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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#405562 | #7613. Inverse Problem | ucup-team3215 | AC ✓ | 1574ms | 28536kb | C++20 | 4.8kb | 2024-05-06 06:41:48 | 2024-05-06 06:41:51 |
Judging History
answer
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <numeric>
#include <vector>
using namespace std;
constexpr int mod = 1e9 + 7;
auto& mul(auto&& a, auto b) { return a = a * (uint64_t) b % mod; }
int inv(int a) { for (int r = 1, b = mod - 2; ; b /= 2, mul(a, a)) if (!b) return r; else if (b % 2) mul(r, a); }
using namespace std;
template <typename K, typename V, int mlf = 8>
struct HT {
int capacity;
vector<pair<K, int>> knx;
vector<V> values;
vector<int> head;
HT(): capacity{4 * mlf}, head(capacity, -1) {
}
void emplace(K k, V v) {
knx.push_back({k, head[k & capacity - 1]});
values.push_back(v);
head[k & capacity - 1] = knx.size() - 1;
maybe_rehash();
}
int find(K k) {
for (int i = head[k & capacity - 1]; ~i; i = knx[i].second) if (knx[i].first == k) return i;
return -1;
}
void clear() {
knx.clear();
values.clear();
head.assign(capacity, -1);
}
void maybe_rehash() {
if (knx.size() * mlf <= capacity) return;
head.assign(capacity *= 2, -1);
for (int i = 0; i < knx.size(); ++i) {
knx[i].second = head[knx[i].first & capacity - 1];
head[knx[i].first & capacity - 1] = i;
}
}
};
vector<HT<int, vector<int>>> high(1);
vector<int> inv_(1);
void gen_high(const vector<int>& prof, int n0, int n, int c, int p, auto&& cur) {
high[n0 - n].emplace(p, cur);
for (c = min(n, c); c > prof[n]; --c) {
int np = p;
for (int i = 0; i < c; ++i) mul(np, inv_[n0 - i]);
cur.push_back(c);
gen_high(prof, n0, n - c, c, np, cur);
cur.pop_back();
}
}
vector<int> qs;
vector<vector<int>> ans;
void solve(const vector<int>& prof, int n0, int n, int c, int p, auto&& cur) {
for (int i = 0; i < qs.size(); ++i) if (ans[i].empty() && ~high[n0 - n].find(mul(+p, qs[i]))) {
ans[i] = cur;
auto& t = high[n0 - n].values[high[n0 - n].find(mul(+p, qs[i]))];
ans[i].insert(ans[i].end(), t.begin(), t.end());
}
int i = 0;
for (; n + c <= n0 && c <= prof[n + c]; ++c) {
for (; i < c; ++i) mul(p, n0 - i);
cur.push_back(c);
solve(prof, n0, n + c, c, p, cur);
cur.pop_back();
}
}
uint64_t eval_high(vector<int> profile) {
int N = profile.size();
vector<uint64_t> cnt(N * N);
cnt[N * N - 1] = 1;
uint64_t ans = 0;
for (int n = N; --n; )
for (int c = N; --c; ) if (cnt[n * N + c]) {
for (int cc = min(n, c); cc > profile[n]; cc--) {
cnt[(n - cc) * N + cc] += cnt[n * N + c];
}
ans += cnt[n * N + c];
}
return ans;
}
uint64_t eval_low(vector<int> profile) {
int N = profile.size();
vector<uint64_t> cnt(N * N);
cnt[0] = 1;
uint64_t ans = 0;
for (int n = 0; n < N; ++n)
for (int c = 0; c <= n; ++c) if (cnt[n * N + c]) {
for (int cc = max(c, 1); n + cc < N && cc <= profile[n + cc]; ++cc) {
cnt[(n + cc) * N + cc] += cnt[n * N + c];
}
ans += cnt[n * N + c];
}
return ans;
}
uint64_t eval(vector<int> profile) {
return eval_high(profile) * 4 + eval_low(profile);
}
vector<int> makeprof(int n, vector<int> from) {
vector<int> prof(n + 1, 0);
int j = n;
for (int i = 0; i < from.size() - 1; ++i) {
while (j >= from[i]) prof[j--] = i;
}
while (j >= 0) prof[j--] = n;
return prof;
}
vector<int> getopt(int n) {
static vector<vector<int>> precalc = [] {
int n = 124;
