最长回文子序列（算法导论15-2

贴代码，总觉得这个和LCS十分的神似，特别是递推式，除了打印答案的判断那边要把m[i][j] == m[i + 1][j - 1] + 2换成s[i]==s[j]。考虑"noni"的情况，m[0][3]==m[1][2]+2,然而并不是打印s[0]和s[3]，所以应该限制条件为s[i]==s[j],这样还少打了几下键盘（逃

palindrome_dp.h

#pragma once

#include <string>
#include <vector>
#include <algorithm>

using std::string;
using std::vector;
using std::max;

void palindrome_ans(const string &s, vector<vector<int> > &m, int i, int j);

void palindrome_dp(const string &s)
{
    const int n = s.size();
    if (n == 0)throw("empty string");
    vector<vector<int> > m(n, vector<int>(n, 0));
    //边界情况
    for (int i = 1;i < n;i++)
        m[i - 1][i] = 0;
    for (int i = 0;i < n;i++)
        m[i][i] = 1;

    for(int l=2;l<=n;l++)
        for (int i = 0;i < n - l + 1;i++)
        {
            int j = i + l - 1;
            if (s[i] == s[j])
                m[i][j] = m[i + 1][j - 1] + 2;
            else
                m[i][j] = max(m[i + 1][j], m[i][j - 1]);
        }
    std::cout << m[2][n - 2] << endl;
    palindrome_ans(s, m, 0, n - 1);
}

void palindrome_ans(const string &s, vector<vector<int> > &m, int i, int j)
{
    if (i > j)return;
    if (i == j)
    {
        std::cout << s[i];
        return;
    }

    if (s[i] == s[j])//m[i][j] == m[i + 1][j - 1] + 2是不行的，s[i]=s[j]的限制条件更强
    {
        std::cout << s[i];
        palindrome_ans(s, m, i + 1, j - 1);
        std::cout << s[j];
    }
    else if (m[i][j] == m[i + 1][j])
        palindrome_ans(s, m, i + 1, j);
    else
        palindrome_ans(s, m, i, j - 1);
}

#include "PalindromeDp.h"

int main(void) {
    palindrome_dp("character");
    palindrome_dp("nowayiton");
    return 0;
}