2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 599d15309e88c813a40baf58
|
2020-12-16 07:37:30 +00:00
|
|
|
|
title: 熵
|
2018-10-10 22:03:03 +00:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --description--
|
|
|
|
|
|
|
|
|
|
任务:
|
|
|
|
|
|
|
|
|
|
计算给定输入字符串的香农熵H.
|
|
|
|
|
|
|
|
|
|
给定谨慎的随机变量$ X $,它是$ N $“符号”(总字符)的字符串,由$ n $个不同的字符组成(对于二进制,n = 2),位/符号中X的香农熵是:
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
$ H*2(X)= - \\ sum* {i = 1} ^ n \\ frac {count_i} {N} \\ log_2 \\ left(\\ frac {count_i} {N} \\ right)$
|
|
|
|
|
|
|
|
|
|
其中$ count_i $是字符$ n_i $的计数。
|
|
|
|
|
|
|
|
|
|
# --hints--
|
|
|
|
|
|
|
|
|
|
`entropy`是一种功能。
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
assert(typeof entropy === 'function');
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("0")`应该返回`0`
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
```js
|
|
|
|
|
assert.equal(entropy('0'), 0);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("01")`应该返回`1`
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert.equal(entropy('01'), 1);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("0123")`应该返回`2`
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
assert.equal(entropy('0123'), 2);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("01234567")`应该返回`3`
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
```js
|
|
|
|
|
assert.equal(entropy('01234567'), 3);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("0123456789abcdef")`应返回`4`
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
```js
|
|
|
|
|
assert.equal(entropy('0123456789abcdef'), 4);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`entropy("1223334444")`应返回`1.8464393446710154`
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert.equal(entropy('1223334444'), 1.8464393446710154);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
2020-08-13 15:24:35 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --solutions--
|
|
|
|
|
|