oj.uz

Submission #391342

# Submission time Handle Problem Language Result Execution time Memory
391342 2021-04-18T15:26:07 Z osaaateiasavtnl Split the sequence (APIO14_sequence) C++14
100 / 100
 1368 ms 88388 KB 
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <fstream>
using namespace std;
#define int long long
#define ii pair <int, int>
#define app push_back
#define all(a) a.begin(), a.end()
#define bp __builtin_popcountll
#define ll long long
#define mp make_pair
#define x first
#define y second
#define Time (double)clock()/CLOCKS_PER_SEC
#define debug(x) std::cerr << #x << ": " << x << '\n';
#define FOR(i, n) for (int i = 0; i < n; ++i)
#define FORN(i, n) for (int i = 1; i <= n; ++i)
#define pb push_back
#define trav(a, x) for (auto& a : x)
using vi = vector<int>;
template <typename T>
std::istream& operator >>(std::istream& input, std::vector<T>& data)
{
    for (T& x : data)
        input >> x;
    return input;
}
template <typename T>
std::ostream& operator <<(std::ostream& output, const pair <T, T> & data)
{
    output << "(" << data.x << "," << data.y << ")";
    return output;
}
template <typename T>
std::ostream& operator <<(std::ostream& output, const std::vector<T>& data)
{
    for (const T& x : data)
        output << x << " ";
    return output;
}
ll div_up(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll div_down(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down 
ll math_mod(ll a, ll b) { return a - b * div_down(a, b); }
#define tcT template<class T
#define tcTU tcT, class U
tcT> using V = vector<T>; 
tcT> void re(V<T>& x) { 
    trav(a, x)
        cin >> a;
}
tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; 
} // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; 
}
ll gcd(ll a, ll b) {
    while (b) {
        tie(a, b) = mp(b, a % b);
    }
    return a;
}
 
struct Line {
    ll k, b, i;
 
    Line() : k(), b(), i() {}
    Line (ll _k, ll _b, ll _i) : k(_k), b(_b), i(_i) {}
 
    ll getVal(ll x) {
        return k * x + b;
    }
};
struct Hull {
    vector<Line> lines;
    vector<ll> borders;
 
    Hull() : lines(), borders() {}
 
    void addLine(Line L) {
        while(!lines.empty()) {
            if (lines.back().getVal(borders.back()) >= L.getVal(borders.back())) {
                lines.pop_back();
                borders.pop_back();
            } else break;
        }
        if (lines.empty()) {
            lines.push_back(L);
            borders.push_back(0LL); //leftmost query
            return;
        }
        if (lines.back().k <= L.k) return;
        ll x = div_up(L.b - lines.back().b, lines.back().k - L.k); //must work for negative!
        lines.push_back(L);
        borders.push_back(x);
    }
    int getMinVal(ll x) {
        int pos = upper_bound(borders.begin(), borders.end(), x) - borders.begin();
        if (pos == 0) return -1;
        pos--;
        return lines[pos].i;
    }
};
 
const int N = 1e5+7, K = 207, INF = 1e18;
signed par[K][N];
int dp1[N], dp2[N];
 
signed main() {
    #ifdef LOCAL
    #else
    #define endl '\n'
    ios_base::sync_with_stdio(0); cin.tie(0);
    #endif
    int n, k;
    cin >> n >> k;
    k++;
    vi a(n);
    cin >> a;
    vi p(n + 1);
    FOR (i, n) {
    	p[i + 1] = p[i] + a[i];
    }
 
    FOR (i, N) {
    	dp1[i] = INF;
    }
    dp1[0] = 0;
 
    FORN (t, k) {
    	Hull h;
    	FOR (i, n + 1) {
    		int j = h.getMinVal(p[i] * 2);
    		if (j != -1) {
    			dp2[i] = dp1[j] + (p[i] - p[j]) * (p[i] - p[j]); 
    			par[t][i] = j;   		
    		}
    		else {
    			dp2[i] = INF;
    		}
    		if (dp1[i] != INF) {
    			h.addLine(Line(-p[i], dp1[i] + p[i] * p[i], i));
    		}
    	}
    	FOR (i, N) {
    		dp1[i] = dp2[i];
    	}
    }
    
 
    cout << (p[n] * p[n] - dp1[n]) / 2 << endl;
    vi cut;
    int i = n;
    for (int t = k; t; --t) {
    	cut.app(i);
    	i = par[t][i];
    }
    reverse(all(cut));
    cut.pop_back();
    cout << cut << endl;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1100 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 1100 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 1100 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 1100 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 1100 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 1100 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 1100 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 1100 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 1100 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 1100 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 1100 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 1100 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 1100 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 1100 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 1100 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 1100 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 1100 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1100 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 1100 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 5 ms 1356 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 1100 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 1100 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 1100 KB contestant found the optimal answer: 933702 == 933702
7 Correct 3 ms 1228 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 1132 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 1100 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 1100 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1100 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 1100 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 16 ms 2160 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 1100 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 13 ms 1868 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 15 ms 2036 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 16 ms 2100 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 1360 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 1228 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 5 ms 1356 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1208 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 1100 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 22 ms 2824 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 1100 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 23 ms 2724 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 20 ms 2508 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 24 ms 2756 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 22 ms 2752 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 1484 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 10 ms 1868 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 1888 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 4 ms 1792 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 119 ms 10584 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 2096 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 71 ms 6960 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 89 ms 7824 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 102 ms 8652 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 94 ms 7252 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 90 ms 8060 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 115 ms 9732 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 9888 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 31 ms 9772 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1241 ms 88388 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 31 ms 10912 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1368 ms 87180 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 780 ms 62020 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1037 ms 68496 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 923 ms 57200 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 932 ms 64372 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1197 ms 80084 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845