Submission #767529

#	Time	Username	Problem	Language	Result	Execution time	Memory
767529		jeroenodb	Split the sequence (APIO14_sequence)	C++14	71 / 100	58 ms	131072 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define INF (int)1e18
#define double long double
#define f first
#define s second
 
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
 
struct line{
    int m, c, i;
};
 
int eval(int x, line a){
    return a.m * x + a.c;
}
 
//(c2 - c1) / (m1 - m2) 
 
bool useless(line a, line b, line c){
    // return intersect(a, c) >= intersect(b, c);
    return (a.c - c.c) * (c.m - b.m) <= (b.c - c.c) * (c.m - a.m);
}
 
void Solve() 
{
    int n, k; cin >> n >> k;
    vector <int> a(n + 1);
    int sum = 0;
    for (int i = 1; i <= n; i++){
        cin >> a[i];
        sum += a[i];
        a[i] += a[i - 1];
    }
    k++;
    
    vector<vector<int>> dp(n + 1, vector<int>(k + 1, INF));
    vector<vector<int32_t>> par(n + 1, vector<int32_t>(k + 1, -1));
    deque<line> dq[k + 2];
    dp[0][0] = 0;
    line ok;
    ok.m = 0; ok.c = 0; ok.i = 0;
    dq[0].push_back(ok);
    
    //dp[i][j] = dp[i1][j - 1] + a[i1] ^ 2 - 2 * a[i1] * a[i] + a[i] ^ 2
    for (int i = 1; i <= n; i++){
        for (int j = k; j >= 1; j--){
            // for (int i1 = 0; i1 < i; i1++){
            //     int val = dp[i1][j - 1] + (a[i] - a[i1]) * (a[i] - a[i1]);
            //     if (val < dp[i][j]){
            //         dp[i][j] = val;
            //         par[i][j] = i1;
            //     }
            // }
            
            if (dq[j - 1].size() == 0) continue;
            
            int x = a[i];
            while (dq[j - 1].size() > 1 && eval(x, dq[j - 1][0]) >= eval(x, dq[j - 1][1])) dq[j - 1].pop_front();
            dp[i][j] = eval(x, dq[j - 1][0]) + a[i] * a[i];
            par[i][j] = dq[j - 1][0].i;
            
            ok.m = - 2 * a[i];
            ok.c = dp[i][j] + a[i] * a[i];
            ok.i = i;
            while (dq[j].size() > 1 && useless(ok, dq[j].back(), dq[j][dq[j].size() - 2])) dq[j].pop_back();
            dq[j].push_back(ok);
        }
    }
    
    int ans = (sum * sum) - (dp[n][k]);
    ans /= 2;
    cout << ans << "\n";
    
    vector <int> go;
    int i = n;
    while (par[i][k] != 0){
        i = par[i][k];
        k--;
        go.push_back(i);
    }
    
    reverse(go.begin(), go.end());
    for (auto x : go) cout << x << " ";
    cout << "\n";
}
 
int32_t main() 
{
    auto begin = std::chrono::high_resolution_clock::now();
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
//    cin >> t;
    for(int i = 1; i <= t; i++) 
    {
        //cout << "Case #" << i << ": ";
        Solve();
    }
    auto end = std::chrono::high_resolution_clock::now();
    auto elapsed = std::chrono::duration_cast<std::chrono::nanoseconds>(end - begin);
    cerr << "Time measured: " << elapsed.count() * 1e-9 << " seconds.\n"; 
    return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29