제출 #220213

#제출 시각아이디문제언어결과실행 시간메모리
220213emil_physmathShortcut (IOI16_shortcut)C++17
0 / 100
5 ms512 KiB
#include "shortcut.h" #include <algorithm> #include <iostream> #include <vector> #include <set> using namespace std; using llong = long long; const int maxN = 3001; llong t3[4 * maxN], t4[4 * maxN], lazy3[4 * maxN], lazy4[4 * maxN]; llong t1[4 * maxN], t2[4 * maxN], lazy1[4 * maxN], lazy2[4 * maxN]; vector<llong> x, val; llong c; void Build(llong* t, llong* lazy, int v, int vl, int vr, const vector<llong>& a) { lazy[v] = 0; if (vl == vr) { t[v] = a[vr]; return; } int vm = (vl + vr) / 2; Build(t, lazy, v * 2, vl, vm, a); Build(t, lazy, v * 2 + 1, vm + 1, vr, a); t[v] = max(t[v * 2], t[v * 2 + 1]); } inline void Push(llong* t, llong* lazy, int v, int vl, int vr) { if (lazy[v]) { if (vl != vr) { lazy[v * 2] += lazy[v]; lazy[v * 2 + 1] += lazy[v]; } t[v] += lazy[v]; lazy[v] = 0; } } void Add(llong* t, llong* lazy, int v, int vl, int vr, int l, int r, llong val) { if (l > vr || vl > r) return; if (l <= vl && vr <= r) { lazy[v] += val; return; } Push(t, lazy, v, vl, vr); int vm = (vl + vr) / 2; Add(t, lazy, v * 2, vl, vm, l, r, val); Add(t, lazy, v * 2 + 1, vm + 1, vr, l, r, val); Push(t, lazy, v * 2, vl, vm); Push(t, lazy, v * 2 + 1, vm + 1, vr); t[v] = max(t[v * 2], t[v * 2 + 1]); } void Add(llong* t1, llong* lazy1, llong* t2, llong* lazy2, int v, int vl, int vr, int l, int r, llong val) { if (l > vr || vl > r) return; if (l <= vl && vr <= r) { lazy1[v] += val; lazy2[v] += val; return; } Push(t1, lazy1, v, vl, vr); Push(t2, lazy2, v, vl, vr); int vm = (vl + vr) / 2; Add(t1, lazy1, t2, lazy2, v * 2, vl, vm, l, r, val); Add(t1, lazy1, t2, lazy2, v * 2 + 1, vm + 1, vr, l, r, val); Push(t1, lazy1, v * 2, vl, vm); Push(t2, lazy2, v * 2, vl, vm); Push(t1, lazy1, v * 2 + 1, vm + 1, vr); Push(t2, lazy2, v * 2 + 1, vm + 1, vr); t1[v] = max(t1[v * 2], t1[v * 2 + 1]); t2[v] = max(t2[v * 2], t2[v * 2 + 1]); } llong Max(llong* t, llong* lazy, int v, int vl, int vr, int l, int r) { if (vl > r || l > vr) return numeric_limits<llong>::min(); Push(t, lazy, v, vl, vr); if (l <= vl && vr <= r) return t[v]; int vm = (vl + vr) / 2; return max(Max(t, lazy, v * 2, vl, vm, l, r), Max(t, lazy, v * 2 + 1, vm + 1, vr, l, r)); } llong cache[maxN][maxN]; bool Poss(int s, int e, llong cur) { if (cache[s][e] != numeric_limits<llong>::min()) return cache[s][e] <= cur; multiset<llong> mx; for (int l = s, r = s - 1; l <= e; ++l) { if (r < l) { r = l; mx.clear(); } else mx.erase(mx.find(x[l] + val[l])); while (r + 1 <= e && x[r + 1] - x[l] <= (x[e] - x[s]) - (x[r + 1] - x[l]) + c) { ++r; mx.insert(x[r] + val[r]); } if (mx.size()) cache[s][e] = max(cache[s][e], *mx.rbegin() - x[l] + val[l]); } mx.clear(); for (int i = s; i <= e; ++i) mx.insert(val[i] - x[i]); for (int l = s, r = s; ; ++l) { while (l > r) { mx.erase(mx.find(val[r] - x[r])); ++r; } while (r <= e && x[r] - x[l] < (x[e] - x[s]) - (x[r] - x[l]) + c) { mx.erase(mx.find(val[r] - x[r])); ++r; } if (r > e) break; if (mx.size()) cache[s][e] = max(cache[s][e], (x[e] - x[s]) + *mx.rbegin() + x[l] + val[l] + c); } return cache[s][e] <= cur; }; long long Brutos(int n, vector<int> l, vector<int> val, int c) { vector<llong> x(n); for (int i = 1; i < n; ++i) x[i] = x[i - 1] + l[i - 1]; llong ans = numeric_limits<llong>::max(); for (int l = 0; l < n; ++l) for (int r = l + 1; r < n; ++r) { llong cur = 0; for (int a = 0; a < n; ++a) { cur = max(cur, (llong)val[a]); for (int b = a + 1; b < n; ++b) { if (b <= l || a >= r) cur = max(cur, val[a] + val[b] + x[b] - x[a]); else