#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
typedef long long ll;
const int N = 2.5e5 + 5;
const ll inf = 1ll << 60;
using namespace std;
vector<ll> dp[N];
set<int> num;
ll size[N], k;
int n;
ll count(int n, ll k) {
if (k < 0 || k > size[n]) return 0;
k = min(k, (ll)size[n] - k);
if (k >= dp[n].size()) return inf + inf;
else return dp[n][k];
}
int main() {
scanf("%d%lld", &n, &k);
for (int i = 1; i <= n; i++) {
size[i] = (ll)i * (i - 1) / 2;
}
dp[0]= dp[1] = vector<ll> {1};
for (int i = 2; i <= n; i++) {
ll tmp = 0;
for (int j = 0; j <= size[i]; j++) {
tmp += count(i - 1, j) - count(i - 1, j - i);
if (tmp > inf) break;
dp[i].push_back(tmp);
}
}
if (size[n] % 2 != 0 || count(n, size[n] / 2) < k) {
puts("NIE");
return 0;
}
puts("TAK");
ll m = size[n] / 2;
for (int i = 1; i <= n; i++) num.insert(i);
for (int i = n - 1; i >= 0; i--) {
ll rem = size[i];
for (int j = max(0ll, m - rem); j <= i; j++) {
ll tmp = count(i, m - j);
if (tmp < k) k -= tmp;
else {
m -= j;
auto it = num.begin();
if (2 * j < i + 1) {
for (int k = 0; k < j; k++) ++it;
} else {
it = num.end();
for (int k = j; k <= i; k++) --it;
}
printf("%d ", *it);
num.erase(it);
break;
}
}
}
puts("");
}
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 | #include <cstdio> #include <cstdlib> #include <cstring> #include <iostream> #include <algorithm> #include <vector> #include <set> typedef long long ll; const int N = 2.5e5 + 5; const ll inf = 1ll << 60; using namespace std; vector<ll> dp[N]; set<int> num; ll size[N], k; int n; ll count(int n, ll k) { if (k < 0 || k > size[n]) return 0; k = min(k, (ll)size[n] - k); if (k >= dp[n].size()) return inf + inf; else return dp[n][k]; } int main() { scanf("%d%lld", &n, &k); for (int i = 1; i <= n; i++) { size[i] = (ll)i * (i - 1) / 2; } dp[0]= dp[1] = vector<ll> {1}; for (int i = 2; i <= n; i++) { ll tmp = 0; for (int j = 0; j <= size[i]; j++) { tmp += count(i - 1, j) - count(i - 1, j - i); if (tmp > inf) break; dp[i].push_back(tmp); } } if (size[n] % 2 != 0 || count(n, size[n] / 2) < k) { puts("NIE"); return 0; } puts("TAK"); ll m = size[n] / 2; for (int i = 1; i <= n; i++) num.insert(i); for (int i = n - 1; i >= 0; i--) { ll rem = size[i]; for (int j = max(0ll, m - rem); j <= i; j++) { ll tmp = count(i, m - j); if (tmp < k) k -= tmp; else { m -= j; auto it = num.begin(); if (2 * j < i + 1) { for (int k = 0; k < j; k++) ++it; } else { it = num.end(); for (int k = j; k <= i; k++) --it; } printf("%d ", *it); num.erase(it); break; } } } puts(""); } |
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