hdu 5.2.7 1053 Entropy
哎哟。。标题就看不懂这是闹哪样。。不如先来学习下单词吧。。
entropy 熵
glyph 象形文字
prefix-free 无前缀
欧克，上题：
Entropy |
| Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) |
| Total Submission(s): 71 Accepted Submission(s): 41 |
|
Problem Description
An entropy encoder is a data encoding method that achieves lossless data compression by encoding a message with “wasted” or “extra” information removed. In other words, entropy encoding removes information that was not necessary in the first place to accurately encode the message. A high degree of entropy implies a message with a great deal of wasted information; english text encoded in ASCII is an example of a message type that has very high entropy. Already compressed messages, such as JPEG graphics or ZIP archives, have very little entropy and do not benefit from further attempts at entropy encoding.
English text encoded in ASCII has a high degree of entropy because all characters are encoded using the same number of bits, eight. It is a known fact that the letters E, L, N, R, S and T occur at a considerably higher frequency than do most other letters in english text. If a way could be found to encode just these letters with four bits, then the new encoding would be smaller, would contain all the original information, and would have less entropy. ASCII uses a fixed number of bits for a reason, however: it’s easy, since one is always dealing with a fixed number of bits to represent each possible glyph or character. How would an encoding scheme that used four bits for the above letters be able to distinguish between the four-bit codes and eight-bit codes? This seemingly difficult problem is solved using what is known as a “prefix-free variable-length” encoding. In such an encoding, any number of bits can be used to represent any glyph, and glyphs not present in the message are simply not encoded. However, in order to be able to recover the information, no bit pattern that encodes a glyph is allowed to be the prefix of any other encoding bit pattern. This allows the encoded bitstream to be read bit by bit, and whenever a set of bits is encountered that represents a glyph, that glyph can be decoded. If the prefix-free constraint was not enforced, then such a decoding would be impossible. Consider the text “AAAAABCD”. Using ASCII, encoding this would require 64 bits. If, instead, we encode “A” with the bit pattern “00”, “B” with “01”, “C” with “10”, and “D” with “11” then we can encode this text in only 16 bits; the resulting bit pattern would be “0000000000011011”. This is still a fixed-length encoding, however; we’re using two bits per glyph instead of eight. Since the glyph “A” occurs with greater frequency, could we do better by encoding it with fewer bits? In fact we can, but in order to maintain a prefix-free encoding, some of the other bit patterns will become longer than two bits. An optimal encoding is to encode “A” with “0”, “B” with “10”, “C” with “110”, and “D” with “111”. (This is clearly not the only optimal encoding, as it is obvious that the encodings for B, C and D could be interchanged freely for any given encoding without increasing the size of the final encoded message.) Using this encoding, the message encodes in only 13 bits to “0000010110111”, a compression ratio of 4.9 to 1 (that is, each bit in the final encoded message represents as much information as did 4.9 bits in the original encoding). Read through this bit pattern from left to right and you’ll see that the prefix-free encoding makes it simple to decode this into the original text even though the codes have varying bit lengths. As a second example, consider the text “THE CAT IN THE HAT”. In this text, the letter “T” and the space character both occur with the highest frequency, so they will clearly have the shortest encoding bit patterns in an optimal encoding. The letters “C”, “I’ and “N” only occur once, however, so they will have the longest codes. There are many possible sets of prefix-free variable-length bit patterns that would yield the optimal encoding, that is, that would allow the text to be encoded in the fewest number of bits. One such optimal encoding is to encode spaces with “00”, “A” with “100”, “C” with “1110”, “E” with “1111”, “H” with “110”, “I” with “1010”, “N” with “1011” and “T” with “01”. The optimal encoding therefore requires only 51 bits compared to the 144 that would be necessary to encode the message with 8-bit ASCII encoding, a compression ratio of 2.8 to 1. |
|
Input
The input file will contain a list of text strings, one per line. The text strings will consist only of uppercase alphanumeric characters and underscores (which are used in place of spaces). The end of the input will be signalled by a line containing only the word “END” as the text string. This line should not be processed.
|
|
Output
For each text string in the input, output the length in bits of the 8-bit ASCII encoding, the length in bits of an optimal prefix-free variable-length encoding, and the compression ratio accurate to one decimal point. |
|
Sample Input
AAAAABCD THE_CAT_IN_THE_HAT END |
|
Sample Output
64 13 4.9 144 51 2.8 |
依旧是朴素的哈夫曼。长长的题目就是让我知道了具体哈夫曼的应用。。
别处拷贝来的中文说明：
假设有一段电文，其中用到 4 个不同字符A, C, S, T，它们在电文中出现的次数分别为 8 ， 2 ， 4 ， 5 。把 8， 2 ， 4 ， 5 当做 4 个叶子的权值构造哈夫曼树如下图所示。在树中令所有左分支取编码为 0 ，令所有右分支取编码为1。将从根结点起到某个叶子结点路径上的各左、右分支的编码顺序排列，就得这个叶子结点所代表的字符的二进制编码，j结果如下图所示。
这些编码拼成的电文不会混淆，因为每个字符的编码均不是其他编码的前缀，这种编码称做前缀编码。关于信息编码是一个复杂的问题，还应考虑其他一些因素。比如前缀编码每个编码的长度不相等，译码时较困难。还有检测、纠错问题都应考虑在内。这里仅对哈夫曼树举了一个应用实例。
真是很有趣啊……到底是怎么想到这么神奇的东西的呢？
试了一下通过回忆（喂！）自己打了一遍哈夫曼的构造。瞄了前一题两次，无编译错（之前题抄还抄错两次- -），一次通过，还挺开心的~
和前题几乎一样的代码- -。。。
#include
#include
#include
using namespace std;
struct{
int weight;
int parent;
int left;
int right;
}node[60];
int main()
{
char ch[100000];
int hash[35];
int i,j,k;
int len;
while(cin>>ch,strcmp(ch,"END")!=0)
{
memset(hash,0,sizeof(hash));
len=strlen(ch);
for(i=0;i 小困惑是。。cout没法儿规范小数点后几位么？不得不用printf了。。。不过printf用起来确实比cout舒服。。。
过年了。奇怪的大年二十九。新的一年要努力。要保持好的心态。要相信自己会变好看，会码代码，会赢得妹子芳心的。无论发生什么都不要自虐了，如果不开心宁可去骚扰妹子吧。虽然可能会被烦……不过无节操这么久了，随意吧。会好好的。即使是末日，也要好好的度过之前的每一天。平凡的快乐的充实的每一天。