if (a <= l && b >= r) cur = max(cur, val[a] + val[b] + x[l] - x[a] + x[b] - x[r] + min(x[r] - x[l], (llong)c)); else if (l <= a && b <= r) cur = max(cur, val[a] + val[b] + min(x[b] - x[a], x[a] - x[l] + x[r] - x[b] + c)); else if (a <= l) cur = max(cur, val[a] + val[b] + x[l] - x[a] + min(x[b] - x[l], x[r] - x[b] + c)); else if (b >= r) cur = max(cur, val[a] + val[b] + x[b] - x[r] + min(x[r] - x[a], x[a] - x[l] + c)); } } ans = min(ans, cur); } return ans; } llong lrout[maxN][maxN]; long long find_shortcut(int n, vector<int> l, vector<int> val_, int c_) { // cerr << "Brutos: " << Brutos(n, l, val_, c_) << '\n'; for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) cache[i][j] = lrout[i][j] = numeric_limits<llong>::min(); c = c_; val.assign(val_.begin(), val_.end()); vector<llong> valc(val.begin(), val.end()); for (llong& x: valc) x += c; x.resize(n); x[0] = 0; for (int i = 1; i < n; ++i) x[i] = x[i - 1] + l[i - 1]; vector<llong> pref(n), suff(n), pathpref(n), pathsuff(n); pref[0] = val[0]; pathpref[0] = val[0]; for (int i = 1; i < n; ++i) { pathpref[i] = max(pathpref[i - 1], pref[i - 1] + x[i] + val[i]); pref[i] = max(pref[i - 1], -x[i] + val[i]); } suff.back() = val.back(); pathsuff.back() = val.back(); for (int i = n - 2; i >= 0; --i) { pathsuff[i] = max(pathsuff[i + 1], suff[i + 1] + (x.back() - x[i]) + val[i]); suff[i] = max(suff[i + 1], -(x.back() - x[i]) + val[i]); } for (int l = 0; l < n; ++l) { Build(t1, lazy1, 1, 0, n - 1, val); Build(t4, lazy4, 1, 0, n - 1, valc); vector<llong> valcr = valc; for (int r = l; r < n; ++r) valcr[r] += x[r] - x[l]; vector<llong> valr = valc; for (int r = l; r < n; ++r) valr[r] += x[r] - x[l]; Build(t2, lazy2, 1, 0, n - 1, valcr); Build(t3, lazy3, 1, 0, n - 1, valr); int r = l, m = l, m1 = l; while (r < n) { lrout[l][r] = max(pathsuff[r], pathpref[l]); while (m <= r && x[m] - x[l] + c < x[r] - x[m]) ++m; while (m1 + 1 <= r && x[m1 + 1] - x[l] <= x[r] - x[m1 + 1] + c) ++m1; /*if (l == 1 && r == 3) for (int i = l; i <= r; ++i) cerr << "tree4[" << i << "] = " << Max(t4, lazy4, 1, 0, n - 1, i, i) << '\n';*/ if (l <= m1 && l) lrout[l][r] = max(lrout[l][r], Max(t3, lazy3, 1, 0, n - 1, l, m1) + x[l] - x[l - 1] + pref[l - 1] + x[l - 1]); if (m1 + 1 <= r && l) lrout[l][r] = max(lrout[l][r], Max(t4, lazy4, 1, 0, n - 1, m1 + 1, r) + x[l] - x[l - 1] + pref[l - 1] + x[l - 1]); lrout[l][r] = max(lrout[l][r], max(pref[l] + suff[r] + x.back() - (x[r] - x[l]) + min(c, x[r] - x[l]), pathsuff[r])); if (m <= r && r + 1 < n) lrout[l][r] = max(lrout[l][r], Max(t1, lazy1, 1, 0, n - 1, m, r) + x[r + 1] - x[r] + suff[r + 1] + (x.back() - x[r + 1])); if (l <= m - 1 && r + 1 < n) lrout[l][r] = max(lrout[l][r], Max(t2, lazy2, 1, 0, n - 1, l, m - 1) + x[r + 1] - x[r] + suff[r + 1] + (x.back() - x[r + 1])); // cerr << "lrout[" << l << "][" << r << "] = " << lrout[l][r] << '\n'; ++r; while (m <= r && x[m] - x[l] + c < x[r] - x[m]) ++m; Add(t1, lazy1, t4, lazy4, 1, 0, n - 1, l, r - 1, x[r] - x[r - 1]); } } llong ans_l = *max_element(val.begin(), val.end()), ans_r = (maxN + 2) * 1000'000'000LL; llong ans = ans_r + 1; while (ans_l <= ans_r) { llong cur = ans_l + (ans_r - ans_l) / 2; if (cur == 1) cerr << ""; bool poss = false; for (int l = 0; l < n; ++l) { int r = l; while (r < n && lrout[l][r] > cur) ++r; if (r < n && Poss(l, r, cur)) { // if (cur == 37) // cerr << l << " ... " << r << '\n'; poss = true; break; } } if (poss) { ans = cur; ans_r = cur - 1; } else ans_l = cur + 1; } return ans; }
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