JAVA算法：最长重复子序列（JAVA）

JAVA算法：最长重复子序列（JAVA）

Longest Repeating Subsequence
Given a string, find length of the longest repeating subseequence such that the two subsequence don’t have same string character at same position, i.e., any i’th character in the two subsequences shouldn’t have the same index in the original string.

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算法设计

package com.bean.algorithm.basic;

public class LongestRepeatingSubsequence {
	// Function to find the longest repeating subsequence
	static int findLongestRepeatingSubSeq(String str) {
		int n = str.length();

		// Create and initialize DP table
		int[][] dp = new int[n + 1][n + 1];

		// Fill dp table (similar to LCS loops)
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) {
				// If characters match and indexes are not same
				if (str.charAt(i - 1) == str.charAt(j - 1) && i != j)
					dp[i][j] = 1 + dp[i - 1][j - 1];

				// If characters do not match
				else
					dp[i][j] = Math.max(dp[i][j - 1], dp[i - 1][j]);
			}
		}
		return dp[n][n];
	}

	// driver program to check above function
	public static void main(String[] args) {
		String str = "aabb";
		System.out.println("The length of the largest subsequence that" + " repeats itself is : "
				+ findLongestRepeatingSubSeq(str));
	}
}

程序运行结果：

The length of the largest subsequence that repeats itself is : 2

另外一种算法设计——递归算法 Recursion

package com.bean.algorithm.basic;

import java.util.Arrays;

public class LongestRepeatingSubsequence2 {
	static int dp[][] = new int[1000][1000];

	// This function mainly returns LCS(str, str)
	// with a condition that same characters at
	// same index are not considered.
	static int findLongestRepeatingSubSeq(char X[], int m, int n) {

		if (dp[m][n] != -1) {
			return dp[m][n];
		}

		// return if we have reached the end of either string
		if (m == 0 || n == 0) {
			return dp[m][n] = 0;
		}

		// if characters at index m and n matches
		// and index is different
		if (X[m - 1] == X[n - 1] && m != n) {
			return dp[m][n] = findLongestRepeatingSubSeq(X, m - 1, n - 1) + 1;
		}

		// else if characters at index m and n don't match
		return dp[m][n] = Math.max(findLongestRepeatingSubSeq(X, m, n - 1), findLongestRepeatingSubSeq(X, m - 1, n));
	}

	// Longest Repeated Subsequence Problem
	static public void main(String[] args) {
		String str = "aabb";
		int m = str.length();
		for (int[] row : dp) {
			Arrays.fill(row, -1);
		}
		System.out.println("The length of the largest subsequence that" + " repeats itself is : "
				+ findLongestRepeatingSubSeq(str.toCharArray(), m, m));

	}
}

程序运行结果：

The length of the largest subsequence that repeats itself is : 2