Discuss in detail the difference between the sliding window algorithm and the KMP algorithm and the scenarios in which they are used.

What is the sliding window algorithm

The sliding window algorithm is an algorithm for solving subarray (or substring) problems within an array (or string). The algorithm works by maintaining a fixed-size window (usually two pointers) that slides over the array to find subarrays that match specific criteria. The basic idea of the algorithm is to traverse the entire array by adjusting the start and end positions of the window to find subarrays that meet specific conditions. This window is usually continuous, but the exact implementation can vary depending on the requirements of the problem.

General steps of sliding window algorithm

The general steps of the sliding window algorithm are as follows:

  1. Initialization: Define two pointers, usually representing the starting position (left) and end position (right) of the window, and initialize them.

  2. Sliding window: Move the right pointer until a condition is met. This condition can be determined according to the specific problem, such as finding a subarray that meets the requirements or reaching a certain state.

  3. Adjust window size: When the right pointer moves to a certain position, if the condition is met, try to reduce the window size, that is, move the left pointer until the condition is no longer met.

  4. Repeat operation: Repeat steps 2 and 3 until the entire array is traversed.

The sliding window algorithm is usually used to solve some optimization problems, such as finding the shortest subarray in an array so that it meets specific conditions, or finding the shortest substring in a string that contains all the characters in the target substring. The time complexity of this algorithm is usually lower because it avoids unnecessary repeated calculations.

How is the sliding window algorithm implemented?

Below I will take a specific problem as an example to demonstrate how to implement the sliding window algorithm using Java code. We take “finding the longest substring without repeated characters in a string” as an example to implement the sliding window algorithm.

import java.util.HashMap;

public class LongestSubstringWithoutRepeating {

    public static int lengthOfLongestSubstring(String s) {
        if (s == null || s.length() == 0) {
            return 0;
        }

        // Used to store characters and their positions in the string
        HashMap<Character, Integer> map = new HashMap<>();
        int maxLength = 0;
        int left = 0;

        for (int right = 0; right < s.length(); right + + ) {
            char currentChar = s.charAt(right);

            // If the character is already in the window, update the position of the left pointer
            if (map.containsKey(currentChar)) {
                left = Math.max(map.get(currentChar) + 1, left);
            }

            //Update character position
            map.put(currentChar, right);

            //Update maximum length
            maxLength = Math.max(maxLength, right - left + 1);
        }

        return maxLength;
    }

    public static void main(String[] args) {
        String input = "abcabcbb";
        int result = lengthOfLongestSubstring(input);
        System.out.println(result); // Output 3 (the corresponding non-repeating character substring is "abc")
    }
}

The above code implements finding the length of the longest substring without repeated characters in a string. The core is to maintain a window, use left and right pointers to represent the left and right boundaries of the window, continuously adjust the size of the window by traversing the string, and use a hash table to record each The last occurrence of a character to enable fast lookup and updates.

What is KMP algorithm

The KMP (Knuth-Morris-Pratt) algorithm is a string matching algorithm used to find the occurrence position of a pattern string in a text string. Its main feature is that whenmatching fails, it can use the partial matching results that have been obtained to avoid unnecessary comparisons, thereby improving matching efficiency.

The core idea of the KMP algorithm is to construct a partial match table (Partial Match Table), also known as the “next array”, which is used to guide jumps in the matching process. This table records the length of the longest equal prefix and suffix for each prefix in the pattern string. By utilizing this table during the matching process, the algorithm can quickly adjust the position of the pattern string when the match fails and continue matching without backtracking to previous positions in the text string.

Basic steps of KMP algorithm

  1. Build a partial match table: Traverse the pattern string, and for each position, find the length of the longest equal prefix and suffix, and record this length in the partial match table.

  2. Matching process: In the process of matching text strings and pattern strings, when the matching fails, the position of the pattern string is adjusted according to the value in the partial matching table and the matching continues.

The time complexity of the KMP algorithm is O(m + n), where m is the length of the pattern string and n is the length of the text string. Compared with the O(mn) complexity of the brute force matching algorithm, the KMP algorithm is more efficient when processing large-scale text strings and pattern strings.

public class KMPAlgorithm {

    public static int[] buildNext(String pattern) {
        int[] next = new int[pattern.length()];
        int j = 0;

        for (int i = 1; i < pattern.length(); i + + ) {
            while (j > 0 & amp; & amp; pattern.charAt(i) != pattern.charAt(j)) {
                j = next[j - 1];
            }

            if (pattern.charAt(i) == pattern.charAt(j)) {
                j + + ;
            }

            next[i] = j;
        }

        return next;
    }

    public static int kmpSearch(String text, String pattern) {
        int[] next = buildNext(pattern);
        int j = 0;

        for (int i = 0; i < text.length(); i + + ) {
            while (j > 0 & amp; & amp; text.charAt(i) != pattern.charAt(j)) {
                j = next[j - 1];
            }

            if (text.charAt(i) == pattern.charAt(j)) {
                j + + ;
            }

            if (j == pattern.length()) {
                return i - j + 1; // Match successful, return to starting position
            }
        }

        return -1; // No match found
    }

    public static void main(String[] args) {
        String text = "ABABCABAB";
        String pattern = "ABAB";
        int result = kmpSearch(text, pattern);
        System.out.println(result); // Output 2
    }
}

In this example, the buildNext method is used to build a partial matching table, while the kmpSearch method implements the matching process of the KMP algorithm.

What is the difference between the two

Application scenarios and implementation principles are somewhat different

  1. Sliding window algorithm:

    • Application scenario: It is mainly used to solve substring problems, that is, to find a continuous substring in a string that meets specific conditions.
    • Implementation principle: By maintaining a variable-size window that slides on the string, while adjusting the size of the window according to the requirements of the problem. This algorithm usually traverses the entire string using two pointers, one pointing to the start of the window and the other pointing to the end of the window.
    • Example application: Minimum covering substring, longest substring without repeating characters, etc.

  2. KMP algorithm (Knuth-Morris-Pratt algorithm):

    • Application scenario: Mainly used to find the occurrence position of a pattern string in a text string.
    • Implementation principle: The KMP algorithm uses the matched information in the pattern string to avoid unnecessary backtracking. It guides the jumps in the matching process by building a partial match table (Partial Match Table). This table records the length of the longest equal prefix and suffix for each prefix of the pattern string.
    • Example app: Find keywords in text and more in a text editor.

Difference:

  • Problem type: The sliding window algorithm is mainly used for substring problems, while the KMP algorithm is mainly used for pattern matching problems.
  • Implementation principle: The sliding window algorithm solves the problem by maintaining a sliding window on the string, while the KMP algorithm uses the constructed partial matching table to optimize the pattern matching process.
  • Application scenarios: The sliding window algorithm is more suitable for continuous substring matching problems, while the KMP algorithm is more suitable for finding the position of pattern strings in text.

Overall, although the sliding window algorithm and the KMP algorithm have different application scenarios, they are both effective tools for solving specific problems in the field of string processing. The choice of which algorithm to use depends on the specific problem requirements.