F - LCS

Problem Statement

You are given strings $\mathrm{ss}$ and $\mathrm{tt}$. Find one longest string that is a subsequence of both $\mathrm{ss}$ and $\mathrm{tt}$.

Notes

A subsequence of a string $\mathrm{xx}$ is the string obtained by removing zero or more characters from $\mathrm{xx}$ and concatenating the remaining characters without changing the order.

Constraints

• $\mathrm{ss}$ and $\mathrm{tt}$ are strings consisting of lowercase English letters.
• $\mathrm{1\le |s|,|t|\le 30001\le |s|,|t|\le 3000}$

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Input

Input is given from Standard Input in the following format:

$\mathrm{ss}$
$\mathrm{tt}$

Output

Print one longest string that is a subsequence of both $\mathrm{ss}$ and $\mathrm{tt}$. If there are multiple such strings, any of them will be accepted.

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Sample Input 1 Copy

Copy

axyb
abyxb

Sample Output 1 Copy

Copy

axb

The answer is axb or ayb; either will be accepted.

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Sample Input 2 Copy

Copy

aa
xayaz

Sample Output 2 Copy

Copy

aa

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Sample Input 3 Copy

Copy

a
z

Sample Output 3 Copy

Copy

The answer is  (an empty string).

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Sample Input 4 Copy

Copy

abracadabra
avadakedavra

Sample Output 4 Copy

Copy

aaadara

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <queue>
#include <map>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <deque>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#define ll              long long
#define PII             pair<int, int>
#define rep(i,a,b)      for(int  i=a;i<=b;i++)
#define dec(i,a,b)      for(int  i=a;i>=b;i--)
using namespace std;
int dir[4][2] = { { 0,1 } ,{ 0,-1 },{ 1,0 },{ -1,0 } };
const long long INF = 0x7f7f7f7f7f7f7f7f;
const int inf = 0x3f3f3f3f;
const double pi = 3.14159265358979323846;
const double eps = 1e-6;
const int mod =1e9+7;
const int N = 1e5+5;
//if(x<0 || x>=r || y<0 || y>=c)

inline ll read()
{
    ll x = 0; bool f = true; char c = getchar();
    while (c < '0' || c > '9') { if (c == '-') f = false; c = getchar(); }
    while (c >= '0' && c <= '9') x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
    return f ? x : -x;
}
ll gcd(ll m, ll n)
{
    return n == 0 ? m : gcd(n, m % n);
}
ll lcm(ll m, ll n)
{
    return m * n / gcd(m, n);
}
bool prime(int x) {
    if (x < 2) return false;
    for (int i = 2; i * i <= x; ++i) {
        if (x % i == 0) return false;
    }
    return true;
}
ll qpow(ll m, ll k, ll mod)
{
    ll res = 1, t = m;
    while (k)
    {
        if (k & 1)
            res = res * t % mod;
        t = t * t % mod;
        k >>= 1;
    }
    return res;
}      

int main()
{
    string s, t;
    cin >> s >> t;
    vector<vector<int>> a(s.size() + 1, vector<int>(t.size() + 1));
    rep(i, 1, s.size())
    {
        rep(j, 1, t.size())
        {
            if (s[i - 1] == t[j - 1])
            {
                a[i][j] = a[i - 1][j - 1] + 1;
            }
            else
            {
                a[i][j] = max(a[i - 1][j], a[i][j - 1]);
            }
        }
    }
    int j = t.size(),i=s.size();
    vector<char> res;
    while (j > 0 && i > 0)
    {
        while (j>0 && a[i][j] == a[i][j - 1])
            j--;
        while (i>0 && a[i][j] == a[i - 1][j])
            i--;
        if(i>0)
            res.push_back(s[i-1]);
        i--, j--;
    }
    for (int i = res.size() - 1; i >= 0; i--)
        cout << res[i];
    return 0;
}