vector<vector<int>> res(n);
vector<int> tmpl(10, n);
while (n-- > 1) {
int64_t bst = eval(makeprof(n, tmpl));
for (int ch = 1; ch--; ) {
for (int i = 1; i < tmpl.size() - 1; ++i)
for (auto d: {-1, 1}) if (tmpl[i] + d >= 0 && tmpl[i] + d <= n + 1) {
tmpl[i] += d;
int64_t cur = eval(makeprof(n, tmpl));
if (cur > bst) tmpl[i] -= d;
else if (cur < bst) ch = 1, bst = cur;
sort(tmpl.rbegin() + 1, tmpl.rend());
}
}
res[n] = tmpl;
}
return res;
}();
return makeprof(n, precalc[n]);
}
int main() {
int tc; cin >> tc;
qs.resize(tc);
ans.resize(tc);
for (int i = 0; i < tc; ++i) {
cin >> qs[i];
if (qs[i] == 1) ans[i] = {-1};
else if (qs[i] == 2) ans[i] = {-1};
qs[i] = inv(qs[i]);
}
for (int n = 1, done = 0; !done++; ++n) {
inv_.push_back(inv(n));
high.push_back({});
for (auto& x: high) x.clear();
gen_high(getopt(n), n, n, n, 1, vector<int>{});
solve(getopt(n), n, 0, 1, mul(n + 1, n + 2), vector<int>{});
for (int i = 0; i < tc; ++i) done &= !ans[i].empty();
}
for (int i = 0; i < tc; ++i) {
if (qs[i] == 1) cout << "1\n";
else {
if (ans[i][0] == -1) ans[i] = {};
cout << accumulate(ans[i].begin(), ans[i].end(), 0) + 2 << "\n1 2\n";
for (int j = 0, k = 2; j < ans[i].size(); ++j)
while (ans[i][j]--) cout << j + 1 << ' ' << ++k << '\n';
}
}
}
详细
Test #1:
score: 100
Accepted
time: 125ms
memory: 3676kb
input:
4 2 360 1 509949433
output:
2 1 2 5 1 2 1 3 2 4 2 5 1 10 1 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10
result:
ok OK (4 test cases)
Test #2:
score: 0
Accepted
time: 1290ms
memory: 28536kb
input:
9 185396120 468170792 837583517 696626231 338497514 762842660 800028852 928391161 733524004
output:
14 1 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 9 12 10 13 10 14 122 1 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 14 17 15 18 15 19 16 20 16 21 17 22 17 23 17 24 18 25 18 26 18 27 19 28 19 29 19 30 20 31 20 32 20 33 21 34 21 35 21 36 22 37 22 38 22 39 22 40 22 41 22 42 23 43 ...
result:
ok OK (9 test cases)
Test #3:
score: 0
Accepted
time: 1574ms
memory: 28444kb
input:
10 338497514 733524004 447182954 415993605 453460670 50499055 648088551 986982752 907925397 315315230
output:
124 1 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 25 24 26 25 27 26 28 27 29 28 30 29 31 30 32 31 33 32 34 33 35 34 36 35 37 35 38 36 39 36 40 37 41 37 42 38 43 38 44 38 45 38 46 39 47 39 48 39 49 39 50 40 51 40 52 40 53 40...
result:
ok OK (10 test cases)
Test #4:
score: 0
Accepted
time: 373ms
memory: 11188kb
input:
10 1 2 3 4 5 6 7 8 9 10
output:
1 2 1 2 102 1 2 1 3 2 4 3 5 4 6 4 7 5 8 5 9 6 10 6 11 7 12 7 13 8 14 8 15 9 16 9 17 9 18 9 19 9 20 9 21 10 22 10 23 10 24 10 25 10 26 10 27 10 28 10 29 11 30 11 31 11 32 11 33 11 34 11 35 11 36 11 37 11 38 11 39 11 40 11 41 11 42 11 43 11 44 11 45 11 46 11 47 11 48 11 49 11 50 11 51 11 52 12 53 12 5...
result:
ok OK (10 test cases)
Test #5:
score: 0
Accepted
time: 205ms
memory: 6988kb
input:
10 269199917 392009324 753889928 751355133 472639410 132096559 331333826 40414701 72847302 475706026
output:
55 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1 30 1 31 1 32 1 33 1 34 1 35 1 36 1 37 1 38 1 39 1 40 1 41 1 42 1 43 1 44 1 45 1 46 1 47 1 48 1 49 1 50 1 51 1 52 1 53 1 54 1 55 84 1 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 ...
result:
ok OK (10 test cases)
Extra Test:
score: 0
Extra Test Passed