結果
| 問題 |
No.1526 Sum of Mex 2
|
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-06-03 00:28:27 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 290 ms / 3,000 ms |
| コード長 | 10,187 bytes |
| コンパイル時間 | 1,497 ms |
| コンパイル使用メモリ | 98,916 KB |
| 最終ジャッジ日時 | 2025-01-21 21:10:03 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 32 |
ソースコード
#include <iostream>
#include <utility>
#include <vector>
using namespace std;
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_BITOP_HPP
#ifndef ATCODER_LAZYSEGTREE_HPP
#define ATCODER_LAZYSEGTREE_HPP 1
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
// #include "atcoder/internal_bit"
namespace atcoder {
template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
struct lazy_segtree {
public:
lazy_segtree() : lazy_segtree(0) {}
explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = internal::ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) { update(i); }
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) const {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) const {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
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);
}
S all_prod() const { return d[1]; }
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <bool (*g)(S)> int max_right(int l) const {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) const {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(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;
}
template <bool (*g)(S)> int min_left(int r) const {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) const {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(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;
}
protected:
int _n, size, log;
mutable std::vector<S> d;
mutable std::vector<F> lz;
void update(int k) const { d[k] = op(d[2 * k], d[2 * k + 1]); }
virtual void all_apply(int k, F f) const {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) const {
all_apply(2 * k, lz[k]);
all_apply(2 * k + 1, lz[k]);
lz[k] = id();
}
};
} // namespace atcoder
#endif // ATCODER_LAZYSEGTREE_HPP
template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
class segtree_beats : public atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> {
using Base = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>;
using Base::lazy_segtree;
void all_apply(int k, F f) const override {
Base::d[k] = mapping(f, Base::d[k]);
if (k < Base::size) {
Base::lz[k] = composition(f, Base::lz[k]);
if (Base::d[k].fail) Base::push(k), Base::update(k);
}
}
};
namespace RangeChMinMaxAddSum {
#include <algorithm>
template <typename Num> inline Num second_lowest(Num a, Num a2, Num c, Num c2) noexcept { // a < a2, c < c2
return a == c ? std::min(a2, c2) : a2 <= c ? a2 : c2 <= a ? c2 : std::max(a, c);
}
template <typename Num> inline Num second_highest(Num a, Num a2, Num b, Num b2) noexcept { // a > a2, b > b2
return a == b ? std::max(a2, b2) : a2 >= b ? a2 : b2 >= a ? b2 : std::min(a, b);
}
using BNum = long long;
constexpr BNum BINF = 1LL << 61;
struct S {
BNum lo, hi, lo2, hi2, sum;
unsigned sz, nlo, nhi;
bool fail;
S() : lo(BINF), hi(-BINF), lo2(BINF), hi2(-BINF), sum(0), sz(0), nlo(0), nhi(0), fail(0) {}
S(BNum x, unsigned sz_ = 1)
: lo(x), hi(x), lo2(BINF), hi2(-BINF), sum(x * sz_), sz(sz_), nlo(sz_), nhi(sz_), fail(0) {}
friend std::ostream &operator<<(std::ostream &os, const S s) {
return os << "[(" << s.lo << "x" << s.nlo << ", " << s.lo2 << ", " << s.hi2 << ", " << s.hi << "x" << s.nhi << "), sz=" << s.sz << ", sum=" << s.sum << "]";
}
};
S e() { return S(); }
S op(S l, S r) {
if (l.lo > l.hi) return r;
if (r.lo > r.hi) return l;
S ret;
ret.lo = std::min(l.lo, r.lo), ret.hi = std::max(l.hi, r.hi);
ret.lo2 = second_lowest(l.lo, l.lo2, r.lo, r.lo2), ret.hi2 = second_highest(l.hi, l.hi2, r.hi, r.hi2);
ret.sum = l.sum + r.sum, ret.sz = l.sz + r.sz;
ret.nlo = l.nlo * (l.lo <= r.lo) + r.nlo * (r.lo <= l.lo);
ret.nhi = l.nhi * (l.hi >= r.hi) + r.nhi * (r.hi >= l.hi);
return ret;
}
struct F {
BNum lb, ub, bias;
F() : lb(-BINF), ub(BINF), bias(0) {}
F(BNum chmax_, BNum chmin_, BNum add) : lb(chmax_), ub(chmin_), bias(add) {}
static F chmin(BNum x) noexcept { return F(-BINF, x, BNum(0)); }
static F chmax(BNum x) noexcept { return F(x, BINF, BNum(0)); }
static F add(BNum x) noexcept { return F(-BINF, BINF, x); };
};
F composition(F fnew, F fold) {
F ret;
ret.lb = std::max(std::min(fold.lb + fold.bias, fnew.ub), fnew.lb) - fold.bias;
ret.ub = std::min(std::max(fold.ub + fold.bias, fnew.lb), fnew.ub) - fold.bias;
ret.bias = fold.bias + fnew.bias;
return ret;
}
F id() { return F(); }
S mapping(F f, S x) {
if (x.sz == 0) return e();
if (x.lo == x.hi or f.lb == f.ub or f.lb >= x.hi or f.ub < x.lo)
return S(std::min(std::max(x.lo, f.lb), f.ub) + f.bias, x.sz);
if (x.lo2 == x.hi) {
x.lo = x.hi2 = std::max(x.lo, f.lb) + f.bias, x.hi = x.lo2 = std::min(x.hi, f.ub) + f.bias;
x.sum = x.lo * x.nlo + x.hi * x.nhi;
return x;
}
if (f.lb < x.lo2 and f.ub > x.hi2) {
BNum nxt_lo = std::max(x.lo, f.lb), nxt_hi = std::min(x.hi, f.ub);
x.sum += (nxt_lo - x.lo) * x.nlo - (x.hi - nxt_hi) * x.nhi + f.bias * x.sz;
x.lo = nxt_lo + f.bias, x.hi = nxt_hi + f.bias, x.lo2 += f.bias, x.hi2 += f.bias;
return x;
}
x.fail = 1;
return x;
}
using segtree = segtree_beats<S, op, e, F, mapping, composition, id>;
} // namespace RangeChMinMaxAddSum
int main() {
ios::sync_with_stdio(false), cin.tie(nullptr);
int N;
cin >> N;
vector<vector<int>> v2is(N);
for (int i = 0; i < N; i++) {
int a;
cin >> a;
v2is[a - 1].push_back(i);
}
vector<pair<int, int>> ranges{{0, N}};
long long ret = 0;
vector<RangeChMinMaxAddSum::S> init;
for (int i = 0; i < N; i++) init.emplace_back(i);
RangeChMinMaxAddSum::segtree tree(init);
for (auto is : v2is) {
if (ranges.empty()) break;
int l = 0;
for (auto i : is) {
tree.apply(l, i + 1, RangeChMinMaxAddSum::F::chmax(i));
l = i + 1;
}
tree.apply(l, N, RangeChMinMaxAddSum::F::chmax(N));
auto tmp = (long long)N * N - tree.all_prod().sum;
ret += tmp;
if (!tmp) break;
}
cout << ret + (long long)N * (N + 1) / 2 << '\n';
}