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#include "sequence.h"
#include <bits/stdc++.h>
#define SZ(s) ((int) ((s).size()))
using namespace std;
// SegTree, copied from AtCoder library {{{
// AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html
//
// Notes:
// - Index of elements from 0 -> n-1
// - Range queries are [l, r-1]
//
// Tested:
// - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j
// - https://oj.vnoi.info/problem/gss
// - https://oj.vnoi.info/problem/nklineup
// - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr
// - https://judge.yosupo.jp/problem/point_add_range_sum
// - https://judge.yosupo.jp/problem/point_set_range_composite
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
template<
class T, // data type for nodes
T (*op) (T, T), // operator to combine 2 nodes
T (*e)() // identity element
>
struct SegTree {
SegTree() : SegTree(0) {}
explicit SegTree(int n) : SegTree(vector<T> (n, e())) {}
explicit SegTree(const vector<T>& v) : _n((int) v.size()) {
log = ceil_pow2(_n);
size = 1<<log;
d = vector<T> (2*size, e());
for (int i = 0; i < _n; i++) d[size+i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
// 0 <= p < n
void set(int p, T x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
// 0 <= p < n
T get(int p) const {
assert(0 <= p && p < _n);
return d[p + size];
}
// Get product in range [l, r-1]
// 0 <= l <= r <= n
// For empty segment (l == r) -> return e()
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= _n);
T sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
T all_prod() const {
return d[1];
}
// Binary search on SegTree to find largest r:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false)
template <bool (*f)(T)> int max_right(int l) const {
return max_right(l, [](T x) { return f(x); });
}
template <class F> int max_right(int l, F f) const {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
T sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
// Binary search on SegTree to find smallest l:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false)
template <bool (*f)(T)> int min_left(int r) const {
return min_left(r, [](T x) { return f(x); });
}
template <class F> int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
T sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
vector<T> d;
void update(int k) {
d[k] = op(d[2*k], d[2*k+1]);
}
};
// }}}
// SegTree examples {{{
// Examples: Commonly used SegTree ops: max / min / sum
struct MaxSegTreeOp {
static int op(int x, int y) {
return max(x, y);
}
static int e() {
return INT_MIN;
}
};
struct MinSegTreeOp {
static int op(int x, int y) {
return min(x, y);
}
static int e() {
return INT_MAX;
}
};
struct SumSegTreeOp {
static long long op(long long x, long long y) {
return x + y;
}
static long long e() {
return 0;
}
};
// using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>;
// using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>;
// using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>;
// }}}
bool can(int n, int eq, const vector<int>& a, const vector<vector<int>>& ids) {
int ln = *max_element(a.begin(), a.end());
for (int median = 0; median <= ln; median++) {
if (SZ(ids[median]) < eq) continue;
vector<int> f(n+1, 0), greater(n+1, 0), less(n+1, 0);
for (int i = 1; i <= n; ++i) {
greater[i] = a[i] > median;
less[i] = a[i] < median;
f[i] = max(-1, min(a[i] - median, 1));
assert(greater[i] - less[i] == f[i]);
}
std::partial_sum(f.begin(), f.end(), f.begin());
SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e> st_max(f);
SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e> st_min(f);
for (int ix = 0, iy = eq-1; iy < SZ(ids[median]); ++ix, ++iy) {
int x = ids[median][ix];
int y = ids[median][iy];
// find [l, r]:
// - l <= x < y <= r
// - less + eq >= greater
// - greater + eq >= less
// - eq >= greater - less >= -eq
// - eq >= (greater(r) - less(r)) - (greater(l-1) - less(l-1)) >= -eq
int max_val = st_max.prod(y, n+1) - st_min.prod(0, x);
int min_val = st_min.prod(y, n+1) - st_max.prod(0, x);
// [-eq, eq] and [min_val, max_val] intersects
if (min_val <= eq && max_val >= -eq) return true;
}
}
return false;
}
int sequence(int n, std::vector<int> a) {
// ids from 1
a.insert(a.begin(), 0);
vector<vector<int>> ids(n + 1);
for (int i = 1; i <= n; ++i) {
ids[a[i]].push_back(i);
}
int left = 1, right = n, res = 1;
while (left <= right) {
int mid = (left + right) / 2;
if (can(n, mid, a, ids)) {
res = mid;
left = mid + 1;
} else {
right = mid - 1;
}
}
return res;
}
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