Submission #1288578

#	Time	Username	Problem	Language	Result	Execution time	Memory
1288578		harryleee	Split the sequence (APIO14_sequence)	C++20	71 / 100	230 ms	196608 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5;
int n, k, trace[maxn + 1][201];
long long bestPos = 0, res = LLONG_MIN/4, pre[maxn + 1];

const long long NEG = LLONG_MIN/4;

struct Line {
    long long m; // slope (a)
    long long b; // intercept (b)
    int id;
    Line(long long _m=0, long long _b=0, int _id=0): m(_m), b(_b), id(_id) {}
};

// check if l2 is unnecessary between l1 and l3
inline bool bad(const Line &l1, const Line &l2, const Line &l3){
    // (b3 - b1) / (m1 - m3) <= (b2 - b1) / (m1 - m2)
    // Cross multiply to avoid floating point.
    long long left  = (long long)(l3.b - l1.b) * (long long)(l1.m - l2.m);
    long long right = (long long)(l2.b - l1.b) * (long long)(l1.m - l3.m);
    return left <= right;
}

struct CHT {
    vector<Line> hull;
    int ptr = 0; // pointer for queries with non-decreasing x

    void clear(){ hull.clear(); ptr = 0; }

    // slopes must be added in non-decreasing order
    void add(Line L){
        // if last slope == new slope, keep the one with bigger intercept
        while(!hull.empty() && hull.back().m == L.m){
            if (hull.back().b >= L.b) return; // new line dominated
            else hull.pop_back(); // remove dominated last line
        }
        while(hull.size() >= 2 && bad(hull[hull.size()-2], hull.back(), L))
            hull.pop_back();
        hull.push_back(L);
        if (ptr >= (int)hull.size()) ptr = (int)hull.size() - 1;
    }

    // query maximum at x; x must be non-decreasing between queries
    pair<long long,int> query(long long x){
        if (hull.empty()) return {NEG, 0};
        while(ptr + 1 < (int)hull.size()){
            long long v1 = (long long)hull[ptr].m * x + (long long)hull[ptr].b;
            long long v2 = (long long)hull[ptr+1].m * x + (long long)hull[ptr+1].b;
            if (v2 >= v1) ++ptr;
            else break;
        }
        long long val = (long long)((long long)hull[ptr].m * x + (long long)hull[ptr].b);
        return {val, hull[ptr].id};
    }
};

// number of levels max k is up to 200 -> allocate 201
CHT lc[201];

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    if (!(cin >> n >> k)) return 0;
    for (int i = 1; i <= n; ++i){
        cin >> pre[i];
        pre[i] += pre[i - 1];
    }

    // init
    for (int j = 0; j <= k; ++j) lc[j].clear();
    lc[0].add(Line(0, 0, 0));

    for (int i = 0; i <= n; ++i){
        for (int j = 0; j <= k; ++j) trace[i][j] = 0;
    }

    for (int i = 1; i <= n; ++i){
        int mxj = min(i, k);
        for (int j = mxj; j >= 1; --j){
            auto g = lc[j-1].query(pre[i] - pre[n]);
            if (g.first == NEG){
                trace[i][j] = 0;
                continue;
            }
            long long dp = g.first + pre[i] * (pre[n] - pre[i]);
            if (j < k) lc[j].add(Line(pre[i], dp, i));
            if (j == k && i < n && dp > res){
                bestPos = i;
                res = dp;
            }
            trace[i][j] = g.second;
        }
    }

    cout << res << '\n';
    vector<int> cuts;
    while (bestPos != 0 && k > 0) {
        cuts.push_back((int)bestPos);
        bestPos = trace[bestPos][k];
        --k;
    }
    reverse(cuts.begin(), cuts.end());
    for (int i = 0; i < (int)cuts.size(); ++i){
        if (i) cout << ' ';
        cout << cuts[i];
    }
    cout << '\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