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답안 #852160

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
852160 2023-09-21T10:42:59 Z chanhchuong123 수열 (APIO14_sequence) C++14
100 / 100
 393 ms 90120 KB 
#include <bits/stdc++.h>
using namespace std;
#define task ""

const long long INF = 1e18 + 0702;
const int MAX = 100010;
int n, k;
int a[MAX];
int pf[MAX];
int trace[MAX][202];
long long dp[2][MAX];

struct Line {
    int m; long long c; int id;

    Line(int _m = 0, long long _c = 0, int _id = 0) {
        m = _m;
        c = _c;
        id = _id;
    }

    long long eval(long long x) {
        return m * x + c;
    }
};

struct ConvexHullTrick {
    vector<Line> lines;
    int pt = 0;

    bool bad(const Line &l1, const Line &l2, const Line &l3) {
        return 1LL * (l1.c - l3.c) * (l2.m - l1.m) <= 1LL * (l1.c - l2.c) * (l3.m - l1.m);
    }

   void add(long long m, long long c, int id) {
        if (lines.size() && lines.back().m == m) {
            long long minC = c;
            while (lines.size() && lines.back().m == m) {
                minC = min(minC, lines.back().c);
                lines.pop_back();
            }
            lines.push_back(Line(m, minC, id));
            return;
        }
        Line line(m, c, id); while (lines.size() >= 2 && bad(lines[lines.size() - 2], lines.back(), line)) lines.pop_back();
        lines.push_back(line); pt = min(pt, int(lines.size()) - 1);
    }

    pair<long long, int> get(int x) {
        if (lines.size() == 1) return make_pair(lines[0].eval(x), lines[0].id); while (pt + 1 < lines.size() && lines[pt + 1].eval(x) >= lines[pt].eval(x)) ++pt;
        return make_pair(lines[pt].eval(x), lines[pt].id);
    }
} cht[2];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(nullptr);

	if (fopen(task".inp", "r")) {
		freopen(task".inp", "r", stdin);
		freopen(task".out", "w", stdout);
	}

	cin >> n >> k; ++k;
	for (int i = 1; i <= n; ++i) {
        cin >> a[i];
        pf[i] = pf[i - 1] + a[i];
	}
	memset(dp, -1, sizeof dp);
	dp[0][0] = 0;
	long long res = 0;
	for (int j = 1; j <= k; ++j) {
        int prv = (j - 1) & 1, cur = j & 1;
        cht[prv].lines.clear();
        cht[prv].pt = 0;
        memset(dp[cur], -1, sizeof dp[cur]);
        for (int i = j; i <= n; ++i) {
            if (dp[prv][i - 1] > -1) cht[prv].add(pf[i - 1], -1LL * pf[i - 1] * pf[i - 1] + dp[prv][i - 1], i - 1);
            pair<long long, int> ans = cht[prv].get(pf[i]);
            if (i == n && j == k) res = ans.first;
            dp[cur][i] = ans.first;
            trace[i][j] = ans.second;
        }
	}
    cout << res << '\n';
    vector<int> posAns;
    do {
        n = trace[n][k--];
        posAns.push_back(n);
    } while (k > 1);
    for (int &id: posAns) {
        cout << id << ' ';
    }
	return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

Compilation message

sequence.cpp: In member function 'std::pair<long long int, int> ConvexHullTrick::get(int)':
sequence.cpp:50:9: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
   50 |         if (lines.size() == 1) return make_pair(lines[0].eval(x), lines[0].id); while (pt + 1 < lines.size() && lines[pt + 1].eval(x) >= lines[pt].eval(x)) ++pt;
      |         ^~
sequence.cpp:50:81: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
   50 |         if (lines.size() == 1) return make_pair(lines[0].eval(x), lines[0].id); while (pt + 1 < lines.size() && lines[pt + 1].eval(x) >= lines[pt].eval(x)) ++pt;
      |                                                                                 ^~~~~
sequence.cpp:50:95: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   50 |         if (lines.size() == 1) return make_pair(lines[0].eval(x), lines[0].id); while (pt + 1 < lines.size() && lines[pt + 1].eval(x) >= lines[pt].eval(x)) ++pt;
      |                                                                                        ~~~~~~~^~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:59:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   59 |   freopen(task".inp", "r", stdin);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:60:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   60 |   freopen(task".out", "w", stdout);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2648 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2652 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2652 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 2652 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 2652 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2652 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2652 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2652 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2680 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2652 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2648 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 2652 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 2652 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2652 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 2648 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2652 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 2652 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2652 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 2652 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2652 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 2652 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 2652 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 2696 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 2652 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 2652 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2652 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2648 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 2652 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2652 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 2648 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 2652 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 2660 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 2648 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 2648 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 2652 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 4700 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4700 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 4828 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4696 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 4700 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 5 ms 4700 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 4700 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 4700 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 4896 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 4696 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 11492 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 11296 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 29 ms 11612 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 11612 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 28 ms 11432 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 28 ms 11492 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 30 ms 11612 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 21 ms 11612 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 25 ms 11612 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 31 ms 11612 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 22 ms 89296 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 24 ms 89120 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 274 ms 89296 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 26 ms 88772 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 393 ms 89296 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 261 ms 87504 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 292 ms 90120 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 215 ms 89040 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 225 ms 89688 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 267 ms 89036 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845