Submission #538448

# Submission time Handle Problem Language Result Execution time Memory
538448 2022-03-17T01:28:53 Z Lobo Split the sequence (APIO14_sequence) C++17
100 / 100
1799 ms 88180 KB
#include<bits/stdc++.h>
using namespace std;

const long long inf = (long long) 1e13 + 10;
const int inf1 = (int) 1e9 + 10;
#define int long long   
#define ll long long
#define dbl long double
#define endl '\n'
#define sc second
#define fr first
#define mp make_pair
#define pb push_back
#define all(x) x.begin(), x.end()

#define maxn 100010

int n, k, a[maxn], ps[maxn];
int dp[maxn][2];
int32_t ant[maxn][202];
vector<pair<pair<int,int>,pair<pair<int,int>,int>>> cht;
//cht -> a,b,l,r
//chtlr -> l,r,a,b

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

dbl interx(int a1, int b1, int a2, int b2) {
    return (dbl) (b2-b1)/(a1-a2);
}

void resetcht() {
    cht.clear();

    cht.pb(mp(mp(-inf1,+inf1),mp(mp(0,0),0)));
}

void attcht(int a, int b, int id) {
    // so vai tirar para a esquerda
    // vai tirando enquanto valer a pena

    int ansl = inf;
    while(cht.size()) {
        int a1 = cht.back().sc.fr.fr;
        int b1 = cht.back().sc.fr.sc;
        int l = cht.back().fr.fr;    
        int r = cht.back().fr.sc;
        int id1 = cht.back().sc.sc;

        if(f(a,b,l) >= f(a1,b1,l)) {
            cht.pop_back();
            ansl = l;
        }
        else if(f(a,b,r) >= f(a1,b1,r)) {
            int x = ceil(interx(a,b,a1,b1));

            cht.pop_back();
            cht.pb(mp(mp(l,x-1),mp(mp(a1,b1),id1)));
            ansl = x;
            break;
        }
        else {
            break;
        }
    }

    if(ansl <= inf1) {
        cht.pb(mp(mp(ansl,inf1),mp(mp(a,b),id)));
    }
}

int idq;
pair<int,int> qrr(int x) {
    idq = min(idq,(int) cht.size()-1);

    while(idq+1 != cht.size()) {
        int a = cht[idq].sc.fr.fr;
        int b = cht[idq].sc.fr.sc;
        int a1 = cht[idq+1].sc.fr.fr;
        int b1 = cht[idq+1].sc.fr.sc;

        if(f(a1,b1,x) >= f(a,b,x)) idq++;
        else break;
    }

    int a = cht[idq].sc.fr.fr;
    int b = cht[idq].sc.fr.sc;
    return mp(f(a,b,x),cht[idq].sc.sc);
}

void solve() {
    cin >> n >> k;
    for(int i = 1; i <= n; i++) {
        cin >> a[i];
        ps[i] = ps[i-1] + a[i];
    }

    for(int j = 1; j <= k; j++) {
        resetcht();
        //dp[0][j] = 0
        idq = 0;
        for(int i = j; i <= n; i++) {
            auto qr = qrr(ps[i]);
            dp[i][j&1] = qr.fr;
            ant[i][j] = qr.sc;
            attcht(ps[i],dp[i][j&1^1]-ps[i]*ps[i],i);
        }
    }

    //dp[i][k] = max(dp[j-1][k-1] + ps[j-1]*(ps[i]-ps[j-1]))
    //dp[j-1][k-1] - ps[j-1]² + ps[j-1]*ps[i]
    //a ordem que vai colocando é crescente entao é só usar um vector bem mais simples
    

    int id = n;
    vector<int> ans;
    for(int j = k; j >= 1; j--) {
        ans.pb(ant[id][j]);
        id = ant[id][j];
    }

    reverse(all(ans));

    cout << dp[n][k&1] << endl;
    for(auto x : ans) cout << x << " ";
    cout << endl;
}

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(0);

    // freopen("in.in", "r", stdin);
    // freopen("out.out", "w", stdout);

    int tt = 1;
    // cin >> tt;
    while(tt--) solve();

}

Compilation message

sequence.cpp: In function 'std::pair<long long int, long long int> qrr(long long int)':
sequence.cpp:77:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<std::pair<long long int, long long int>, std::pair<std::pair<long long int, long long int>, long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   77 |     while(idq+1 != cht.size()) {
      |           ~~~~~~^~~~~~~~~~~~~
sequence.cpp: In function 'void solve()':
sequence.cpp:107:33: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  107 |             attcht(ps[i],dp[i][j&1^1]-ps[i]*ps[i],i);
      |                                ~^~
# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 340 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 340 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 340 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 224 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 340 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 340 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 340 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 340 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 340 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 340 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 340 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 468 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 468 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 468 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 468 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 468 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 468 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 468 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 468 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 468 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 1 ms 1236 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 1236 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 20 ms 1248 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 1236 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 13 ms 1244 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 13 ms 1240 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 19 ms 1244 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 21 ms 1244 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 1236 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 1236 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 7 ms 8976 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 7 ms 8976 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 200 ms 9024 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 8 ms 9036 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 98 ms 8976 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 118 ms 8976 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 143 ms 9036 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 126 ms 9036 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 134 ms 8960 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 168 ms 8992 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 62 ms 85688 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 62 ms 85660 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1799 ms 87736 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 61 ms 88180 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1578 ms 85980 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1173 ms 85972 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1405 ms 87112 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 1208 ms 87008 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1173 ms 86516 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1676 ms 86648 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845