Комбинаторика

//1
#include <iostream>
#include <vector>

using namespace std;

int factorial[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};

vector<int> getPermutation(int n, long long k) {
    vector<int> permutation(n);
    vector<bool> used(n + 1);

    for (int i = 0; i < n; i++) {
        int usedPermutations = (k - 1) / factorial[n - i - 1] + 1;
        int j = 1, position = 0;

        for (; j < n + 1; j++) {
            if (!used[j])
                position++;
            if (usedPermutations == position)
                break;
        }
        permutation[i] = j;
        used[j] = true;
        k = (k - 1) % factorial[n - 1 - i] + 1;
    }
    return permutation;
}

int main() {
    int n, k;
    cin >> n >> k;
    auto answer = getPermutation(n, k);
    for (auto &i : answer)
        cout << i << ' ';
    return 0;
}

// 2
#include <iostream>
#include <vector>

using namespace std;


vector<int> combination;

void printCombination() {
    for (int i: combination)
        cout << i << ' ';
    cout << '\n';
}

void nextCombination(int i, int n, int k) {
    if (k == 0) {
        printCombination();
        return;
    }
    for (; i <= n - k; i++) {
        combination.push_back(i + 1);
        nextCombination(i + 1, n, k - 1);
        combination.pop_back();
    }
}

int main() {
    int n, k;
    cin >> n >> k;

    nextCombination(0, n,  k);

    return 0;
}

//3
#include <iostream>
#include <vector>
using namespace std;

int placement_amount(int n, int m) {
    int res = 1;
    for (int i = n; i >= n - m + 1; i--)
        res *= i;
    return res;
}

void genPlacementByNum(int m, int n, int k, vector<int> &placement) {
    vector<bool> used(n);
    int _n = n - 1, _k = k - 1;
    for (int i = 0; i < k; i++) {
        int block_cnt = m / placement_amount(_n, _k);
        m -= block_cnt * placement_amount(_n, _k);
        int position = 0;
        block_cnt++;
        while (block_cnt) {
            if (!used[position])
                --block_cnt;
            position++;
        }
        used[position - 1] = true;
        placement[i] = position;
        _n--; _k--;
    }
}


    int main() {
        int n, k, m;
        cin >> n;
        cin >> k;
        cin >> m;
        vector<int> ans(k);
        genPlacementByNum(m - 1, n, k, ans);

        for (auto &i : ans)
            cout << i << ' ';
        return 0;
    }