动态规划求解最长公共子序列

#include<iostream>
#include<algorithm>
using namespace std;
void Print_LCS(int **b, string X,int m, int n);
void LCS_Length(string X, string Y)
{
    int m = X.length();
    int n = Y.length();
    X = "0" + X;
    Y = "0" + Y;
    int **b = new int*[m + 1];
    for (int i = 0; i < m + 1; i++)
    {
        b[i] = new int[n + 1];
    }
    int **c = new int*[m + 1];
    for (int i = 0; i < m + 1;i++)
    {
        c[i] = new int[n + 1];
    }
    for (int i = 1; i < m + 1; i++)
        c[i][0] = 0;
    for (int j = 0; j < n + 1; j++)
        c[0][j] = 0;
    for (int i = 1; i <= m; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            if (X.at(i) == Y.at(j))
            {
                c[i][j] = c[i - 1][j - 1] + 1;
                b[i][j] = 1;
            }    
            else if (c[i - 1][j]>=c[i][j - 1])
            {
                c[i][j] = c[i - 1][j];
                b[i][j] = 0;
            }
            else
            {
                c[i][j] = c[i][j - 1];
                b[i][j] = -1;
            }
        }
    }
    Print_LCS(b,X,m,n);
    cout << "\n";
}
void Print_LCS(int **b, string X,int m, int n)
{
    if (m == 0 || n == 0)
        return;
    if (b[m][n] == 1)
    {
        Print_LCS(b,X,m-1,n-1);
        cout << X.at(m)<< "  ";
    }
    else if (b[m][n] == 0)
    {
        Print_LCS(b,X, m - 1, n);
    }
    else
    {
        Print_LCS(b, X,m , n-1);
    }
}
//带有备忘的LCS_LENGTH
int LoopUp_LCS(string X, string Y, int **C,int m, int n)
{
    if (C[m][n] > -1)
        return C[m][n];
    if (m == 0 || n == 0)
        C[m][n] = 0;
    else
    {
        if (X.at(m - 1) == Y.at(n - 1))
            C[m][n] = LoopUp_LCS(X,Y,C,m-1,n-1) + 1;
        else
        {
            C[m][n] = max(LoopUp_LCS(X, Y, C, m - 1, n), LoopUp_LCS(X, Y, C, m, n-1));
        }
    }
    return C[m][n];
}
int**Memoized_LCS_Length(string X, string Y)
{
    int m = X.length();
    int n = Y.length();
    X = "0" + X;
    Y = "0" + Y;
    int **C = new int*[m + 1];
    for (int i = 0; i < m + 1; i++)
    {
        C[i] = new int[n + 1];
    }
    for (int i = 0; i < m + 1; i++)
    {
        for (int j = 0; j < n + 1; j++)
        {
            C[i][j] = -1;
        }
    }

    LoopUp_LCS(X,Y,C,m,n);
    return C;
}
//KMP

int *Compute2_Prefix_Function(string P,int m)
{
    int *t = new int[m + 1];
    t[1] = 0;
    int k = 0;
    for (int q = 2; q <= m; q++)
    {
        while (k > 0 && P[k + 1] != P[q])
            k = t[k];
        if (P[k + 1] == P[q])
            k = k + 1;
        t[q] = k;
    }
    for (int i = 1; i <= m; i++)
    {
        cout << t[i] << " ";
    }
    cout << "\n";
    return t;
}
void KMP2_Matcher(string T, string P)
{
    int n = T.length();
    int m = P.length();
    T = "0" + T;
    P = "0" + P;
    int *t = Compute2_Prefix_Function(P, m);
    int q = 0;
    for (int i = 1; i <= n; i++)
    {
        while (q > 0 && P[q + 1] != T[i])
            q = t[q];
        if (P[q + 1] == T[i])
            q = q + 1;
        if (q == m)
        {
            cout << "macther at " << i - m;
            q = t[q];
        }
    }
    cout << "\n";

}


int main()
{
    string X = "ABCBDAB";
    string Y = "BDCABA";
    LCS_Length(X,Y);
    int **C = Memoized_LCS_Length(X, Y);
    for (unsigned  i = 0; i < X.length() + 1; i++)
    {
        for (unsigned j = 0; j < Y.length(); j++)
        {
            cout << C[i][j] << "\t";
        }
        cout << "\n";
    }
    cout << "\n";
    X = "ababababbc";
    Y = "ababbc";
    KMP2_Matcher(X,Y);
    return 0;
}