CareerCup

You can solve this as quickly as you can read the list of prisoners and the list of friends (O(n)).

Each prisoner has an individual danger score (ids) which is known and a net danger score (nds) which is unknown. Thus

class prisoner{
	int ids
	int nds
	void prisoner(int danger){
		ids=danger
		nds=danger
	}
}

Friendship is symmetric. Thus every time you find out "A is friends with B" you simply do A.nds+=B.ids and B.nds+=A.ids. Every time you do this, see if either A.nds or B.nds is greater than the current record for "highest nds.

Book-keeping note: The friendship list may contain redundant information. Eg finding out "A is friends with B and B is friends with A will cause you to add their scores twice. A fortiori if everything is redundantly listed then this algo will still find the most dangerous prisoner, but everyone's nds will be inflated 2x.

Time Complexity: O(n)

When some node is visted then compute net danger rank(NDR) and also add current node individual rank in the friend node net danger rank(NDR) then remove current node from the friendslist of friend .

for eg: if A has friends B and C
then acc to transitivity B also has friend A......
When you visit A then compute NDR of A with the help of its friends and also add A's IDR in B's NDR and remove A node from B's Friend List. So need of visiting A again while computing NDR for B.

public class PrisionerVO {
	
	private int idr;
	private int ndr;
	
	private List<Character> friendList;

	public int getNdr() {
		return ndr;
	}

	public void setNdr(int ndr) {
		this.ndr = ndr;
	}

	public int getIdr() {
		return idr;
	}

	public void setIdr(int idr) {
		this.idr = idr;
	}

	public List<Character> getFriendList() {
		return friendList;
	}

	public void setFriendList(List<Character> friendList) {
		this.friendList = friendList;
	}
	
	@Override
	public String toString() {
		
		return "\tIndividual Danger Rank:"+ idr +"\nNet Danger Rank:" + ndr+ "\nFriend List:"+ friendList+"\n---------------\n\n";
	}
	
}

public Character computerMaxDangerRank(Map<Character,PrisionerVO> prisionerMap){
		Set<Character> keySet = prisionerMap.keySet();
		
		int maxDR = 0;
		Character maxDRPrisioner = null;
		//key is prisionerName
		for(Character key:keySet){
			PrisionerVO currPrisioner = prisionerMap.get(key);
			List<Character> friendList = currPrisioner.getFriendList();
			
			//idr is individual danger rank
			int idr = currPrisioner.getIdr();
			
			//ndr is net danger rank of a prisioner
			int ndr = idr;
			if(friendList!=null && friendList.size()!=0)
			{
				for(Character friend:friendList){
					PrisionerVO friendPrisioner = prisionerMap.get(friend);	
					
					friendPrisioner.setNdr(friendPrisioner.getNdr()+idr);
					//adding friend idr current ndr
					ndr= ndr +  friendPrisioner.getIdr();
					//removing the current node from the friends list 
					friendPrisioner.getFriendList().remove(key);
					//i++;
				}
			}
			ndr = ndr + currPrisioner.getNdr();
			currPrisioner.setNdr(ndr);				
			
			if(ndr>maxDR){
				maxDR=ndr;
				maxDRPrisioner = key;
			}
		}
		
		return maxDRPrisioner;
	}

The time complexity is not actually O(n^2). Its O(VE) where V = # of vertices (or the prisoners in this case) and E = # of edges (friendship between prisoners). There is no better way that visiting each vertex(prisoner) and each edge(friendship) to solve this.