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Submission #142566

# Submission time Handle Problem Language Result Execution time Memory
142566 2019-08-09T17:17:56 Z 12tqian Split the sequence (APIO14_sequence) C++14
71 / 100
 457 ms 131072 KB 
#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

const double PI = 4 * atan(1);

#define sz(x) (int)(x).size()
#define ll long long
#define ld long double
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define pii pair <int, int>
#define vi vector<int>
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define vpi vector<pair<int, int>>
#define vpd vector<pair<double, double>>
#define pd pair<double, double>

#define f0r(i,a) for(int i=0;i<a;i++)
#define f1r(i,a,b) for(int i=a;i<b;i++)
#define trav(a, x) for (auto& a : x)

void fast_io(){
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    cout.tie(NULL);
}
void io(string taskname){
    string fin = taskname + ".in";
    string fout = taskname + ".out";
    const char* FIN = fin.c_str();
    const char* FOUT = fout.c_str();
    freopen(FIN, "r", stdin);
    freopen(FOUT, "w", stdout);
    fast_io();
}
const int MAXN = 1e5 + 5;
const int MAXK = 2e2 + 5;
ll dp[MAXK][MAXN];
ll pre[MAXN];
vector<ll> a;
ll get(int l, int r){return pre[r] - (l == 0? 0: pre[l-1]);}
int bef[MAXK][MAXN];

pair<pair<long long, long long> , int> f(pair<pair<long long, long long>, int> a, pair<pair<long long, long long>, int> b) {
    /* point of intersection */
    long long x = ((long long)(b.f.second-a.f.second))/(a.f.first-b.f.first);
    long long y = a.f.first * x + a.f.second;
    return mp(make_pair(x, y), b.s);
}

struct cht {
    vector<long long> pts;
    vector<pair<pair<long long, long long>, int> > taken;
    void add(ll m, ll b, int idx){
        addLine(mp(mp(m, b), idx));
    }
    void addLine(pair<pair<long long, long long>, int> i) {
        if (taken.size() <= 1) {
            if (taken.empty()) { taken.push_back(i); }
            else {
                if (i.first.f == taken.back().first.f) {
                    if (taken.back().f.second > i.f.second) {
                        taken.pop_back();
                        taken.push_back(i);
                    }
                }
                else {
                    pts.push_back(f(i, taken.back()).first.f);
                    taken.push_back(i);
                }
            }
        }
        else {
            if (i.f.first == taken.back().first.f) {
                if (taken.back().second > i.f.second) {
                    taken.pop_back(); pts.pop_back();
                    pts.push_back(f(i, taken.back()).f.first);
                    taken.push_back(i);
                }
            }
            else {
                while (taken.size() >= 2) {
                    pair<pair<long long, long long>, int> l1 = taken[taken.size()-1];
                    pair<pair<long long, long long>, int> l2 = taken[taken.size()-2];
                    if (f(i, l2) > f(l1, l2)) { break; }
                    else { taken.pop_back(); pts.pop_back(); }
                }
                pts.push_back(f(i, taken.back()).f.first);
                taken.push_back(i);
            }
        }
    }

    pair<ll, int> query(long long x) {
        int idx = lower_bound(pts.begin(), pts.end(), x) - pts.begin();
        return mp(taken[idx].f.first * x + taken[idx].f.second, taken[idx].s);
    }
};
cht hull[MAXK];
int main(){
    fast_io();
    int n, k;
    cin >> n >> k;
    k++;
    f0r(i, n){
        int ai;
        cin >> ai;
        a.eb(ai);
        if(i == 0) pre[i] = ai;
        else pre[i] = pre[i-1] + ai;
    }
    ll res = pre[n-1]*pre[n-1];
    f0r(i, n){
        dp[1][i] = get(0, i)*get(0, i);
        bef[1][i] = -1;
        hull[1].add(-2*pre[i], pre[i]*pre[i] + dp[1][i], i);
    }
    f1r(i, 2, k+1){
        int best = i-2;

        f1r(j,i-1, n){
            if(j == i-1){
                bef[i][j] = i-2;
                dp[i][j] = dp[i-1][i-2] + get(i-1, i-1)*get(i-1, i-1);
                bef[i][j] = i-2;
                hull[i].add(-2*pre[j], pre[j]*pre[j] + dp[i][j], j);
            }
            else{
                pair<ll, int> q = hull[i-1].query(pre[j]);
                dp[i][j] = q.f + pre[j]*pre[j];
                bef[i][j] = q.s;
                hull[i].add(-2*pre[j], pre[j]*pre[j]+ dp[i][j], j);
            }
            //bef[i][j] = best;
        }
    }
    res -= dp[k][n-1];
    res/=2;
   // cout << dp[3][4] << endl;
    cout << res << endl;
    vi ans;
    int f = k;
    int s = n-1;
    while(bef[f][s] != -1){
        ans.eb(bef[f][s]);
        s = bef[f][s];
        f--;

    }
    reverse(all(ans));
    for(int x: ans) cout << x+1 << " ";
    cout << endl;

    return 0;
}

Compilation message

sequence.cpp:1:0: warning: ignoring #pragma comment  [-Wunknown-pragmas]
 #pragma comment(linker, "/stack:200000000")
 
sequence.cpp: In function 'int main()':
sequence.cpp:134:13: warning: unused variable 'best' [-Wunused-variable]
         int best = i-2;
             ^~~~
sequence.cpp: In function 'void io(std::__cxx11::string)':
sequence.cpp:47:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(FIN, "r", stdin);
     ~~~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:48:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(FOUT, "w", stdout);
     ~~~~~~~^~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 376 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 376 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 376 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 504 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 376 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 376 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 376 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 376 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 376 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 376 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 376 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 376 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 376 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 376 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 1016 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 376 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 504 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 3 ms 504 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 760 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 504 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 504 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 632 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 504 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 504 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 7 ms 3576 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 376 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 6 ms 2680 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 6 ms 3192 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 7 ms 3576 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 4 ms 1272 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 1016 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 4 ms 1528 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 632 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 632 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 33 ms 11768 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 632 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 31 ms 10844 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 27 ms 9084 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 33 ms 11512 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 34 ms 11896 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 9 ms 2680 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 14 ms 5084 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 2168 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 7 ms 2040 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 331 ms 99152 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 9 ms 2708 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 166 ms 45404 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 178 ms 44244 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 247 ms 73020 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 201 ms 59568 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 227 ms 66304 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 292 ms 84768 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 63 ms 19940 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 62 ms 19808 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 457 ms 131072 KB Execution killed with signal 9 (could be triggered by violating memory limits)
4 Halted 0 ms 0 KB -