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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#338984 | #7605. Yet Another Mex Problem | jrjyy | WA | 1ms | 3996kb | C++14 | 6.0kb | 2024-02-26 15:58:35 | 2024-02-26 15:58:37 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
using i128 = __int128_t;
constexpr i64 inf = 1e12;
using P = std::complex<i64>;
auto dot(const P &a, const P &b) {
return (std::conj(a) * b).real();
}
auto cross(const P &a, const P &b) {
return (std::conj(a) * b).imag();
}
struct ConvexHull {
std::vector<P> s;
int pos = 0;
void add(const P &x) {
assert(s.empty() || s.back().real() <= x.real());
while (s.size() >= 2 && cross(x - s.back(), x - s.end()[-2]) <= 0) {
s.pop_back();
}
s.push_back(x);
}
i64 lst = -inf;
i64 query(i64 x) {
assert(lst <= x);
lst = x;
if (s.empty()) {
return -inf;
}
P p(x, 1);
while (pos + 1 < int(s.size()) && dot(s[pos], p) <= dot(s[pos + 1], p)) {
++pos;
}
return dot(s[pos], p);
}
};
struct Interval {
int l, r, b, e, x;
};
struct Solver {
std::vector<std::vector<P>> sf;
std::vector<std::vector<int>> sg;
std::vector<ConvexHull> f, g;
std::vector<P> points;
Solver() {}
void addF(int u, int l, int r, int p, const P &x) {
sf[u].push_back(x);
if (p == r - 1) {
std::reverse(sf[u].begin(), sf[u].end());
for (auto x : sf[u]) {
f[u].add(x);
}
}
if (r - l == 1) {
return;
}
int m = (l + r) / 2;
if (p < m) {
addF(u << 1, l, m, p, x);
} else {
addF(u << 1 | 1, m, r, p, x);
}
}
void addG(int u, int l, int r, int ql, int qr, int x) {
if (r <= ql || qr <= l) {
return;
}
if (ql <= l && r <= qr) {
sg[u].push_back(x);
return;
}
int m = (l + r) / 2;
addG(u << 1, l, m, ql, qr, x);
addG(u << 1 | 1, m, r, ql, qr, x);
}
i64 queryF(int u, int l, int r, int ql, int qr, i64 x) {
if (r <= ql || qr <= l) {
return -inf;
}
if (ql <= l && r <= qr) {
return f[u].query(x);
}
int m = (l + r) / 2;
return std::max(queryF(u << 1, l, m, ql, qr, x), queryF(u << 1 | 1, m, r, ql, qr, x));
}
i64 queryG(int u, int l, int r, int p, i64 x) {
if (p == l) {
for (auto x : sg[u]) {
g[u].add(points[x]);
}
}
i64 res = g[u].query(x);
if (r - l > 1) {
int m = (l + r) / 2;
if (p < m) {
res = std::max(res, queryG(u << 1, l, m, p, x));
} else {
res = std::max(res, queryG(u << 1 | 1, m, r, p, x));
}
}
return res;
}
void solve(int n, const std::vector<i64> &sum, const std::vector<Interval> &intervals) {
sf.resize(4 << std::__lg(n));
f.resize(4 << std::__lg(n));
sg.resize(4 << std::__lg(n + 1));
g.resize(4 << std::__lg(n + 1));
const int m = int(intervals.size());
points.resize(m);
std::vector<int> ord(m);
std::iota(ord.begin(), ord.end(), 0);
std::sort(ord.begin(), ord.end(), [&](int x, int y) {
return intervals[x].x < intervals[y].x;
});
for (auto i : ord) {
addG(1, 0, n + 1, intervals[i].b, intervals[i].e, i);
}
std::sort(ord.begin(), ord.end(), [&](int x, int y) {
return intervals[x].b < intervals[y].b;
});
for (int i = 0, j = 0; i <= n; ++i) {
i64 dp = i == 0 ? 0 : queryG(1, 0, n + 1, i, sum[i]);
// std::cerr << "dp " << i << ": " << dp << "\n";
if (i == n) {
std::cout << dp << "\n";
return;
}
addF(1, 0, n, i, P(-sum[i], dp));
while (j < m && intervals[ord[j]].b == i + 1) {
auto v = intervals[ord[j]];
// std::cerr << i << ": " << ord[j] << " " << v.l << " " << v.r << " = " <<
// queryF(1, 0, n, v.l, v.r, v.x) << "\n";
