Hi! I'm pretty new to competitive programming and right now having some trouble with a pretty straight forward problem.

I just can't seem to grasp why my solution to the problem 1773E keeps getting time limit exceeded, I have already check the resolution and as far as I'm aware it is meant to be O(nlogn), did I made some mistake on the data structures used, or is it just way to slow of a solution ?

As far as I could tell the one that I had implemented was O(nlogn), but I could be way off.

code:

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

int check_sorted(vector<int> tower, vector<int> nums, unordered_map<int, int> pos) {
    int not_sorted = 0;
    for(int i = 0; i < tower.size() - 1; i++){
        int next_pos = pos[tower[i]] + 1;
        if (tower[i + 1] != nums[next_pos]) { not_sorted++; }
    }
    return not_sorted;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    cin >> n;
    vector<vector<int>> towers(n);
    vector<int> nums;
    for(int j = 0; j < n; j++) {
        int k;
        cin >> k;
        for (int i = 0; i< k; i++){
            int num;
            cin >> num;
            towers[j].push_back(num);
            nums.push_back(num);
        }
    }
    unordered_map<int, int> pos;
    sort(nums.begin(), nums.end());
    for (int i = 0; i < nums.size(); i++){
        pos[nums[i]] = i;
    }
    int not_sorted = 0;
    for (int i = 0; i < n; i++){
        not_sorted += check_sorted(towers[i], nums, pos);
    }
    int split = not_sorted;
    int combine = n + not_sorted - 1;
    cout << split << " " << combine << endl;
}