Submission #518879

# Submission time Handle Problem Language Result Execution time Memory
518879 2022-01-25T02:41:34 Z joshjms Split the sequence (APIO14_sequence) C++14
100 / 100
758 ms 82740 KB
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ld long double

#define fi first
#define se second
#define pb push_back

#define sp " "
#define debug(x) cout << #x << " => " << x << "\n"

const int mod = 1e9 + 7;
const ld err = 1e-6;

int n, k;
ll dp[100005], ne[100005], arr[100005], p[100005];
int backtrack[205][100005];
int aqua;

vector <int> ans;

struct line{
    ll m, c, idx;
    ll f(int x){
        return m * x + c;
    }
    ld intersect(line l){
        return (ld) (c - l.c) / (l.m - m);
    }
};

void solve(){
    cin >> n >> k;
    for(int i = 1; i <= n; i++){
        cin >> arr[i];
        p[i] = p[i - 1] + arr[i];
    }
    fill(dp, dp + n + 1, 0);
    for(int i = 0; i <= k; i++){
        deque <line> dq;
        dq.push_front({-p[i], dp[i], i});
        for(int j = i + 1; j <= n; j++){
            while(dq.size() > 1 && dq.back().f(p[n] - p[j]) <= dq[dq.size() - 2].f(p[n] - p[j]))
                dq.pop_back();
            ne[j] = p[j] * (p[n] - p[j]) + dq.back().f(p[n] - p[j]);
            backtrack[i][j] = dq.back().idx;
            line cur = {-p[j], dp[j], j};
            while(dq.size() > 1 && cur.intersect(dq[1]) >= dq[0].intersect(dq[1]))
                dq.pop_front();
            dq.push_front(cur);
        }
        for(int j = i + 1; j <= n; j++){
            dp[j] = ne[j];
            ne[j] = 0;
        }
    }
    cout << dp[n] << "\n";
    aqua = n;
    for(int i = k; i >= 1; i--){
        aqua = backtrack[i][aqua];
        ans.push_back(aqua);
    }
    for(int i = ans.size() - 1; i >= 0; i--)
        cout << ans[i] << " ";
    cout << "\n";
}  

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    solve();
}
# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 332 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 332 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 332 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 332 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 332 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 332 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 332 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 332 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 332 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 332 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 332 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 332 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 332 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 332 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 332 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 332 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 0 ms 332 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 332 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 588 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 332 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 332 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 332 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 460 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 332 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 332 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 332 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 332 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 1356 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 332 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 972 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 1228 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 1356 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 588 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 460 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 588 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 332 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 1996 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 332 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 1932 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 1740 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 1996 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 1996 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 716 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 972 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 2 ms 844 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 972 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 55 ms 9412 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 844 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 47 ms 5928 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 58 ms 6804 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 54 ms 7248 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 38 ms 6084 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 46 ms 6896 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 56 ms 8568 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 19 ms 5540 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 19 ms 5676 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 545 ms 82740 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 18 ms 6464 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 758 ms 82384 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 489 ms 59076 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 546 ms 63184 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 393 ms 52196 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 416 ms 59004 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 529 ms 74756 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845