动态规划求最长公共子序列源程序

参考算法导论，得出源程序如下：

//
//动态规划法求最长公共子序列，参考算法导论15.4
//


#include<iostream>
#include <vector>

using namespace std;

void lcs_length(const vector<char>& X, const vector<char>& Y,
                vector<vector<int> >& c, vector<vector<char> >& b)
                //X[1..m],Y[1..n],c[0..m,0..n],b[1..m][1..n]，故要经过相应的转换
{
    int i=0,j=0;
    int m = X.size();
    int n = Y.size();
    for (i=1; i<=m; ++i)
        c[i][0] = 0;
    for (j=0; j<=n; ++j)
        c[0][j] = 0;
    for (i=1; i<=m; ++i)
        for (j=1; j<=n; ++j)
        {
            if (X[i-1] == Y[j-1])
            {
                c[i][j] = c[i-1][j-1]+1;
                b[i-1][j-1] = 'x';
            } 
            else if (c[i-1][j] >= c[i][j-1])
            {
                c[i][j] = c[i-1][j];
                b[i-1][j-1] = 'u';
            }
            else
            {
                c[i][j] = c[i][j-1];
                b[i-1][j-1] = 'l';
            }
        }
}

void print_lcs(const vector<vector<char> >& b, const vector<char> X, 
               int i, int j)
{
    if (-1==i ||0 ==-1)
        return;
    if ('x' == b[i][j])
    {
        print_lcs(b,X,i-1,j-1);
        cout << X[i];
    }
    else if ('u' == b[i][j])
        print_lcs(b,X,i-1,j);
    else
        print_lcs(b,X,i,j-1);

}

int main()
{
    vector<char> X, Y;
    vector<vector<int> > c;
    vector<vector<char> >b; //注意，这里两个尖括号之间要有空格，不然会被认为是符号">>"
    int i=0, j=0, m=0, n=0;
    cin >> m >> n;
    X.resize(m);
    Y.resize(n);
    b.resize(m);
    c.resize(m+1);
    cout << "input the element of X" << endl;
    for (i=0; i<m; ++i)
    {
        cin >> X[i];
        b[i].resize(n);
        c[i].resize(n+1);
    }
    c[m].resize(n+1);
    cout << "input the element of Y" << endl;
    for (i=0; i<n; ++i)
        cin >> Y[i];
    lcs_length(X,Y,c,b);
    for (i=0; i<=m; ++i){
        for (j=0; j<=n; ++j)
            cout << c[i][j] <<' ';
        cout << endl;
    }
    cout << endl;
    for (i=0; i<m; ++i){
        for (j=0; j<n; ++j)
            cout << b[i][j] <<' ';
        cout << endl;
    }
    print_lcs(b,X,m-1,n-1);
    cout << endl;
    return 0;
}