points[ord[j]] = P(v.x, queryF(1, 0, n, v.l, v.r, v.x));
assert(points[ord[j]].imag() >= -inf / 2);
// std::cerr << ord[j] << ": " << points[ord[j]] << "\n";
++j;
}
}
}
};
int main() {
std::cin.tie(nullptr)->sync_with_stdio(false);
int n, k;
std::cin >> n >> k;
std::vector<int> a(n);
std::vector<std::vector<int>> pos(n + 1, {-1});
for (int i = 0; i < n; ++i) {
std::cin >> a[i];
pos[a[i]].push_back(i);
}
std::map<int, int> mp;
for (int i = 0; i <= n; ++i) {
mp[i] = i;
}
std::vector<Interval> intervals;
auto add = [&](int l, int r, int b, int e, int x) {
// L: [l, r), R: [b, e), mex[L, R) = x
l = std::max(l, r - k);
if (b - r >= k) {
return;
}
intervals.push_back({l, r, b, std::min(e, l + k + 1), x});
for (int i = l + k + 1; i < e && i - r < k; ++i) {
intervals.push_back({i - k, r, i, i + 1, x});
}
};
for (int x = 0; x <= n; ++x) {
pos[x].push_back(n);
for (int i = 0; i < int(pos[x].size()) - 1; ++i) {
int l = pos[x][i] + 1, r = pos[x][i + 1];
int v = std::prev(mp.upper_bound(l))->second;
if (v >= r) {
continue;
}
for (auto it = mp.emplace(l, v).first; it->second < r; it = mp.erase(it)) {
add(it->first, std::next(it)->first, it->second + 1, r + 1, x);
}
mp[l] = r;
}
}
std::vector<i64> sum(n + 1);
for (int i = 0; i < n; ++i) {
sum[i + 1] = sum[i] + a[i];
}
// for (auto [l, r, b, e, x] : intervals) {
// std::cerr << l << " " << r << " " << b << " " << e << " " << x << "\n";
// }
Solver().solve(n, sum, intervals);
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3624kb
input:
5 3 3 4 0 0 3
output:
10
result:
ok 1 number(s): "10"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3580kb
input:
8 4 0 1 2 0 3 1 4 1
output:
26
result:
ok 1 number(s): "26"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
10 5 0 2 0 1 2 1 0 2 2 1
output:
33
result:
ok 1 number(s): "33"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3640kb
input:
20 10 3 1 3 2 3 3 0 1 3 0 2 3 3 3 3 1 3 0 0 3
output:
160
result:
ok 1 number(s): "160"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3948kb
input:
30 10 14 15 10 1 14 1 8 0 12 8 6 15 1 8 9 12 15 10 11 12 7 10 10 3 3 10 8 14 13 13
output:
172
result:
ok 1 number(s): "172"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
40 3 0 4 2 4 3 1 5 5 2 3 4 2 1 1 1 5 5 4 1 3 3 0 1 0 2 0 1 4 2 1 5 3 0 4 0 0 0 5 3 3
output:
51
result:
ok 1 number(s): "51"
Test #7:
score: 0
Accepted
time: 0ms
memory: 3664kb
input:
50 20 29 6 30 26 8 11 22 26 24 8 30 25 19 12 28 19 28 4 13 9 2 23 30 15 21 5 30 5 19 17 25 29 2 28 20 16 0 4 26 23 22 30 3 25 29 5 29 24 11 27
output:
378
result:
ok 1 number(s): "378"
Test #8:
score: 0
Accepted
time: 1ms
memory: 3996kb
input:
80 15 2 13 20 11 12 10 19 17 3 7 10 2 14 11 9 17 19 11 17 15 10 18 11 11 14 5 20 8 8 12 13 17 14 19 11 20 13 2 12 2 19 12 6 7 3 4 11 16 1 12 4 16 17 4 1 2 5 11 17 12 13 7 8 12 2 4 15 20 18 1 1 13 1 14 6 5 20 12 12 11
output:
0
result:
ok 1 number(s): "0"
Test #9:
score: -100
Wrong Answer
time: 1ms
memory: 3928kb
input:
100 30 41 50 33 22 1 34 7 14 31 44 46 49 49 23 33 12 9 41 25 23 22 1 49 45 45 8 10 49 37 23 48 17 32 44 38 21 29 27 23 27 47 44 6 12 7 2 18 12 9 43 20 26 26 8 14 25 18 48 2 41 49 7 48 38 10 45 34 27 17 12 1 19 9 29 50 13 25 21 9 13 26 15 6 9 5 13 47 30 26 17 40 0 21 6 25 24 22 31 43 16
output:
1568
result:
wrong answer 1st numbers differ - expected: '1308', found: '1568'