oj.uz

Submission #73081

# Submission time Handle Problem Language Result Execution time Memory
73081 2018-08-27T15:16:30 Z polyfish Split the sequence (APIO14_sequence) C++14
71 / 100
 1485 ms 132096 KB 
//I love armpit fetish
 
#include <bits/stdc++.h>
using namespace std;
 
#define debug(x) cerr << #x << " = " << x << '\n';
#define BP() cerr << "OK!\n";
#define PR(A, n) {cerr << #A << " = "; for (int _=1; _<=n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define PR0(A, n) {cerr << #A << " = "; for (int _=0; _<n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define FILE_NAME "data"
 
typedef pair<int64_t, int64_t> line;
 
const int MAX_N = 100007;
const int MAX_K = 207;
const int64_t INF = 1e18;
 
int n, k, a[MAX_N];
int64_t ps[MAX_N], f[MAX_N][MAX_K];
 
struct convex_hull {
    vector<line> d;
    int head;
 
    void reset() {
        d.clear();
        head = 0;
    }
 
    convex_hull() {
        reset();
    }
 
    bool bad(line l1, line l2, line l3) {
        return (l1.second - l3.second) * (l2.first - l1.first)
                <= (l1.second - l2.second) * (l3.first - l1.first);
    }
 
    void add_line(int64_t a, int64_t b) {
        d.push_back(line(a, b));
        while (d.size()>2 && bad(d[d.size()-3], d[d.size()-2], d.back()))
            d.erase(d.end() - 2);
    }
 
    int64_t get(int64_t x) {
        if (d.size()==0)
            return -INF;
        head = min(head, (int)d.size()-1);
        while (head+1<d.size() && d[head].first * x + d[head].second
                                < d[head+1].first * x + d[head+1].second)
            ++head;
        return d[head].first * x + d[head].second;
    }
};
 
void enter() {
    cin >> n >> k;
    ++k;
    for (int i=1; i<=n; ++i) {
        cin >> a[i];
        ps[i] = ps[i-1] + a[i];
    }
}
 
void trace(int pos, int nPart) {
    if (pos==0)
        return;
    for (int i=pos-1; i>=0; --i) {
        if (f[pos][nPart] == f[i][nPart-1] + ps[i] * (ps[pos] - ps[i])) {
            trace(i, nPart-1);
            break;
        }
    }
    if (pos!=n) {
        cout << pos << ' ';
    }
}
 
void dp() {
    f[0][0] = 0;
    convex_hull CH;
    for (int i=1; i<=k; ++i)
        f[0][i] = -INF;
    for (int i=1; i<=n; ++i)
        f[i][0] = -INF;
    for (int j=1; j<=k; ++j) {
        CH.reset();
        if (f[0][j-1]!=-INF)
            CH.add_line(ps[0], f[0][j-1] - 1LL * ps[0] * ps[0]);
        for (int i=1; i<=n; ++i) {
            f[i][j] = max(-INF, CH.get(ps[i]));
            // if (i==6 && j==7) {
            //     cerr << ps[i] << ' ' << f[i][j-1] - 1LL * ps[i] * ps[i] << '\n';
            // }
            // if (i==7 && j==7) {
            //     //cerr << CH.d[4].first << ' ' << CH.d[4].second << '\n';
            //     debug(CH.d[4].first * ps[7] + CH.d[4].second);
            //     debug(CH.d[5].first * ps[7] + CH.d[5].second);
            // }
            if (f[i][j-1]!=-INF)
                CH.add_line(ps[i], f[i][j-1] - 1LL * ps[i] * ps[i]);
        }
    }
    cout << f[n][k] << '\n';
    trace(n, k);
}
 
int main() {
	#ifdef OFFLINE_JUDGE
		freopen(FILE_NAME".inp", "r", stdin);
		freopen(FILE_NAME".out", "w", stdout);
	#endif
	ios::sync_with_stdio(0); cin.tie(0);
	enter();
	dp();
}

Compilation message

sequence.cpp: In member function 'int64_t convex_hull::get(int64_t)':
sequence.cpp:49:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while (head+1<d.size() && d[head].first * x + d[head].second
                ~~~~~~^~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 3 ms 472 KB contestant found the optimal answer: 999 == 999
3 Correct 3 ms 472 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 540 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 540 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 3 ms 580 KB contestant found the optimal answer: 1 == 1
7 Correct 3 ms 640 KB contestant found the optimal answer: 1 == 1
8 Correct 3 ms 640 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 640 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 640 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 640 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 640 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 640 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 640 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 640 KB contestant found the optimal answer: 805 == 805
16 Correct 3 ms 640 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 3 ms 640 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 716 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 716 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 716 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 4 ms 716 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 3 ms 716 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 716 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 716 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 716 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 716 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 716 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 892 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 892 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 892 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 3 ms 1020 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 4 ms 1020 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 1020 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 1020 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 4 ms 1020 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 1020 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 1076 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 2392 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 4 ms 2392 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 8 ms 2416 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 5 ms 2416 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 2416 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 2416 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 9 ms 2416 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 9 ms 2432 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 2436 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 2436 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 17292 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 17 ms 17292 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 111 ms 17420 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 19 ms 17548 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 79 ms 17600 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 99 ms 17600 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 85 ms 17704 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 69 ms 17704 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 85 ms 17928 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 118 ms 17928 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1485 ms 132096 KB Time limit exceeded (wall clock)
2 Halted 0 ms 0 KB -