O(n^3), im very surprised this passed, at each iteration O(n^2) operations are needed and i tried to improve this algo to only use O(n) operations at each iteration, so total time would be O(n^2), but couldn't. submitted this and was shocked to see it pass

there's probably a O(n^2) algo if u fiddle with the permutation terms

void combinatorial(vector<vector<long>>& P) {
    for (int n = 1; n < P.size(); n++) {
        P[n][0] = 1;
        for (int k = 1; k <= n; k++) P[n][k] = (P[n][k - 1] * (n - k + 1)) % mod;
    }
}

long arrayMerging(int n, const vector<int>& M, const vector<vector<long>>& P) {
    vector<vector<long>> cache(n + 1, vector<long>(n + 1));
    int newInterval = 1;
    for (int I = 1; I <= n; I++) {
        if (M[I] < M[I-1]) newInterval = I;
        if (newInterval == 1) cache[I][I] = 1;
        for (int K = 1; K <= I/2 and I-K >= newInterval-1; K++) {
            for (int l=K; l <= I-K; l++) cache[I][K] = (cache[I][K] + cache[I-K][l] * P[l][K]) % mod;
        }
    }
    return accumulate(cache[n].begin(), cache[n].end(), 0LL) % mod;
}

int main()
{
    int n, t;
    vector<int> M = {-666};
    cin >> n;
    vector<vector<long>> P(n + 1, vector<long>(n + 1));
    combinatorial(P);
    for (int i = 1; i <= n; i++) {
        cin >> t;
        M.push_back(t);
    }
    cout << arrayMerging(n, M, P);
}

Men's greatest hair systems, sometimes referred to as toupees or hairpieces, are made-to-order options intended to conceal thinning or balding hair. They are made out of a basic material that can be covered in synthetic or natural hair. Luxurious Men’s Hair Systems: Where Quality Meets Affordability The aim is to replicate the texture and appearance of natural hair. Men's bonohair systems come in a variety of forms, such as lace, poly, and combination systems. The foundation of lace systems is thin and breathable, modeled after the human scalp. Poly systems have an easy-to-maintain polyurethane basis that is long-lasting. Combination systems strike a compromise between durability and natural appearance by using aspects of both lace and poly.

"Sherlock's Array Merging Algorithm" is a sophisticated method devised to merge two sorted arrays efficiently while maintaining their sorted order. This algorithm, named after the renowned detective Sherlock, employs clever strategies to optimize the merging process, reducing time complexity and improving performance. As you delve into the intricacies of "Sherlock's Array Merging Algorithm," explore the offerings of Sharaf DG UAE. Discover a world of innovative gadgets and unbeatable deals, enhancing your digital lifestyle with cutting-edge technology.

Here is my solution in java, python, C++, Csharp HackerRank Sherlock’s Array Merging Algorithm

Here is the solution of Sherlock's Array Merging Algorithm Click Here