#include <iostream>
#include <vector>
#include <list>
#include <stdint.h>
#include <assert.h>
using namespace std;
const uint64_t max_k = 1000000000000000000ULL;
static vector<vector<uint64_t>> I;
static uint64_t count(uint32_t n, uint64_t k);
void precompute(uint32_t n)
{
if (I.empty()) {
I.push_back({});
I.push_back({});
I.push_back({});
I.push_back({1,2});
}
for (uint32_t i = I.size(); i <= n; i++) {
uint64_t K = i*(i-1)/4 + 1;
I.push_back({});
vector<uint64_t> &new_row = I[i];
uint64_t sum = 0;
uint32_t j;
for (j = 0; j < K; j++) {
sum += count(i-1, j);
if (sum > max_k) break;
if (j >= i) sum -= count(i-1, j-i);
new_row.push_back(sum);
}
}
}
uint64_t count(uint32_t n, uint64_t k)
{
if (k==0) return 1;
if (k==1) return n == 0 ? 0 : n - 1;
uint64_t x = uint64_t(n)*(n-1)/2;
if (k > x) return 0;
if (k > x/2) k = x - k;
assert(k <= x/2);
precompute(n);
auto &R = I[n];
return k < R.size() ? R[k] : max_k + 1;
}
vector<int> kth_stable_n_permutation(uint32_t n, uint64_t k)
{
vector<int> R;
uint64_t pairs = uint64_t(n)*(n-1)/2;
if (pairs % 2 != 0) return {};
uint64_t i = pairs/2;
vector<int> A;
bool remove = false;
uint32_t remove_from = 0, remove_to = 0;
for (uint32_t j=1; j<=n; j++) A.push_back(j);
uint32_t N = n;
while (N) {
assert(A.size() == N + (remove ? remove_to - remove_from + 1 : 0));
uint32_t j_end = N;
if (i + 1 < j_end) j_end = i + 1;
uint64_t x = uint64_t(N-1)*(N-2)/2;
uint32_t j = 0;
if (i > x) j = i - x;
for (; j < j_end; j++) {
uint64_t dk = count(N-1, i-j);
if (dk >= k) {
if (!remove) {
R.push_back(A[j]);
remove_from = remove_to = j;
remove = true;
} else {
uint32_t J = j;
if (j >= remove_from) J += remove_to - remove_from + 1;
assert(J < A.size());
R.push_back(A[J]);
if (J == remove_from - 1) {
remove_from = J;
} else if (J == remove_to + 1) {
remove_to = J;
} else {
A.erase(A.begin() + remove_from, A.begin() + remove_to + 1);
remove_from = remove_to = j;
}
}
N--;
i -= j;
break;
}
k -= dk;
}
if (j == j_end) return {};
}
assert(R.size() == n);
return R;
}
int main()
{
uint32_t n;
uint64_t k;
cin >> n >> k;
assert(1 <= n);
assert(n <= 250000);
assert(1 <= k);
assert(k <= max_k);
vector<int> P = kth_stable_n_permutation(n, k);
if (P.empty()) {
cout << "NIE" << endl;
} else {
cout << "TAK" << endl;
for (size_t i = 0; i < P.size()-1; i++) {
cout << P[i] << " ";
}
cout << P.back() << endl;
}
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 | #include <iostream> #include <vector> #include <list> #include <stdint.h> #include <assert.h> using namespace std; const uint64_t max_k = 1000000000000000000ULL; static vector<vector<uint64_t>> I; static uint64_t count(uint32_t n, uint64_t k); void precompute(uint32_t n) { if (I.empty()) { I.push_back({}); I.push_back({}); I.push_back({}); I.push_back({1,2}); } for (uint32_t i = I.size(); i <= n; i++) { uint64_t K = i*(i-1)/4 + 1; I.push_back({}); vector<uint64_t> &new_row = I[i]; uint64_t sum = 0; uint32_t j; for (j = 0; j < K; j++) { sum += count(i-1, j); if (sum > max_k) break; if (j >= i) sum -= count(i-1, j-i); new_row.push_back(sum); } } } uint64_t count(uint32_t n, uint64_t k) { if (k==0) return 1; if (k==1) return n == 0 ? 0 : n - 1; uint64_t x = uint64_t(n)*(n-1)/2; if (k > x) return 0; if (k > x/2) k = x - k; assert(k <= x/2); precompute(n); auto &R = I[n]; return k < R.size() ? R[k] : max_k + 1; } vector<int> kth_stable_n_permutation(uint32_t n, uint64_t k) { vector<int> R; uint64_t pairs = uint64_t(n)*(n-1)/2; if (pairs % 2 != 0) return {}; uint64_t i = pairs/2; vector<int> A; bool remove = false; uint32_t remove_from = 0, remove_to = 0; for (uint32_t j=1; j<=n; j++) A.push_back(j); uint32_t N = n; while (N) { assert(A.size() == N + (remove ? remove_to - remove_from + 1 : 0)); uint32_t j_end = N; if (i + 1 < j_end) j_end = i + 1; uint64_t x = uint64_t(N-1)*(N-2)/2; uint32_t j = 0; if (i > x) j = i - x; for (; j < j_end; j++) { uint64_t dk = count(N-1, i-j); if (dk >= k) { if (!remove) { R.push_back(A[j]); remove_from = remove_to = j; remove = true; } else { uint32_t J = j; if (j >= remove_from) J += remove_to - remove_from + 1; assert(J < A.size()); R.push_back(A[J]); if (J == remove_from - 1) { remove_from = J; } else if (J == remove_to + 1) { remove_to = J; } else { A.erase(A.begin() + remove_from, A.begin() + remove_to + 1); remove_from = remove_to = j; } } N--; i -= j; break; } k -= dk; } if (j == j_end) return {}; } assert(R.size() == n); return R; } int main() { uint32_t n; uint64_t k; cin >> n >> k; assert(1 <= n); assert(n <= 250000); assert(1 <= k); assert(k <= max_k); vector<int> P = kth_stable_n_permutation(n, k); if (P.empty()) { cout << "NIE" << endl; } else { cout << "TAK" << endl; for (size_t i = 0; i < P.size()-1; i++) { cout << P[i] << " "; } cout << P.back() << endl; } return 0; } |
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