可能对于相同的字符串对有不同的最长公共子序列?

huangapple go评论152阅读模式
英文:

Possible to have different Longest Common Subsequence for same pair of Strings?

问题

private static String[][] memo; // memoization

public static String lcsMemoized(String[] p, String[] q, int pLen, int qLen) {
    String result = "";
    // base case
    if (pLen == 0 || qLen == 0) return "";
    else if (memo[pLen][qLen] != null) return memo[pLen][qLen];
    else if (p[pLen - 1].equals(q[qLen - 1])) {
        // common last character
        result = lcsMemoized(p, q, pLen - 1, qLen - 1) + p[pLen - 1];
    } else {
        String op1 = lcsMemoized(p, q, pLen - 1, qLen);
        String op2 = lcsMemoized(p, q, pLen, qLen - 1);
        if (op2.length() > op1.length()) result = op2;
        else result = op1;
    }
    memo[pLen][qLen] = result;
    return result;
}

请注意,上述代码仅为翻译,可能无法执行,因为它依赖于您提供的上下文和其他代码部分。

英文:

I have two input strings:

String1 = 3 9 8 3 9 7 9 7 0<br>
String2 = 3 3 9 9 9 1 7 2 0

Now, If I assess Left-To-Right, then LCS obtained : 3 3 9 9 7 0<br>
But, If I assess Right-To-Left, then another possible LCS: 3 9 9 9 7 0

Here's a picture to explain it (hopefully) better:

可能对于相同的字符串对有不同的最长公共子序列?

I wanted to understand if this is normal, or am I making a mistake ?

my code for generating LCS is below, which gives the Right-To-Left scenario output:

private static String[][] memo; // memoization

public static String lcsMemoized(String[] p, String[] q, int pLen, int qLen) {
    String result = &quot;&quot;;
    // base case
    if (pLen == 0 || qLen == 0) return &quot;&quot;;
    else if (memo[pLen][qLen] != null) return memo[pLen][qLen];
    else if (p[pLen - 1].equals(q[qLen - 1])) {
        // common last character
        result = lcsMemoized(p, q, pLen - 1, qLen - 1) + p[pLen - 1];
    } else {
        String op1 = lcsMemoized(p, q, pLen - 1, qLen);
        String op2 = lcsMemoized(p, q, pLen, qLen - 1);
        if (op2.length() &gt; op1.length()) result = op2;
        else result = op1;
    }
    memo[pLen][qLen] = result;
    return result;
}

答案1

得分: 0

可以完全可能有两个或更多的最长公共子序列。
一个简单的例子:1231和1321都有两个最长公共子序列:121和131。

英文:

It's perfectly possible to have two or more LCS.
A trivial example: 1231 and 1321 have 2 LCS: 121 and 131.

答案2

得分: 0

不仅可以有多个最长公共子序列(LCS),而且可能有很多个。考虑长度为 2m 的字符串,1 2 1 2 1 2 ... 1 2,以及另一个相同长度的字符串,2 1 2 1 2 1 ... 2 1。这两个字符串的最长公共子序列数量为 2^m!

英文:

Not only can there be multiple LCSs, there can be many. Consider the string of length 2m, 1 2 1 2 1 2 ... 1 2 and another string of the same length, 2 1 2 1 2 1 ... 2 1. The two of these have <code>2<sup>m</sup></code> LCSs!

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  • 本文由 发表于 2020年7月23日 21:24:38
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