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답안 #345290

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
345290 2021-01-07T07:12:30 Z DrearyJoke 수열 (APIO14_sequence) C++17
100 / 100
 1522 ms 99788 KB 
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<bool> vb;
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;

template <typename T, typename U> std::istream&operator>>(std::istream&i, pair<T,U>&p) {i >> p.x >> p.y; return i;}
template<typename T>std::istream&operator>>(std::istream&i,vector<T>&t) {for(auto&v:t){i>>v;}return i;}
template <typename T, typename U> std::ostream&operator<<(std::ostream&o, const pair<T,U>&p) {o << p.x << ' ' << p.y; return o;}
template<typename T>std::ostream&operator<<(std::ostream&o,const vector<T>&t) {if(t.empty())o<<'\n';for(size_t i=0;i<t.size();++i){o<<t[i]<<" \n"[i == t.size()-1];}return o;}

#define deb(x) cout << '>' << #x << ':' << x << endl;
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define END '\n'
#define inf 9e18
#define ff first
#define ss second
#define pb push_back

const ll maxVal = 1e18;

struct Line {
    ll m, c, idx;
    Line (ll _m, ll _c, ll _idx) {
        m = _m;
        c = _c;
        idx = _idx;
    }
    ll eval(ll x) {
        return m * x + c;
    }
    ll getX(Line L) {
        if (m == L.m) {
            if (c > L.c) return maxVal;
            else return -maxVal;
        }
        return (L.c - c) / (m - L.m);
    }
};

struct LowerHull {
    deque<Line> A;
    void addLine(ll m, ll c, ll idx) {
        Line now(m, c, idx);
        while((int)A.size() >= 2 && now.getX(A[0]) >= A[0].getX(A[1])) A.pop_front();
        A.push_front(now);
    }
    pair<ll, int> query(ll x) {
        if (A.empty()) return {0, 0};
        while((int)A.size() >= 2 && A.back().eval(x) <= A[(int)A.size() - 2].eval(x)) A.pop_back();
        return {A.back().eval(x), A.back().idx};
    }
};

void solve(){
    int n, k;
    cin >> n >> k;
    vll A(n + 1), pref(n + 1, 0), suf(n + 2, 0);
    for (int i = 1; i <= n; ++i) cin >> A[i], pref[i] = pref[i - 1] + A[i];
    for (int i = n; i; --i) suf[i] = suf[i + 1] + A[i];
    // vvll dp(n + 1, vll(k + 1, 0));
    vvi par(n + 1, vi(k + 1, 0));
    ll ans = 0;
    int beg;
    vector<LowerHull> hulls(k + 1);
    for (int i = 1; i < n; ++i) {
        vector<array<ll, 3>> cur(k + 1);
        for (int j = 1; j <= k; ++j) {
            // cout << "CURRENT: " << i << " " << j << " " << l << END;
            // cout << dp[l - 1][j - 1] << " " << pref[i] << " " << pref[l - 1] << " " << suf[i + 1] << END;
            ll x = suf[i + 1];
            auto u = hulls[j - 1].query(x);
            ll val = pref[i] * suf[i + 1] + u.ff;
            // ll val = dp[l - 1][j - 1] + (pref[i] - pref[l - 1]) * (suf[i + 1]);
            // cout << i << " " << j << " " << u.ff << " " << u.ss << END;
            par[i][j] = u.ss;
            ll m = -pref[i], c = val, idx = i;
            cur[j] = {m, c, idx};
            // dp[i][j] = max(dp[i][j], dp[l - 1][j - 1] + (pref[i] - pref[l - 1]) * (suf[i + 1]));

            if (j == k) {
                if (val >= ans) ans = val, beg = i;
            }
        }
        for (int j = 1; j <= k; ++j) {
            hulls[j].addLine(cur[j][0], cur[j][1], cur[j][2]);
        }
    }
    // for (int i = 1; i <= n; ++i) {
    //     for (int j = 1; j <= k; ++j) cout << dp[i][j] << " ";
    //     cout << END;
    // }
    // cout << "LO\n";
    // for (int i = 1; i <= n; ++i) {
    //     for (int j = 1; j <= k; ++j) cout << par[i][j] << " ";
    //     cout << END;
    // }
    // cout << "HULLS\n";
    // for (int i = 1; i <= k - 1; ++i) {
    //     cout << "For " << i << " moves: \n";
    //     for (auto u: hulls[i].A) {
    //         cout << u.m << " " << u.c << " " << u.idx << END;
    //     }
    // }
    int idx = k;
    vi fin;
    while(k) fin.pb(beg), beg = par[beg][k--]; 
    cout << ans << END << fin;
}
int main()
{
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    int t = 1;
    // cin >> t;
    while(t--){
        solve();
    }
    return 0;
}
/*
7 3
4 1 3 4 0 2 3
*/

Compilation message

sequence.cpp: In function 'void solve()':
sequence.cpp:115:9: warning: unused variable 'idx' [-Wunused-variable]
  115 |     int idx = k;
      |         ^~~

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 364 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 364 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 364 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 364 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 364 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 364 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 364 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 364 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 396 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 388 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 364 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 364 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 492 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 364 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 364 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 364 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 364 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 364 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 364 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 364 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 364 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 364 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 748 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 364 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 620 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 748 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 748 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 492 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 364 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 492 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 492 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 492 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 1644 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 520 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 10 ms 1484 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 1388 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 14 ms 1524 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 11 ms 1772 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 620 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 900 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 1516 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 1644 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 131 ms 10512 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 1516 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 76 ms 7020 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 82 ms 7408 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 95 ms 8352 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 93 ms 7532 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 88 ms 7788 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 107 ms 9452 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 39 ms 11628 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 33 ms 11756 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1522 ms 99788 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 37 ms 12652 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1498 ms 97812 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1106 ms 69860 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1157 ms 80028 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 974 ms 68092 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 948 ms 74092 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1415 ms 90348 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845