前言：最近快到FDS考试了，po重刷了一下学校的题目，自己整理了一些解析orz 因为po在自己找解析和学习的过程中非常痛苦，所以在此共享一下我的题目和自己写的解题思路，欢迎各位指出错误~全章节预计会陆续更新，可在专栏查看~

HW7

1. In Union/Find algorithm, if Unions are done by size, the depth of any node must be no more than N/2, but not O(logN).

 F 深度最大为（log2N）+1。 

2. The array representation of a disjoint set（不相交集） containing numbers 0 to 8 is given by { 1, -4, 1, 1, -3, 4, 4, 8, -2 }. Then to union the two sets which contain 6 and 8 (with union-by-size), the index of the resulting root and the value stored at the root are: 

A.1 and -6

B.4 and -5

C.8 and -5

D.8 and -6

B；注意并查集的表示方法；把小的集合合并在大的集合上

3. A relation R is defined on a set S. If for every element e in S, "e R e" is always true, then R is said to be __ over S.

A.consistent

B.symmetric

C.transitive

D.reflexive

D

(Reflexive自反性) a R a, for all a ∈ S.

(Symmetric) a R b if and only if b R a.

(Transitive) a R b and b R c implies that a R c.

4.Let T be a tree created by union-by-size with N nodes, then the height of T can be . 

A.at most log2​(N)+1

B.at least log2​(N)+1

C.as large as N

D.anything that is greater than 1

A；见题2

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