最长公共子序列（LCS）问题

#include <iostream>
#define N 1000
using namespace std;

//c[i][j]存储str1[1...i]与str2[1...j]的最长公共子序列的长度
int c[N][N];
//flag[i][j]标记是那种子问题
//flag[i][j]==0为str1[i]==str2[j]
//flag[i][j]==1为c[i-1][j]>=s[i][j-1]
//flag[i][j]==-1为c[i-1][j]<s[i][j-1]
int flag[N][N];

int getLCSlength(string str1, string str2)
{
    int len1 = str1.size();
    int len2 = str2.size();
    for (int i = 0; i <= len1; i++)
    {
        for (int j = 0; j <= len2; j++)
        {
            if (i == 0 || j == 0)
                c[i][j] = 0;
            else if (str1[i - 1] == str2[j - 1])
            {
                c[i][j] = c[i - 1][j - 1] + 1;
                flag[i][j] = 0;
            }
            else if (c[i - 1][j] >= c[i][j - 1]){
                c[i][j] = c[i - 1][j];
                flag[i][j] = 1;
            }
            else{
                c[i][j] = c[i][j - 1];
                flag[i][j] = -1;
            }
        }
    }
    return c[len1][len2];
}

void getLCS(string s1, string s2,int len,string &lcs)
{
    int i = s1.size();
    int j = s2.size();
    while(i&&j)
    {
        if(flag[i][j]==0)
        {
            lcs[--len] = s1[i-1];
            i--;
            j--;
        }
        else if(flag[i][j]==1) //往上
            i--;
        else if(flag[i][j]==-1)//往左
            j--;
    }

}

int main()
{
    string str1,str2,lcs;

    cout<<"请输入字符串1："<<endl;
    cin>>str1;
    cout<<"请输入字符串2："<<endl;
    cin>>str2;

    int lcsLen = getLCSlength(str1,str2);
    cout<<"最长公共子序列长度："<<lcsLen<<endl;


    getLCS(str1,str2,lcsLen,lcs);
    cout<<"最长公共子序列为：";
    for(int i=0;i<lcsLen;i++)
        cout<<lcs[i];
    return 0;
}