
• recursiveGenKSubsets( subset, n, k)
• // subset indicated what integers are selected
  into the subset.
• // n indicate the range 1, 2, ..n
• // k size of subset
• public static recursiveGenKSubset(boolean
  subset, int n, int k)
• // Base case 1 n k. So all members in 1,
  ..., n will be selected into the subset
• // Base case 2 k 0. NO number in 1, , n
  will be selected into the subset.
• // Recursive case 1 Select number n, then
  create subsets of size (k-1) in 1, , n-1.
• // Recursive case 2 Do NOT select number n,
  then create subsets of size (k) in 1, , n-1.

2
New graph representation
class myNewGraph String Vertices int
Edges // different from before int numVertices,
numEdges
3
New graph representation

• Constructor
• pubic myNewGraph(int capacity)
• Vertices new Stringcapacity
• Edges new intcapacity1
• //At first, vertices all have 0 neighbors
• for(int i 0 i lt capacity i)
• Edgesi0 0
• methods
• public void addVertex(String v)
• // Assume v is does not already exist.
• public void addEdge(String v1, String v2)
• // Assume both v1 and v2 already exist.
• // Assume edge between v1 and v2 does not
  already exist.
• public void deleteVertex(String v)

4
public void addVertex(String v)

• Assume v is does not already exist
• Q What to do if Vertices is already full?
• How to change Vertices and Edges?

class myNewGraph String Vertices int
Edges // different from before int numVertices,
numEdges
5
public void addEdge(String v1, String v2)

• Assume both v1 and v2 already exist.
• Assume edge between v1 and v2 does not already
  exist.
• If v1 has index i, v2 has index j,
• Q What to do if the Edgesi or Edgesj is
  full?
• How to expand Edgesi or Edgesj?

class myNewGraph String Vertices int
Edges // different from before int numVertices,
numEdges
6
public void deleteVertex(String v)

• Assume v already exists
• Suppose v has index i,
• - Change Vertices move Verteicesi1,,
  numVertices-1 to the front by 1 slot.
• - Change Edges
• - Move row (i1), , row numVertices-1 up by 1
  row.
• - Decrement indices gt i in Edges
• - Delete i from its neighbors adjacencies.

class myNewGraph String Vertices int
Edges // different from before int numVertices,
numEdges