hdu 4468 spy(KMP应用，5级）

1. Introduction

HDU 4468 is a problem that involves the application of the Knuth-Morris-Pratt (KMP) algorithm. The problem requires the implementation of the KMP algorithm to find a specific string pattern within a given text string. This problem falls under the difficulty level of 5.

2. Problem Statement

The problem statement of HDU 4468 revolves around the concept of espionage. In this scenario, there is a spy who needs to decode a secret message hidden within a text. The spy knows the pattern of the secret message, but it is hidden within a large text string. The objective is to find the starting positions of all occurrences of the pattern within the text.

2.1 Example

As an example, consider the following:

Text: ABCABACDABCABABC

Pattern: ABC

In this case, the pattern "ABC" can be found at positions 1, 8, 12, and 15 within the text string. The expected output would be:

1 8 12 15

3. Solution Approach

The solution to this problem involves using the KMP algorithm. The KMP algorithm is a string-matching algorithm that finds the starting positions of occurrences of a pattern within a text. It uses pre-processing to create a table, known as the "failure function", which helps in skipping unnecessary comparisons.

3.1 KMP Algorithm

The KMP algorithm can be summarized in the following steps:

Pre-process the pattern to create the failure function.

Iterate over the text string while matching characters with the pattern.

When a mismatch occurs, use the failure function to determine the next position to compare.

Continue until all occurrences of the pattern are found.

3.2 Implementation

Below is a Python implementation of the KMP algorithm for solving the HDU 4468 problem:

def compute_failure_function(pattern):

    failure_function = [0] * len(pattern)
    k = 0
    for q in range(1, len(pattern)):
        while k > 0 and pattern[k] != pattern[q]:
            k = failure_function[k - 1]
        if pattern[k] == pattern[q]:
            k += 1
        failure_function[q] = k
    return failure_function
def kmp_search(text, pattern):
    failure_function = compute_failure_function(pattern)
    indices = []
    n = len(text)
    m = len(pattern)
    q = 0
    for i in range(n):
        while q > 0 and pattern[q] != text[i]:
            q = failure_function[q - 1]
        if pattern[q] == text[i]:
            q += 1
        if q == m:
            indices.append(i - m + 1)
            q = failure_function[q - 1]
    return indices
text = "ABCABACDABCABABC"
pattern = "ABC"
print(kmp_search(text, pattern))

4. Complexity Analysis

The KMP algorithm has a time complexity of O(m + n), where m is the length of the pattern and n is the length of the text. This is because the algorithm iterates over the text string once, and at each position, it makes at most one comparison with the pattern. The preprocessing step to compute the failure function takes O(m) time.

5. Conclusion

In conclusion, HDU 4468 is a problem that requires the implementation of the KMP algorithm to find the starting positions of all occurrences of a pattern within a given text. The KMP algorithm is an efficient string-matching algorithm that leverages pre-processing to achieve a time complexity of O(m + n). By using the KMP algorithm, the spy in this problem can successfully decode the secret message hidden within the text.