Question 4
I am running an instance of a Disjoint data structure, which is to the right.
I do a bunch of operations on it, and when I call Print(), it prints the
following:
Elts: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Links: -1 0 -1 2 0 2 2 2 0 5 2 -1 -1 17 17 11 17 2 17 17
Ranks: 2 1 3 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1
Answer the following questions:
- A: How many disjoint sets did I start with when I first started running the program?
- B: How many disjoint sets are there now?
- C: How many times has Union() been called?
- D: Union-by-size is most definitely not the implementation here. Why?
- E: What are the sizes of each set?
- F: Suppose I want to prove that the implementation uses path compression.
I can do that by calling either Union() or Find(), and then
Print(). Tell me which call it is (Union() or Find()), what the
parameter(s) should be, and how the Print() statement will prove whether path
compression is being implemented. I want specifics here, not vague junk
like "call Union() on two sets and the ranks fields will tell you
whether path compression is being used." That answer is a zero.
|
#include <vector>
#include <iostream>
#include <cstdio>
using namespace std;
class Disjoint {
public:
Disjoint(int nelements);
int Union(int s1, int s2);
int Find(int element);
void Print();
protected:
vector <int> links;
vector <int> ranks;
};
|
|