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Submission #928927

# Submission time Handle Problem Language Result Execution time Memory
928927 2024-02-17T08:18:38 Z Foolestboy Split the sequence (APIO14_sequence) C++14
100 / 100
 423 ms 84420 KB 
#include <bits/stdc++.h>

#define SQR(x)    (1LL * ((x) * (x)))
#define MASK(i)   (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
#define fi        first
#define se        second
#define pb        push_back
#define all(x)    x.begin(), x.end()
#define rall(x)   x.rbegin(), x.rend()
#define sz(s)     (int)s.size()
#define prev      __prev
#define next      __next
#define left      __left
#define right     __right

#define mp make_pair
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vll vector<ll>

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef unsigned int ui;

using namespace std;

const int mod = 1e9 + 7;
const int INF = 1e9 + 7;
const ll INFLL = (ll)2e18 + 7LL;
const ld PI = acos(-1);

const int dx[] = {1, -1, 0, 0, -1, 1, 1, -1};
const int dy[] = {0, 0, 1, -1, -1, -1, 1, 1};

template<class BUI, class TRONG>
    bool minimize(BUI &x, const TRONG y){
        if(x > y){
            x = y;
            return true;
        } else return false;
    }
template<class BUI, class TRONG>
    bool maximize(BUI &x, const TRONG y){
        if(x < y){
            x = y;
            return true;
        } else return false;
    }

/* Author : Bui Nguyen Duc Trong, Luong Van Chanh High School for the gifted*/
/* Template is copied by Trong */

                           /** Losing in Provincial Contests **/
                                    /** TRYING HARDER**/
                                   /**      ORZ     **/

/* -----------------[ MAIN CODE GOES HERE ]----------------- */

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int N = 1e5 + 10;

int n, k;
int a[N];

struct Line{
    ll a, b;
    int id;

    Line() : a(0), b(0) {}

    Line(ll a, ll b, int id) : a(a), b(b), id(id) {}

    ll f(ll x) { return a * x + b; }

};

struct ConvexHullTrick{
    vector<Line> vec;
    int iter = 0;

    void reset(){
        vec.clear();
        iter = 0;
    }

    ld inter(Line A, Line B){
        return (ld)(A.b - B.b) / (B.a - A.a);
    }

    void insertLine(Line l){
        if(!vec.empty() && l.a == vec.back().a){
            if(vec.back().b <= l.b) vec.back() = l;
//            if(maximize(vec.back().b, l.b)) vec.back() = l;
        }
        else{
            while(sz(vec) >= 2 && inter(l, vec.back()) <= inter(vec.back(), vec[sz(vec) - 2])) vec.pop_back();
            vec.push_back(l);
        }
    }

    pair<ll, int> query(ll x){
        if(vec.empty()) return {-INFLL, 0};
        minimize(iter, sz(vec) - 1);
        while(iter + 1 < sz(vec) && vec[iter + 1].f(x) >= vec[iter].f(x)) ++iter;
        return mp(vec[iter].f(x), vec[iter].id);
    }

} cht;

ll f[N][2];
int trace[N][202];

void solve(){
    cin >> n >> k;
    for(int i = 1; i <= n; i++){
        cin >> a[i]; a[i] += a[i - 1];
    }
    memset(f, -0x3f, sizeof f);
    for(int i = 0; i <= n; i++) f[i][0] = 0;
    for(int j = 1; j <= k; j++){
        cht.reset();
        for(int i = 1; i <= n; i++) f[i][j & 1] = -INFLL;
        for(int i = 1; i <= n; i++){
            if(f[i - 1][(j - 1) & 1] >= 0) cht.insertLine(Line(a[i - 1], f[i - 1][(j - 1) & 1] - 1LL * a[i - 1] * a[i - 1], i));
            auto [x, y] = cht.query(a[i]);
            f[i][j & 1] = x;
            trace[i][j] = y;
        }
    }
//    cout << "huhu " << trace[n][k] << '\n';
    int r = n;
    vector<int> ans;
    for(int i = k; i >= 1; i--){
        ans.push_back(trace[r][i] - 1);
        r = trace[r][i] - 1;
    }
    cout << f[n][k & 1] << '\n';
    reverse(all(ans));
    ll tot = 0, s = 0;
    vector<int> tmp = ans;
    tmp.insert(tmp.begin(), 0);
    tmp.push_back(n);
    for(int i = 1; i < sz(tmp); i++){
        int sum = a[tmp[i]] - a[tmp[i - 1]];
        tot += s * sum;
        s += sum;
    }
    assert(tot == f[n][k & 1]);
    for(int x : ans) cout << x << ' '; cout << '\n';
}

/*
2 1
0 0
*/

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    const bool multitest = 0;
    int tt = 1; if(multitest) cin >> tt;

    while( tt-- ){

        solve();

    }

    return 0;
}

Compilation message

sequence.cpp: In function 'void solve()':
sequence.cpp:129:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
  129 |             auto [x, y] = cht.query(a[i]);
      |                  ^
sequence.cpp:153:5: warning: this 'for' clause does not guard... [-Wmisleading-indentation]
  153 |     for(int x : ans) cout << x << ' '; cout << '\n';
      |     ^~~
sequence.cpp:153:40: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'for'
  153 |     for(int x : ans) cout << x << ' '; cout << '\n';
      |                                        ^~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2908 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2908 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2904 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 2908 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 2908 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2908 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2908 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2904 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2908 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2908 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2908 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 2908 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 2908 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2908 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 2904 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2908 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 2908 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2908 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2908 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 2908 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2908 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 2908 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 2908 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 2908 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 2908 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 2908 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2908 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2904 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2908 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 2908 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2908 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 2908 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 2908 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 2908 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 2908 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 2908 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 2908 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 5212 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 4 ms 5228 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 5212 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 4 ms 5212 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 4 ms 5212 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 4 ms 5228 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 4 ms 5460 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 5212 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 2 ms 5212 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 11548 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 11548 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 32 ms 11804 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 11800 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 24 ms 11548 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 27 ms 11548 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 31 ms 11804 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 21 ms 12056 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 23 ms 11804 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 31 ms 11804 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 24 ms 84160 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 21 ms 83404 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 348 ms 83760 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 21 ms 84420 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 423 ms 83660 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 294 ms 83400 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 309 ms 83916 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 243 ms 83916 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 259 ms 83656 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 346 ms 83588 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845