제출 #753027

#제출 시각아이디문제언어결과실행 시간메모리
753027I_love_Hoang_Yen서열 (APIO23_sequence)C++17
0 / 100
2075 ms49744 KiB
#include "sequence.h" #include <bits/stdc++.h> #define SZ(s) ((int) ((s).size())) using namespace std; // Lazy Segment Tree, copied from AtCoder {{{ // Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp // Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html // // Notes: // - Index of elements from 0 // - Range queries are [l, r-1] // - composition(f, g) should return f(g()) // // Tested: // - https://oj.vnoi.info/problem/qmax2 // - https://oj.vnoi.info/problem/lites // - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix // - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder // - https://atcoder.jp/contests/practice2/tasks/practice2_l // - https://judge.yosupo.jp/problem/range_affine_range_sum int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } template< class S, // node data type S (*op) (S, S), // combine 2 nodes S (*e) (), // identity element class F, // lazy propagation tag S (*mapping) (F, S), // apply tag F on a node F (*composition) (F, F), // combine 2 tags F (*id)() // identity tag > struct LazySegTree { LazySegTree() : LazySegTree(0) {} explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {} explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) { log = 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); } } // 0 <= p < n 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); } // 0 <= p < n S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } // Get product in range [l, r-1] // 0 <= l <= r <= n // For empty segment (l == r) -> return e() S prod(int l, int r) { 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() { return d[1]; } // 0 <= p < n 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); } // Apply f on all elements in range [l, r-1] // 0 <= l <= r <= n 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); } } // 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 (*g)(S)> int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template <class G> int max_right(int l, G g) { 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; } // 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 (*g)(S)> int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template <class G> int min_left(int r, G g) { 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; } private: int _n, size, log; vector<S> d; vector<F> lz; void update(int k) { d[k] = op(d[2*k], d[2*k+1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) { all_apply(2*k, lz[k]); all_apply(2*k+1, lz[k]); lz[k] = id(); } }; // }}} // 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 -1; } }; struct MinSegTreeOp { static int op(int x, int y) { return min(x, y); } static int e() { return 1000111000; } }; using F = int; int mapping(F f, int s) { return f + s; } F composition(F f, F g) { return f + g; } F id() { return 0; } // using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>; // using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>; // }}} bool can(int n, int eq, const vector<int>& a, const vector<vector<int>>& ids) { int ln = *max_element(a.begin(), a.end()); LazySegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e, F, mapping, composition, id> st_max(n + 1); LazySegTree<int, MinSegTreeOp::op, MinSegTreeOp::e, F, mapping, composition, id> st_min(n + 1); vector<int> f(n+1, 0), greater(n+1, 0), less(n+1, 0); for (int median = 0; median <= ln; median++) { if (median == 0) { st_max.set(0, 0); st_min.set(0, 0); for (int i = 1; i <= n; ++i) { greater[i] = a[i] > median; less[i] = a[i] < median; f[i] = f[i-1] + (greater[i] - less[i]); st_max.set(i, f[i]); st_min.set(i, f[i]); } } else { // greater is affected? for (int i : ids[median]) { // previously: greater = 1, now: greater = 0 st_max.apply(i, n+1, -1); st_min.apply(i, n+1, -1); } // less is affected? for (int i : ids[median-1]) { // previously: less = 0, now: less = 1 st_max.apply(i, n+1, -1); st_min.apply(i, n+1, -1); } } for (int i = 1; i <= n; ++i) { greater[i] = a[i] > median; less[i] = a[i] < median; f[i] = f[i-1] + (greater[i] - less[i]); assert(st_max.get(i) == f[i]); assert(st_min.get(i) == f[i]); } if (SZ(ids[median]) < eq) continue; 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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