結果

問題 No.913 木の燃やし方
ユーザー satanicsatanic
提出日時 2019-10-19 03:24:41
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,879 ms / 3,000 ms
コード長 7,932 bytes
コンパイル時間 1,548 ms
コンパイル使用メモリ 140,464 KB
実行使用メモリ 358,672 KB
最終ジャッジ日時 2023-09-08 10:30:54
合計ジャッジ時間 40,195 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 115 ms
351,040 KB
testcase_01 AC 115 ms
351,108 KB
testcase_02 AC 114 ms
351,044 KB
testcase_03 AC 123 ms
351,228 KB
testcase_04 AC 124 ms
351,208 KB
testcase_05 AC 127 ms
351,300 KB
testcase_06 AC 120 ms
351,128 KB
testcase_07 AC 117 ms
351,200 KB
testcase_08 AC 804 ms
358,264 KB
testcase_09 AC 773 ms
358,120 KB
testcase_10 AC 766 ms
358,112 KB
testcase_11 AC 782 ms
358,120 KB
testcase_12 AC 825 ms
358,588 KB
testcase_13 AC 1,051 ms
358,392 KB
testcase_14 AC 1,015 ms
358,088 KB
testcase_15 AC 1,011 ms
358,200 KB
testcase_16 AC 815 ms
358,368 KB
testcase_17 AC 770 ms
358,200 KB
testcase_18 AC 769 ms
358,280 KB
testcase_19 AC 853 ms
358,636 KB
testcase_20 AC 887 ms
358,508 KB
testcase_21 AC 1,879 ms
358,396 KB
testcase_22 AC 1,679 ms
358,500 KB
testcase_23 AC 1,503 ms
358,556 KB
testcase_24 AC 1,454 ms
358,496 KB
testcase_25 AC 1,418 ms
358,504 KB
testcase_26 AC 1,089 ms
358,648 KB
testcase_27 AC 1,077 ms
358,672 KB
testcase_28 AC 1,156 ms
358,500 KB
testcase_29 AC 1,104 ms
358,656 KB
testcase_30 AC 1,623 ms
358,504 KB
testcase_31 AC 1,082 ms
358,492 KB
testcase_32 AC 1,076 ms
358,508 KB
testcase_33 AC 1,076 ms
358,528 KB
testcase_34 AC 1,296 ms
358,588 KB
testcase_35 AC 1,321 ms
358,556 KB
testcase_36 AC 1,449 ms
358,588 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>
#include <fstream>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest& ...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)std::cin>>w;
// output
template<typename T>void MACRO_OUT(const T t) { std::cout << t; }
template<typename First, typename...Rest>void MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); }
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t: " << (dist) << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t: ";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}
#define SHOWSTACK(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.top() << " ";tmp.pop();}std::cerr << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define REP(w, n) for(int w=0;w<int(n);++w)
#define RREP(w, n) for(int w=int(n)-1;w>=0;--w)
#define IN(a, x, b) (a<=x && x<b)
template<class T> inline T CHMAX(T & a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;

template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

// type/const
#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                    // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-10;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T> & a, const T & val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>> & a, const T & val) { for (auto& b : a) FILL(b, val); }
// ------------>8------------------------------------->8------------

constexpr int B = 450;
constexpr int N = 200005;
constexpr int NB = N / B + 1;
struct SEG {
	signed min[N];
};
SEG seg[NB];

V<int> mycalc(int n, V<int> a) {
	V<int> c(n + 1, 0);
	REP(i, n) c[i + 1] = c[i] + a[i];

	V<int> v(n + 1, 0);
	REP(i, n + 1) v[i] = i * i - c[i];

	REP(si, NB) {
		REP(i, N) seg[si].min[i] = INFINT;
	}

	REP(si, NB) {
		int l = si * B, r = (si + 1) * B;
		CHMIN(r, n + 1);
		if (l >= r) break;

