oj.uz

Submission #240711

# Submission time Handle Problem Language Result Execution time Memory
240711 2020-06-20T20:44:01 Z WhaleVomit Split the sequence (APIO14_sequence) C++14
100 / 100
 839 ms 84216 KB 
#include <bits/stdc++.h>
 
using namespace std;
 
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define all(v) v.begin(), v.end()
#define sz(v) (int)v.size()
 
#define MOO(i, a, b) for(int i=a; i<b; i++)
#define M00(i, a) for(int i=0; i<a; i++)
#define MOOd(i,a,b) for(int i = (b)-1; i >= a; i--)
#define M00d(i,a) for(int i = (a)-1; i>=0; i--)
 
#define FAST ios::sync_with_stdio(0); cin.tie(0);
#define finish(x) return cout << x << '\n', 0;
#define dbg(x) cerr << ">>> " << #x << " = " << x << "\n";
#define _ << " _ " <<
 
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int,int> pi;
typedef pair<ld,ld> pd;
typedef complex<ld> cd;

struct line {
    ll m;
    ll b;
    int idx;
    line(ll mm, ll bb, int idxp) {
        m = mm;
        b = bb;
        idx = idxp;
    }
};

bool leftOf(line l1, line l2, line l3) { // is intersection of l1 and l3 to the left of l1 and l2?
    if(l2.m == l3.m) return 1;
    return (l3.b-l1.b)*(l1.m-l2.m) <= (l2.b-l1.b)*(l1.m-l3.m);
}

ll eval(ll x, line l) {
    return l.m * x + l.b;
}

bool better(ll x, line l1, line l2) { // l2(x) >= l1(x)?
    return eval(x, l2) >= eval(x, l1);
}

const int MAX_N = 100100;
const int MAX_K = 202;
int n, k;
const ll inf = 1e17;
ll arr[MAX_N];
ll psum[MAX_N];
ll dp[MAX_N][2];
int lastsplit[MAX_N][MAX_K];
 
int main() { FAST
    cin >> n >> k;
    for(int i = 1; i <= n; i++) {
        cin >> arr[i];
        psum[i] = psum[i-1] + arr[i];
    }
    for(int j = 1; j <= k; j++) {
        for(int i = 0; i <= n; i++) {
            dp[i][j] = -inf;
        }
    }
    for(int j = 1; j <= k; j++) {
        int jj = j&1;
        deque<line> dq;
        dq.pb(line(psum[n],0,0));
        for(int i = 1; i <= n; i++) {
            while(sz(dq) >= 2 && better(psum[i], dq[0], dq[1])) dq.pop_front();
            
            dp[i][jj] = -psum[i] * psum[i] + eval(psum[i], dq[0]);
            lastsplit[i][j] = dq[0].idx;

            line l3 = line(psum[n]+psum[i], dp[i][jj^1]-psum[i]*psum[n],i);
            while(sz(dq) >= 2 && leftOf(dq[sz(dq)-2], dq[sz(dq)-1], l3)) dq.pop_back();
            dq.pb(l3);
        }
    }
    int besIdx = 1;
    for(int i = 1; i <= n; i++) {
        if(dp[i][k&1] > dp[besIdx][k&1]) {
            besIdx = i;
        }
    }
    ll mx = dp[besIdx][k&1];
    vi v;
    int cur = k;
    while(cur != 0) {
        v.pb(besIdx);
        besIdx = lastsplit[besIdx][cur];
        cur--;
    }
    cout << mx << "\n";
    M00(i, k) {
        if(i != 0) cout << " ";
        cout << v[i];
    }
    cout << "\n";
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 5 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 5 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 4 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 4 ms 256 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 4 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 5 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 4 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 4 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 4 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 4 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 4 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 5 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 4 ms 384 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 4 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 5 ms 384 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 5 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 5 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 5 ms 384 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 4 ms 384 KB contestant found the optimal answer: 687136 == 687136
9 Correct 4 ms 384 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 4 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 512 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 4 ms 512 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 5 ms 512 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 5 ms 512 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 512 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 6 ms 512 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 6 ms 512 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 512 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 5 ms 512 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 5 ms 512 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1152 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 5 ms 1280 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 13 ms 1152 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 1280 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 12 ms 1152 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 1152 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 11 ms 1152 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 1280 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 1280 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 1280 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 8704 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 8764 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 71 ms 8744 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 10 ms 8704 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 54 ms 8704 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 60 ms 8824 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 63 ms 8744 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 47 ms 8704 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 54 ms 8704 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 66 ms 8832 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 56 ms 83576 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 60 ms 83980 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 682 ms 84216 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 61 ms 84216 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 839 ms 83960 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 589 ms 83704 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 595 ms 84216 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 480 ms 84088 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 505 ms 83960 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 622 ms 83964 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845