oj.uz

Submission #960804

# Submission time Handle Problem Language Result Execution time Memory
960804 2024-04-11T04:32:48 Z vjudge1 Split the sequence (APIO14_sequence) C++17
100 / 100
 702 ms 82068 KB 
#include "bits/stdc++.h"
    // @JASPER'S BOILERPLATE
    using namespace std;
    using ll = long long;
    #define FOR(i, a, b) for(int i = a; i <= b; i++)
    #define FORD(i, a, b) for(int i = a; i >= b; i--)
    #define REP(i, b) for(int i = 0; i < b; i++)
    #define PER(i, b) for(int i = b - 1; i >= 0; i--)
    #define fi first
    #define se second
    #ifdef JASPER
    #include "debug.h"
    #else
    #define debug(...) 166
    #endif
     
    using pii = pair < int, int >;
    const ll INF = 1e18;
    const int MOD = 1e9 + 7;
    const int N = 1e5 + 5;
    const int K = 205;
    // Query for min;
    struct ConvexHull {
        struct Line {
            ll a, b, id;
            Line (ll _a = 0, ll _b = 0, ll _id = -1) { a = _a; b = _b; id = _id; };
            ll cal(ll x) { return a * x + b; }
            long double cross(Line o) { return (long double) (b - o.b) / (long double) (o.a - a); }
        };
        deque <Line> q;
        void add(ll a, ll b, ll id) {
        Line nLine = Line(a, b, id);
        // need to change when a is increasing or decreasing
        while (q.size() >= 2 
            && (q.back().cross(nLine) <= q.back().cross(q[q.size() - 2]) 
                || (q.back().a == nLine.a && q.back().b <= nLine.b)))
            q.pop_back();
        q.push_back(nLine);
    }
     
        pair <ll, int> qry(ll x) {
            while (q.size() >= 2 && q[0].cal(x) <= q[1].cal(x))
                q.pop_front();
            return {q[0].cal(x), q[0].id};
        }
    };
    int n, k;
    ll dp[2][N];
    ll prf[N];
    int opt[K][N];
    // dp[i][k] = max j / (dp[j][k−1] + (pi − pj)⋅(pn − pi))
    void run_case() {
        cin >> n >> k;
        for (int i = 1; i <= n; ++i) {
            int x; cin >> x;
            prf[i] = prf[i - 1] + x;
        }
     
        // Base case, k = 0
        for (int step = 1; step <= k + 1; ++step) {
            ConvexHull hull;
            hull.add(0, 0, -1);
     
            for (int i = 1; i <= n; ++i) {
                pair <ll, int> ret = hull.qry(prf[i]);
                dp[1][i] = ret.fi + prf[i] * (prf[n] - prf[i]);
                opt[step][i] = ret.se;
                
                if (step != 1)
                    hull.add(prf[i], dp[0][i] - prf[i] * prf[n], i);
            }
            for (int i = 1; i <= n; ++i)
                dp[0][i] = dp[1][i];
        }
        cout << dp[0][n] << "\n";
        vector <int> ids;
        for (int i = k + 1, id = n; i > 0; --i) {
            if (id != n)
                ids.push_back(id);
            id = opt[i][id];
        }
        reverse(ids.begin(), ids.end());
        for (int x : ids) cout << x << " ";
        cout << "\n";
    }
     
    signed main() {
        cin.tie(0) -> sync_with_stdio(0);
        #ifdef JASPER
            freopen("in1", "r", stdin);
        #endif
     
        int Test = 1;
        //cin >> Test;
        for (int test = 1; test <= Test; test++){
     
            run_case();
        }
    }

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2396 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 4444 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 4444 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 2396 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 2392 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2396 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 2408 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2548 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 2404 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 9 ms 20828 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 6492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 4444 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 10584 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 6492 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 4444 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 6492 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2396 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 17 ms 50008 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2392 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 7 ms 49756 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 6 ms 50012 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 8 ms 58204 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 18780 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 12636 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 4 ms 22876 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2396 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 50268 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2392 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 44376 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 9 ms 40028 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 46424 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 44380 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 16732 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 33116 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2648 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 2908 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 61 ms 42344 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 2648 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 43 ms 44184 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 51 ms 52316 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 52 ms 51024 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 42 ms 50064 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 49 ms 46932 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 60 ms 50436 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 5824 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 17 ms 5976 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 577 ms 82068 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 16 ms 6204 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 702 ms 81944 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 459 ms 58316 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 489 ms 62396 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 390 ms 52552 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 402 ms 58660 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 532 ms 74328 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845