Longest palindrome subsequence

最新推荐文章于 2019-12-19 12:33:42 发布

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最新推荐文章于 2019-12-19 12:33:42 发布

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原文链接：http://www.cnblogs.com/shengguang/p/8440098.html

本文介绍了一种高效算法，用于查找给定输入字符串中的最长回文子序列，并提供了具体的实现代码示例。通过动态规划的方法，该算法能有效地解决这一问题。

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A palindrome is a nonempty string over some alphabet that reads the same forward
and backward. Examples of palindromes are all strings of length 1, civic,
racecar, and aibohphobia (fear of palindromes).
Give an efficient algorithm to find the longest palindrome that is a subsequence
of a given input string. For example, given the input character, your algorithm
should return carac. What is the running time of your algorithm?

struct Palindrome {
    std::string strPalindrome;
    std::string strFront;
    std::string strEnd;
};

using VectorOfVectorOfIntermediate = std::vector<std::vector<Palindrome>>;

std::string findLongestPalindrome(const std::string &strInput) {
    VectorOfVectorOfIntermediate vecVecIntermediate = VectorOfVectorOfIntermediate(strInput.size(), std::vector<Palindrome>(strInput.size() + 1));
    for ( int i = 0; i < strInput.size(); ++ i ) {
        vecVecIntermediate[i][1].strPalindrome = strInput[i];
        vecVecIntermediate[i][1].strFront = "";
        vecVecIntermediate[i][1].strEnd = "";
    }

    for ( int i = 0; i < strInput.size() - 1; ++ i ) {
        if ( strInput[i] == strInput[i + 1 ]) {
            vecVecIntermediate[i][2].strPalindrome = strInput.substr(i, 2 );
            vecVecIntermediate[i][2].strFront = "";
            vecVecIntermediate[i][2].strEnd = "";
        }else {
            vecVecIntermediate[i][2].strPalindrome = strInput[i];
            vecVecIntermediate[i][2].strEnd = strInput[i+1];
        }
    }

    for ( int L = 3; L <= strInput.size(); L += 1 ) {
        for ( int n = 0; n <= strInput.size() - L; ++ n ) {
            size_t findPos;

            Palindrome p2 = vecVecIntermediate[n][L-1];
            p2.strEnd.push_back ( strInput[n + L - 1] );
            findPos = p2.strFront.find_first_of ( p2.strEnd );
            if ( findPos != std::string::npos) {
                auto charFind = p2.strFront[findPos];
                p2.strPalindrome.insert ( p2.strPalindrome.begin(), charFind );
                p2.strPalindrome.push_back ( charFind );
                p2.strFront = p2.strFront.substr ( 0, findPos );
                findPos = p2.strEnd.find ( charFind );
                p2.strEnd = p2.strEnd.substr ( findPos + 1 );
            }

            Palindrome p3 = vecVecIntermediate[n+1][L-1];
            p3.strFront.insert ( p3.strFront.begin(), strInput[n] );
            findPos = p3.strFront.find_first_of ( p3.strEnd );
            if ( findPos != std::string::npos) {
                auto charFind = p3.strFront[findPos];
                p3.strPalindrome.insert ( p3.strPalindrome.begin(), charFind );
                p3.strPalindrome.push_back ( charFind );
                p3.strFront = p3.strFront.substr ( 0, findPos );
                findPos = p3.strEnd.find ( charFind );
                p3.strEnd = p3.strEnd.substr ( findPos + 1 );
            }

            std::vector<Palindrome> vecP{p2, p3};
            int nMaxIndex = 0;
            for ( int index = 1; index < vecP.size(); ++ index ) {
                if ( vecP[index].strPalindrome.length() > vecP[nMaxIndex].strPalindrome.length() ) {
                    nMaxIndex = index;
                }
            }
            vecVecIntermediate[n][L] = vecP[nMaxIndex];
        }
    }
    return vecVecIntermediate[0][strInput.size()].strPalindrome;
}

void Test_findLongestPalindrome()
{
    {
        std::string strTestCase("a");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("aa");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("ab");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("abbac");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("abcdefghijkjhgfed");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("character");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }

    {
        std::string strTestCase("GEEKS FOR GEEKS");
        auto strPalindrome = findLongestPalindrome ( strTestCase );
        std::cout << "Test case " << strTestCase << ", result " << strPalindrome << std::endl;
    }
}