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由权值分别为3，8，6，2，5的叶子结点生成一棵哈夫曼树，它的带权路径长度为（）。

由权值分别为3，8，2，4，3的叶子结点生成一棵哈夫曼树，它的带权路径长度为（）。

由权值分别为8，4，6，5，7的叶子结点生成一棵哈夫曼树，它的带权路径长度为（）。

为五个使用频率不同的字符设计哈夫曼编码，下列方案中哪个不可能是哈夫曼编码？

一段文本中包含对象{a,b,c,d,e}，其出现次数相应为{3,2,4,2,1}，则经过哈夫曼编码后，该文本所占总位数为：

在图中给定的红黑树中插入 1，哪些结点的颜色会改变？
（含图）

向一棵初始为空的红黑树中顺序插入 41; 38; 31; 12; 19; 8，则关于最终得到的红黑树，下列句子中哪句是错的？

The array representation of a disjoint set 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:

已知不相交集合用数组表示为{ 4, 6, 5, 2, -3, -4, 3 }。若集合元素从1到7编号，则调用Union(Find(7),Find(1))（按规模求并，并且带路径压缩）后的结果数组为：

The array representation of a disjoint set 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:

已知不相交集合用数组表示为{ 4, 6, 5, 2, -3, -4, 3 }。若集合元素从1到7编号，则调用Union(Find(7),Find(1))（按规模求并，并且带路径压缩）后的结果数组为：

The array representation of the disjoint sets is given by { 2, –4, 2, 2, -3, 5, 6, 9, -2 }. Keep in mind that the elements are numbered from 1 to 9. After invoking Union(Find(7), Find(9)) with union-by-size, which elements will be changed in the resulting array?

In a disjoint set problem, given a set of m elements S = { 1, 2, 3, ..., m } and n ( 0<n<m ) distinct relations, the set S must have __ equivalence classes.

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

在并查集问题中，已知集合元素0~8所以对应的父结点编号值分别是{ 1, -4, 1, 1, -3, 4, 4, 8, -2 }（注：−n表示树根且对应集合大小为n），那么将元素0和8所在的集合合并（要求必须将小集合并到大集合）后，该集合对应的树根和父结点编号值分别是多少？

已知a、b两个元素均是所在集合的根结点，且分别位于数组分量3和2位置上，其parent值分别为-3,-2。问：将这两个集合按集合大小合并后，a和b的parent值分别是多少？

The array representation of the disjoint sets is given by { 3, 1, -5, 2, 1, -3, -1, 6, 6 }. Keep in mind that the elements are numbered from 1 to 9. After invoking Union(Find(4), Find(8)) with union-by-size, which elements will be changed in the resulting array?

The array representation of the disjoint sets is given by { 4, 1, 2, -5, 1, -3, 9, -1, 6 }. Keep in mind that the elements are numbered from 1 to 9. After invoking Union(Find(3), Find(7)) with union-by-size, which elements will be changed in the resulting array?

In a weighted graph, if the length of the shortest path from b to a is 10, and there exists an edge of weight 3 between c and b, then how many of the following statements is/are TRUE?

The length of the shortest path from c to a must be 13.

The length of the shortest path from c to a must be 7.

The length of the shortest path from c to a must be no greater than 13.

The length of the shortest path from c to a must be no less than 7.

若要求在找到从S到其他顶点最短路的同时，还给出不同的最短路的条数，我们可以将Dijkstra算法略作修改，增加一个count[]数组：count[V]记录S到顶点V的最短路径有多少条。则count[V]应该被初始化为：

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