Submission #999511

#	Time	Username	Problem	Language	Result	Execution time	Memory
999511		fryingduc	Split the sequence (APIO14_sequence)	C++17	100 / 100	1356 ms	84312 KiB

sequence

#include "bits/stdc++.h"
using namespace std;

const int maxn = 1e5 + 5;
const long long inf = 1e18;
int n, a[maxn], k;
int ps[maxn];
long long pref[maxn];
long long f[maxn], g[maxn];
int trace[maxn][205];
int pos, mid;
long long res;
int now;

inline long long cost(int l, int r) {
    return (1ll * (1ll * ps[r] - ps[l - 1]) * (1ll * ps[r] - ps[l - 1]) - (pref[r] - pref[l - 1])) >> 1;
}
inline void calc(int l, int r, int optl, int optr) {
    if(l > r) return;
    res = inf;
    pos = -1;
    mid = (l + r) / 2;
    for(int i = min(mid, optr); i >= optl; --i) {
        if(g[i - 1] + cost(i, mid) < res) {
            res = g[i - 1] + cost(i, mid);
            pos = i;
        }
    }
    f[mid] = res;
    trace[mid][now] = pos - 1;
    if(l <= mid - 1) calc(l, mid - 1, optl, pos);
    if(mid + 1 <= r) calc(mid + 1, r, pos, optr);
}
void solve() {
    cin >> n >> k;
    for(int i = 1; i <= n; ++i) {
        cin >> a[i];
        pref[i] = pref[i - 1] + a[i] * a[i];
        ps[i] = ps[i - 1] + a[i];
    }
    for(int i = 1; i <= n; ++i) {
        g[i] = cost(1, i);
    }
    long long total_sum = g[n];
    for(now = 1; now <= k; ++now) {
        calc(1, n, 1, n);
        for(int j = 1; j <= n; ++j) {
            g[j] = f[j];
            f[j] = 0;
        }
    }
    cout << total_sum - g[n] << '\n';
    vector<int> vec;
    while(k) {
        vec.push_back(trace[n][k]);
        n = trace[n][k];
        assert(n > 0);
        --k;
    }
    reverse(vec.begin(), vec.end());
    for(auto i:vec) cout << i << " ";
}
signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    solve();
    return 0;
}

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