Longest_Increasing_Subsequence (LIS)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

#define MAX_N 20
#define EMPTY_VALUE -1

int mem[MAX_N];
int next_index[MAX_N];

int f(int i, vector<int> &A) {
    if (mem[i] != EMPTY_VALUE) {
        return mem[i];
    }

    int ans = 0;
    for (int j = i + 1; j < A.size(); j++) {
        if (A[j] > A[i]) {
            int subResult = f(j, A);
            if (subResult > ans) {
                ans = subResult;
                next_index[i] = j;
            }
        }
    }

    mem[i] = ans + 1;
    return mem[i];
}

vector<int> findLIS(vector<int> A) {
    int ans = 0;

    for (int i = 0; i < A.size(); i++) {
        mem[i] = EMPTY_VALUE;
        next_index[i] = EMPTY_VALUE;
    }

    int start_index = -1;

    for (int i = 0; i < A.size(); i++) {
        int result = f(i, A);
        if (result > ans) {
            ans = result;
            start_index = i;
        }
    }

    vector<int> lis;
    while (start_index != -1) {
        lis.push_back(A[start_index]);
        start_index = next_index[start_index];
    }
    return lis;
}

int main() {
    vector<int> input;
    int n, val;

    cout << "Enter the number of elements: ";
    cin >> n;

    cout << "Enter the elements: ";
    for (int i = 0; i < n; i++) {
        cin >> val;
        input.push_back(val);
    }

    vector<int> lis = findLIS(input);

    cout << "Longest Increasing Subsequence: ";
    for (int num : lis) {
        cout << num << " ";
    }
    cout << endl;
    cout << "Length of LIS: " << lis.size() << endl;

    return 0;
}