		RFOR(i, l, r) {
			int ma = 0;
			FOR(j, l, i) {
				if (v[j] >= v[i]) continue;
				int k = (v[i] - v[j]) / (2 * (i - j)) - 1;
				while (v[j] < v[i] - 2 * (i - j) * k) ++k;
				CHMAX(ma, k);
			}
			FOR(x, ma, N) {
				if (seg[si].min[x] < INFINT) break;
				seg[si].min[x] = i;
			}
		}
	}

	V<int> ans(n);
	V<int> mi(NB, INFLL); // -1 : 更新不要, -2 : 全部調べる, k>=0 : kで更新
	std::map<int, PAIR> map;

	RREP(i, n) {
		V<int> info(NB, -1);
		auto get = [&](int x) {
			auto it = map.upper_bound(x);
			int a, b; std::tie(a, b) = it->second;
			return a * x + b;
		};

		int r = i + 1;
		int updIdx = -1;
		if (r == n) {
			map[n + 1] = PAIR(-2 * r, r * r + c[r]);
			REP(j, NB) info[j] = n;
		}
		else {
			int a = -2 * r, b = r * r + c[r];
			if (get(r) >= a * r + b) {
				map.clear();
				map[n] = PAIR(a, b);
				REP(j, NB) info[j] = r;
			}
			else if (get(0) < a * 0 + b) {
				// info[x] = -1
			}
			else {
				while (!map.empty()) {
					auto it = map.begin();
					int ta, tb; std::tie(ta, tb) = it->second;
					int tx = it->first;
					if (ta * tx + tb >= a * tx + b) {
						map.erase(it);
						continue;
					}
					else {
						int y = -(tb - b) / (ta - a) - 2;
						while ((ta * y + tb) - (a * y + b) > 0) ++y;
						map[y] = PAIR(a, b);
						int sy = y / B;
						REP(j, sy) info[j] = r;
						info[sy] = -2;
						break;
					}
				}
				if (map.empty()) {
					map[n] = PAIR(a, b);
				}
			}
		}
		info[i / B] = -2;

		int res = INFLL;

		REP(si, NB) {
			int l = si * B, r = (si + 1) * B;
			CHMIN(r, i + 1);
			if (l >= r) break;

			if (info[si] == -1) {
				CHMIN(res, mi[si]);
			}
			else if (info[si] == -2) {
				int smi = INFLL;
				FOR(j, l, r) {
					CHMIN(smi, get(j) + v[j]);
				}
				CHMIN(res, smi);
				mi[si] = smi;
			}
			else {
				int tx = seg[si].min[info[si]];
				mi[si] = get(tx) + v[tx];
				CHMIN(res, mi[si]);
			}
		}
		ans[i] = res;
	}
	return ans;
}

V<int> slow(int n, V<int> a) {
	V<int> ans(n, INFLL);
	REP(l, n) {
		int sum = 0;
		FOR(r, l, n) {
			sum += a[r];
			FOR(k, l, r + 1) {
				CHMIN(ans[k], sum + (r - l + 1) * (r - l + 1));
			}
		}
	}
	return ans;
}

signed main() {
	INIT;

	if(1){
		VAR(int, n);
		VEC(int, a, n);
		auto ans = mycalc(n, a);
		REP(i, n) {
			OUT(ans[i])BR;
		}
		return 0;
	}

	auto system_now = std::chrono::system_clock::now();
	std::mt19937 mt(std::chrono::duration_cast<std::chrono::microseconds>(system_now.time_since_epoch()).count());
	std::uniform_int_distribution<> rand(/* min */-100, /* max */100);
	int n = 10;

	while (true) {
		V<int> a(n);
		REP(i, n) a[i] = rand(mt);

		auto mv = mycalc(n, a);
		auto sv = slow(n, a);

		if (mv != sv) {
			SHOW(n);
			SHOWVECTOR(a);
			SHOWVECTOR(mv);
			SHOWVECTOR(sv);
			VAR(int, x);
		}
	}

	/*auto ans = mycalc(n, a);

	REP(i, n) {
		OUT(ans[i])BR;
	}*/

	return 0;
}
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