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Submission #363777

# Submission time Handle Problem Language Result Execution time Memory
363777 2021-02-07T09:05:21 Z BartolM Split the sequence (APIO14_sequence) C++17
100 / 100
 714 ms 83932 KB 
#include <bits/stdc++.h>

using namespace std;

#define X first
#define Y second
#define mp make_pair
#define pb push_back
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <int, pii> pip;
typedef pair <pii, int> ppi;
typedef pair <ll, ll> pll;
typedef pair <ll, int> pli;

const int INF=0x3f3f3f3f;
const ll MAX=(ll)INF*INF;
const int N=1e5+5;
const int K=202;

int n, k;
ll dp[2][N];
int bac[N][K];
ll pref[N];
ll dp2[20][20];

int ind, koji[N];
vector <pll> v;

int ccw(pll a, pll b, pll c) {
    ll ret=a.X*(b.Y-c.Y)+b.X*(c.Y-a.Y)+c.X*(a.Y-b.Y);
    if (ret>0) return 1;
    if (ret<0) return -1;
    return 0;
}

ll f(pll pp, ll x) {
    return pp.X*x+pp.Y;
}

void dodaj(pll pp, int br) {
    while (v.size()>1 && ccw(v[(int)v.size()-2], v.back(), pp)>=0) v.pop_back();
    koji[v.size()]=br;
    v.pb(pp);
}

pli query(ll x) {
    ind=min(ind, (int)v.size()-1);
    while (ind+1<(int)v.size() && f(v[ind], x)<=f(v[ind+1], x)) ++ind;
    return mp(f(v[ind], x), koji[ind]);
}

void backtrack() {
    pii pp=mp(n, k);
    while (pp.Y) {
        pp.X=bac[pp.X][pp.Y--];
        printf("%d ", pp.X);
    }
}

void solve() {
    int b=1;
    for (int j=1; j<=k; ++j) {
        v.clear();
        ind=0;
        for (int i=1; i<=j; ++i) dodaj(mp(pref[i], dp[!b][i]-pref[i]*pref[i]), i);
        for (int i=j+1; i<=n; ++i) {
            pli curr=query(pref[i]);
            bac[i][j]=curr.Y;
            dp[b][i]=curr.X;
            dodaj(mp(pref[i], dp[!b][i]-pref[i]*pref[i]), i);
        }
        b^=1;
    }
    printf("%lld\n", dp[!b][n]);
}

void brut() {
    fill(dp2[0], dp2[0]+20, -MAX);
    dp2[0][0]=0;
    for (int i=1; i<=n; ++i) {
        for (int j=1; j<=k; ++j) {
            for (int l=0; l<i; ++l) {
                ll curr=dp2[l][j-1]+pref[l]*(pref[i]-pref[l]);
                if (curr>=dp2[i][j]) dp2[i][j]=curr, bac[i][j]=l;
            }
        }
    }
    printf("%lld\n", dp2[n][k]);
}

void load() {
    scanf("%d %d", &n, &k);
    for (int i=1; i<=n; ++i) {
        scanf("%lld", &pref[i]);
        pref[i]+=pref[i-1];
    }
}

int main() {
    load();
    if (n<=10) brut();
    else solve();
    backtrack();
    return 0;
}

Compilation message

sequence.cpp: In function 'void load()':
sequence.cpp:93:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   93 |     scanf("%d %d", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:95:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   95 |         scanf("%lld", &pref[i]);
      |         ~~~~~^~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 108 == 108
2 Correct 0 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 0 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 0 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 0 ms 364 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 364 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 364 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 0 ms 364 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 364 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 512 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 492 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 492 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 492 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 492 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 620 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 492 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 492 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1132 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 1260 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 5 ms 1132 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 1132 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 1132 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 1132 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 1132 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 4 ms 1132 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 1132 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 1132 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 8812 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 8 ms 8812 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 42 ms 8808 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 7 ms 8808 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 38 ms 8812 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 42 ms 8812 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 45 ms 8808 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 31 ms 8808 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 36 ms 8808 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 43 ms 8808 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 60 ms 83420 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 63 ms 83420 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 600 ms 83812 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 64 ms 83932 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 714 ms 83420 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 472 ms 83420 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 517 ms 83804 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 391 ms 83804 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 437 ms 83676 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 543 ms 83676 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845