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### COS 226 Exercises on Union-Find

**1. **
[Exercise 1.5, revised]
Draw the resulting tree after running the quick-union algorithm (Program 1.2)
on the sequence:
0-2, 1-4, 2-5, 3-6, 0-4, 6-0, 1-3

Caveat: your tree should be produced exactly as in Program 1.2, so don't
interchange the roles of i and j.

**2. **
Can the following `id[]` array result when running weighted quick
union without path compression? Explain why this is impossible or
give a sequence of operations which results in this array.

0 0 1 2 4 4 4 5 3 1 0

Hint: refer to Property 1.3.