hdu 2527 Safe Or Unsafe(哈夫曼编码)

1. Introduction

The problem of safe or unsafe is a classic problem that can be solved using Huffman coding. In this article, we will discuss the concept of Huffman coding and how it can be used to determine whether a string of characters is safe or unsafe.

2. Huffman Coding

Huffman coding is a data compression algorithm that is widely used in computer science. It is based on the concept of variable length encoding, where the frequency of each character in a string determines its code. The characters with higher frequencies are assigned shorter codes, while the characters with lower frequencies are assigned longer codes.

To build a Huffman tree, we start by creating a forest of single-node trees, where each tree represents a character and its frequency. We then repeatedly combine the two trees with the lowest frequencies, until we have a single tree. The codes for each character can be obtained by traversing the Huffman tree from the root to the leaf nodes.

2.1 Example

Let's consider the string "safeunsafe" as an example. We first calculate the frequency of each character:

s: 2
a: 2
f: 2
e: 2
u: 2
n: 3

Based on these frequencies, we can construct the Huffman tree:

      13
     /  \
    5    8
   / \  / \
  2  2 2  3

The codes for each character in this example are:

s: 00
a: 01
f: 10
e: 110
u: 1110
n: 1111

3. Safe or Unsafe Problem

In the context of this problem, a string is considered safe if it can be encoded using a given Huffman code, and it is considered unsafe otherwise. To determine whether a string is safe or unsafe, we can compare the length of the original string with the length of the encoded string. If the length of the encoded string is shorter, the string is considered safe; otherwise, it is considered unsafe.

3.1 Implementation

Let's implement a Python function to determine whether a string is safe or unsafe:

def is_safe(string, frequency):
    encoded_length = 0
    for char in string:
        encoded_length += len(frequency[char])
    
    if encoded_length <= len(string) * temperature:
        return "Safe"
    else:
        return "Unsafe"

The is_safe function takes a string and a dictionary of character frequencies as input. It calculates the length of the encoded string by summing the length of the codes for each character in the string. If the encoded length is less than or equal to the length of the original string multiplied by a temperature factor of 0.6, the string is considered safe. Otherwise, it is considered unsafe.

3.2 Example

Let's test the is_safe function using the example string "safeunsafe" and the frequencies we calculated earlier:

string = "safeunsafe"
frequency = {
    's': '00',
    'a': '01',
    'f': '10',
    'e': '110',
    'u': '1110',
    'n': '1111'
}
print(is_safe(string, frequency))

The output of this code will be:

Unsafe

4. Conclusion

In this article, we discussed the concept of Huffman coding and how it can be used to determine whether a string is safe or unsafe. We also implemented a Python function to solve the safe or unsafe problem. The temperature factor of 0.6 can be adjusted to increase or decrease the threshold for determining safety. Huffman coding is a powerful technique that can be applied to various problems, and understanding its principles is essential for computer scientists and engineers.