【模板】最长相同子序列

/*
LCS

BDCABA
ABCBDAB

dp[1][2] = 1
dp[1][1] = 0
dp[2][1] = 0

//子串：连续
//子序列：可以不连续 
// LCS

dp[i][j]//第一个字符串在第i个字符前且第二个串在第j个字符前可构成的最长子序列的长度 

dp[i][j] =             0                          i=0 || j=0
                dp[i-1][j-1]+1             str1[i]==str2[j]
            max(dp[i-1][j],dp[i][j-1])     str1[i]!=str2[j]
*/
#include<cstdio>
#include<cstring>
#include<stack>
#include<algorithm>
using namespace std;
int main()
{
    char str1[20];
    char str2[20];
    scanf ("%s %s",str1+1,str2+1);
    str1[0] = str2[0] = '0';
    int l1 = strlen(str1)-1;
    int l2 = strlen(str2)-1;
    int dp[20][20] = {0};//0                          i=0 || j=0
    
    for (int i = 1 ; i <= l1 ; i++)
    {
        for (int j = 1 ; j <= l2 ; j++)
        {
            if (str1[i] == str2[j])//dp[i-1][j-1]+1             str1[i]==str2[j]
                dp[i][j] = dp[i-1][j-1] + 1;
            else
                dp[i][j] = max(dp[i-1][j],dp[i][j-1]);//max(dp[i-1][j],dp[i][j-1])     str1[i]!=str2[j]
        }
    }
    
    //回溯求LCS 
    int pos1 = l1;
    int pos2 = l2;
    stack<char> S;
    while (pos1 > 0 && pos2 > 0)
    {
        if (str1[pos1] == str2[pos2])
        {
            S.push(str1[pos1]);
            pos1--;
            pos2--;
        }
        else if (dp[pos1-1][pos2] > dp[pos1][pos2-1])
            pos1--;
        else
            pos2--;
    }
    while (!S.empty())
    {
        printf ("%c%c",S.top(),(S.size() == 1) ? '
' : ' ');
        S.pop();
    }
    printf ("%d
",dp[l1][l2]);
    return 0;
}