Submission #966349

#	Time	Username	Problem	Language	Result	Execution time	Memory
966349		MisterReaper	Split the sequence (APIO14_sequence)	C++17	100 / 100	979 ms	83688 KiB

sequence

#include <bits/stdc++.h>

using i64 = long long;

struct line {
    i64 a, b;
    line(i64 _a, i64 _b) : a(_a), b(_b) {}
    long double intersect(line rhs) {
        return (long double)(b - rhs.b) / (rhs.a - a);
    }
    i64 eval(i64 x) {
        return a * x + b;
    }
    bool operator== (line rhs) {
        return a == rhs.a && b == rhs.b;
    }
};
long double intersect(line a, line b, line c) {
    return (a.b - b.b) * (c.a - b.a) >= (b.b - c.b) * (b.a - a.a);
}
namespace std {
    std::string to_string(line l) {
        return '(' + to_string(l.a) + "x + " + to_string(l.b) + ')';
    }
};

#ifdef DEBUG 
    #include "debug.h"
#else
    #define debug(...) void(23)
#endif

constexpr int maxN = 1E5 + 5;
constexpr int maxK = 200 + 5;

int A[maxN], go[maxK][maxN];
i64 p[maxN];

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int N, K;
    std::cin >> N >> K;

    for(int i = 1; i <= N; i++) {
        std::cin >> A[i];
    }

    for(int i = 1; i <= N; i++) {
        p[i] = p[i - 1] + A[i];
    }

    std::deque<std::pair<line, int>> dq;
    auto size = [&]() -> int { return (int) dq.size(); };
    auto Add = [&](line l, int idx) -> void {
        while(size() >= 2 && (intersect(l, dq[0].first, dq[1].first))) {
            dq.pop_front();
        }
        if(size() && l == dq[0].first) {
            dq.pop_front();
        }
        dq.emplace_front(l, idx);
    };
    auto Query = [&](i64 x) -> std::pair<i64, int> {
        while(size() >= 2 && dq[size() - 1].first.intersect(dq[size() - 2].first) >= x) {
            dq.pop_back();
        }
        auto ans = std::pair{dq[size() - 1].first.eval(x), dq[size() - 1].second};
        return ans;
    };

    std::vector<i64> dp(N + 1);
    for(int k = 1; k <= K; k++) {
        dq.clear();
        Add({0, 0}, 0);
        std::vector<i64> ndp(N + 1);
        for(int i = 1; i <= N; i++) {
            // for(int j = 0; j < i; j++) {
            //     if(dp[k - 1][j] + 1LL * (p[i] - p[j]) * (p[N] - p[i]) >= dp[k][i]) {
            //         go[k][i] = j;
            //         dp[k][i] = dp[k - 1][j] + 1LL * (p[i] - p[j]) * (p[N] - p[i]);
            //     }
            // }

            auto [v, j] = Query(p[N] - p[i]);
            ndp[i] = v + 1LL * p[i] * (p[N] - p[i]);
            go[k][i] = j;
            Add(line{-p[i], dp[i]}, i);
            debug(dq);

            debug(k, i, ndp[i], go[k][i]);
        }
        dp = std::move(ndp);
    }

    int ans = 1;
    for(int i = 1; i < N; i++) {
        if(dp[i] >= dp[ans]) {
            ans = i;
        }
    }

    std::cout << dp[ans] << '\n';

    std::vector<int> v;
    for(int k = K; k >= 1; k--) {
        v.emplace_back(ans);
        ans = go[k][ans];
    }

    for(int i = K - 1; i >= 0; i--) {
        std::cout << v[i] << " \n"[i == 0];
    }

    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