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답안 #944232

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
944232 2024-03-12T12:05:52 Z wapas 수열 (APIO14_sequence) C++14
89 / 100
 1139 ms 88972 KB 
// code by wapas
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

struct CHT {
    const ll inf = 1e9;
    vector<pair<ll, ll>> lineStk = {};
    vector<ll> pointStk = {};
    vector<int> idxStk = {};
    ll isMin = 1;
    void toggleMinMax() {
        isMin *= -1;
    }
    void add(ll a, ll b = 0, int idx = -1) {
        a *= isMin; b *= isMin;
        while (lineStk.size()) {
            auto [p, q] = lineStk.back();
            if (a == p) {
                if (b > q) {
                    lineStk.pop_back();
                    pointStk.pop_back();
                    idxStk.pop_back();
                }
                else break;
                continue;
            }
            auto k = pointStk.back();
            ll prev = p * k + q, curr = a * k + b;
            if (curr >= prev) {
                lineStk.pop_back();
                pointStk.pop_back();
                idxStk.pop_back();
            }
            else {
                break;
            }
        }
        if (lineStk.size()) {
            auto [p, q] = lineStk.back();
            if (a != p) {
                ll num = q - b, den = a - p;
                ll t = (num + den - 1) / den;
                lineStk.push_back({ a, b });
                pointStk.push_back(t);
                idxStk.push_back(idx);
            }
        }
        else {
            lineStk.push_back({ a, b });
            pointStk.push_back(-inf);
            idxStk.push_back(idx);
        }
    }
    ll query(ll t) {
        int l = 0, r = pointStk.size();
        while (l + 1 < r) {
            int m = (l + r) / 2;
            if (pointStk[m] <= t) l = m;
            else r = m;
        }
        return l;
    }
    ll value(ll t, ll idx) {
        return (lineStk[idx].first * t + lineStk[idx].second) * isMin;
    }
    void replace(CHT &o) {
        swap(lineStk, o.lineStk);
        swap(pointStk, o.pointStk);
        swap(idxStk, o.idxStk);
        swap(isMin, o.isMin);
    }
};

void solution(int t) {
    ll N, K; cin >> N >> K;
    vector<ll> S(N + 1);
    for (int i = 1; i <= N; i++) {
        ll x; cin >> x;
        S[i] = x;
        S[i] += S[i - 1];
    }
    vector<ll> cache(N + 1, 0);
    vector<vector<int>> prev(K + 1, vector<int>(N + 1, -1));
    CHT cht;
    for (int n = 1; n <= N; n++) cht.add(S[n], - S[n] * S[n], n);
    for (int k = 1; k <= K; k++) {
        CHT ncht;
        vector<ll> ncache(N + 1, 0);
        for (int n = 1; n <= N; n++) {
            int i = cht.query(S[n]);
            ncache[n] = cht.value(S[n], i);
            prev[k][n] = cht.idxStk[i];
            ncht.add(S[n], ncache[n] - S[n] * S[n], n);
        }
        cht.replace(ncht);
        swap(cache, ncache);
    }
    vector<int> history = {};
    int k = K, n = N;
    while (prev[k][n] != -1) {
        history.push_back(prev[k][n]);
        n = prev[k--][n];
    }
    sort(history.begin(), history.end());
    for (int i = 1; i < history.size(); i++) if (history[i] <= history[i - 1]) history[i] = history[i - 1] + 1;
    if (history.back() == N) history[K - 1] -= 1;
    cout << (ll) cache[N] << "\n";
    for (auto e : history) cout << e << " ";
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    // int T; cin >> T;
    int T = 1;
    for (int t = 0; t < T; t++) {
        solution(t);
    }
}

Compilation message

sequence.cpp: In member function 'void CHT::add(ll, ll, int)':
sequence.cpp:20:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   20 |             auto [p, q] = lineStk.back();
      |                  ^
sequence.cpp:42:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   42 |             auto [p, q] = lineStk.back();
      |                  ^
sequence.cpp: In function 'void solution(int)':
sequence.cpp:108:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  108 |     for (int i = 1; i < history.size(); i++) if (history[i] <= history[i - 1]) history[i] = history[i - 1] + 1;
      |                     ~~^~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 348 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 348 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 344 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 348 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 456 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 348 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 348 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 348 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 348 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 348 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 348 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 348 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 344 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 348 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 456 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 348 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 348 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 348 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 348 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 348 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 348 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 344 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 500 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 348 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 604 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 348 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 348 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Incorrect 1 ms 604 KB Integer 200 violates the range [1, 199]
7 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 344 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1332 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 348 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 10 ms 1332 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 1116 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 10 ms 1116 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 9 ms 1332 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 600 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 604 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 1200 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 1228 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 104 ms 9320 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 1592 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 64 ms 5996 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 58 ms 6764 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 76 ms 7324 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 60 ms 6196 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 72 ms 6872 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 93 ms 8608 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 25 ms 10452 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 10284 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1139 ms 88972 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 27 ms 11136 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1124 ms 88112 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 605 ms 62444 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 818 ms 68984 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 664 ms 58040 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 784 ms 65108 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 990 ms 80568 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845