is longest common subsequence np complete code example

Example 1: longest common subsequence codefroces

#include<bits/stdc++.h>
using namespace std;

const int MAX = 1001;

int dp[MAX][MAX];
bool visited[MAX][MAX];
int x, y;
string s1, s2;

int lcs(int i, int j)
{
    if(i == x || j == y)
        return 0;

    if(visited[i][j])
        return dp[i][j];

    visited[i][j] = true;
    int ans = 0;
    if(s1[i] == s2[j])
    {
        ans = max(ans, 1+lcs(i+1, j+1));
    }
    else
    {
        ans = max(ans, lcs(i+1, j));
        ans = max(ans, lcs(i, j+1));
    }

    dp[i][j] = ans;
    return ans;
}

int main()
{
    cin >> x >> y;
    cin >> s1 >> s2;

    for(int i=0; i<=x; i++)
    {
        for(int j=0; j<=y; j++)
        {
            visited[i][j] = false;
        }
    }

    cout << lcs(0, 0);
    return 0;
}

Example 2: longest increasing subsequence when elements hae duplicates

#include <iostream>
#include <algorithm>
using namespace std;
 
// define maximum possible length of X and Y
#define N 20
 
// lookup[i][j] stores the length of LCS of subarray X[0..i-1], Y[0..j-1]
int lookup[N][N];
 
// Function to find LCS of array X[0..m-1] and Y[0..n-1]
void LCS(int X[], int Y[], int m, int n)
{
    // return if we have reached the end of either array
    if (m == 0 || n == 0)
        return;
 
    // if last element of X and Y matches
    if (X[m - 1] == Y[n - 1])
    {
        LCS(X, Y, m - 1, n - 1);
        cout << X[m - 1] << " ";
        return;
    }
    // else when the last element of X and Y are different
 
    if (lookup[m - 1][n] > lookup[m][n - 1])
        LCS(X, Y, m - 1, n);
    else
        LCS(X, Y, m, n - 1);
}
 
// Function to find length of Longest Common Subsequence of
// array X[0..m-1] and Y[0..n-1]
void findLCS(int X[], int Y[], int m, int n)
{
    // first row and first column of the lookup table
    // are already 0 as lookup[][] is globally declared
 
    // fill the lookup table in bottom-up manner
    for (int i = 1; i <= m; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            // if current element of X and Y matches
            if (X[i - 1] == Y[j - 1])
                lookup[i][j] = lookup[i - 1][j - 1] + 1;
 
            // else if current element of X and Y don't match
            else
                lookup[i][j] = max(lookup[i - 1][j], lookup[i][j - 1]);
        }
    }
 
    // find longest common sequence
    LCS(X, Y, m, n);
}
 
// Function to remove duplicates from a sorted array
int removeDuplicates(int X[], int n)
{
    int k = 0;
    for (int i = 1; i < n; i++)
        if (X[i] != X[k])
            X[++k] = X[i];
 
    // return length of sub-array containing all distinct characters
    return k + 1;
}
 
// Iterative function to find length of longest increasing subsequence (LIS)
// of given array using longest common subsequence (LCS)
void findLIS(int X[], int n)
{
    // create a copy of the original array
    int Y[n];
    for (int i = 0; i < n; i++)
        Y[i] = X[i];
 
    // sort the copy of the original array
    sort(Y, Y + n);
 
    // remove all the duplicates from Y
    int m = removeDuplicates (Y, n);
 
    // perform LCS of both
    findLCS(X, Y, n, m);
}
 
// Longest Increasing Subsequence using LCS
int main()
{
    int X[] = { 100,1,100,1,100 };
    int n = sizeof(X)/sizeof(X[0]);
 
    cout << "The LIS is ";
    findLIS(X, n);
 
    return 0;
}