05-树9 Huffman Codes

05-树9 Huffman Codes

In 1953, David A. Huffman published his paper "A Method for the Construction of Minimum-Redundancy Codes", and hence printed his name in the history of computer science. As a professor who gives the final exam problem on Huffman codes, I am encountering a big problem: the Huffman codes are NOT unique. For example, given a string "aaaxuaxz", we can observe that the frequencies of the characters 'a', 'x', 'u' and 'z' are 4, 2, 1 and 1, respectively. We may either encode the symbols as {'a'=0, 'x'=10, 'u'=110, 'z'=111}, or in another way as {'a'=1, 'x'=01, 'u'=001, 'z'=000}, both compress the string into 14 bits. Another set of code can be given as {'a'=0, 'x'=11, 'u'=100, 'z'=101}, but {'a'=0, 'x'=01, 'u'=011, 'z'=001} is NOT correct since "aaaxuaxz" and "aazuaxax" can both be decoded from the code 00001011001001. The students are submitting all kinds of codes, and I need a computer program to help me determine which ones are correct and which ones are not.

1953年，David A. Huffman发表了他的论文“构建最小冗余码的方法”，因此在计算机科学史上印刷了他的名字。 作为给霍夫曼代码提出期末考试问题的教授，我遇到了一个大问题：霍夫曼代码并不是唯一的。 例如，给定一个字符串“aaaxuaxz”，我们可以观察到字符“a”，“x”，“u”和“z”的频率分别为4,2,1和1。 我们可以将符号编码为{'a'= 0，'x'= 10，'u'= 110，'z'= 111}，或者换为{'a'= 1，'x'= 01 ，'u'= 001，'z'= 000}，都将字符串压缩为14位。 另一组代码可以给出{'a'= 0，'x'= 11，'u'= 100，'z'= 101}，但{'a'= 0，'x'= 01，'u '= 011，'z'= 001}不正确，因为“aaaxuaxz”和“aazuaxax”都可以从代码00001011001001解码。学生们正在提交各种代码，我需要一个计算机程序来帮助我确定哪个 一些是正确的，哪些不是。

Input Specification:

Each input file contains one test case. For each case, the first line gives an integer N (2≤N≤63), then followed by a line that contains all the N distinct characters and their frequencies in the following format:

每个输入文件包含一个测试用例。 对于每种情况，第一行给出整数N（2≤N≤63），然后是一行，其中包含所有N个不同的字符及其频率，格式如下：

c[1] f[1] c[2] f[2] ... c[N] f[N]

where c[i] is a character chosen from {'0' - '9', 'a' - 'z', 'A' - 'Z', '_'}, and f[i] is the frequency of c[i] and is an integer no more than 1000. The next line gives a positive integer M (≤1000), then followed by M student submissions. Each student submission consists of N lines, each in the format:

其中c [i]是从{'0' - '9'，'a' - 'z'，'A' - 'Z'，'_'}中选择的字符，而f [i]是c的频率 [i]并且是一个不超过1000的整数。下一行给出正整数M（≤1000），然后是M学生提交。 每个学生提交的内容都包括N行，每个的格式如下：

c[i] code[i]

where c[i] is the i-th character and code[i] is an non-empty string of no more than 63 '0's and '1's.

其中c [i]是第i个字符，code [i]是一个不超过63'0和'1'的非空字符串。

Output Specification:

For each test case, print in each line either "Yes" if the student's submission is correct, or "No" if not.

Note: The optimal solution is not necessarily generated by Huffman algorithm. Any prefix code with code length being optimal is considered correct.

对于每个测试用例，如果学生的提交正确，则在每行打印“是”，否则打印“否”。

注意：最优解不一定是由霍夫曼算法生成的。 任何代码长度最佳的前缀代码都被认为是正确的。

Sample Input:

7
A 1 B 1 C 1 D 3 E 3 F 6 G 6
4
A 00000
B 00001
C 0001
D 001
E 01
F 10
G 11
A 01010
B 01011
C 0100
D 011
E 10
F 11
G 00
A 000
B 001
C 010
D 011
E 100
F 101
G 110
A 00000
B 00001
C 0001
D 001
E 00
F 10
G 11

Sample Output:

Yes
Yes
No
No