Submission #567700

#	Time	Username	Problem	Language	Result	Execution time	Memory
567700		ac2hu	Split the sequence (APIO14_sequence)	C++14	50 / 100	2075 ms	36192 KiB

sequence

#include <bits/stdc++.h>
#ifdef DEBUG
#include "../templates/debug.h"
#else 
#define deb(x...)
#endif
using namespace std;
using ll = long long;
constexpr ll sq(ll a){
    return a*a;
}
struct Z{/*{{{*/
    vector<ll> vals;
    int n;
    Z(vector<int> &a){
        n = a.size();
        vals.resize(n , 0);
        vals[0] = a[0];
        for(int i = 1;i<n;i++){
            vals[i] = vals[i - 1] + a[i];
        }
    }
    ll operator()(int l,int r){
        if(l > r)return 0;
        assert(n > r);
        assert(l <= r);
        assert(l >= 0);
        int temp = vals[r];
        if(l != 0)temp -= vals[l - 1];
        return temp;
    }
};/*}}}*/
struct line{
    ll m, c; int idx;
    ll get(ll x){
        return m*x + c;
    }
};
long double intersect(line a,line b){
    return (long double)(a.c - b.c)/(a.m - b.m);
}
struct hull : deque<line>{
    line get(ll x){
        ll mx = -1e18;
        int idx = -1;
        for(int i = 0;i<size();i++){
            if(at(i).get(x) >= mx){
                mx = at(i).get(x);
                idx = i;
            }
        }
        return at(idx);
        // int l = 0,r = (int)size() - 2;
        // while(l < r){
        //     int mid = (l + r - 1)/2;
        //     if(at(mid + 1).get(x) <= at(mid).get(x)){
        //         r = mid;
        //     }
        //     else{
        //         l = mid + 1;
        //     }
        // }
        // return at(l);
    }
    void add(line nw){
        while(size() >= 2 && intersect(at(0), at(1)) >= intersect(at(0), nw))
            pop_front();
        push_front(nw);
    }
};
signed main(){
    iostream::sync_with_stdio(false);
    cin.tie(nullptr);cout.tie(nullptr);
    int n, K;cin >> n >> K;
    vector<int> a(n);
    for(auto &e : a)cin >> e;
    Z pref(a);
    vector<vector<ll>> dp(n + 1, vector<ll>(K + 1, -1e17));
    vector<vector<int>> jump(n + 1, vector<int>(K + 1, -1));
    vector<hull> hulls(K + 10);
    dp[0][0] = 0;
    hulls[0].add({0, 0, 0});
    for(int i = 1;i<=n;i++){
        dp[i][0] = 0;
        for(int k = 1;k<=K;k++){
            if((int)hulls[k - 1].size() > 0){
                line gg = hulls[k - 1].get(pref(i,n - 1));
                dp[i][k] = pref.vals[i - 1]*pref(i,n - 1) + gg.get(pref(i, n - 1));
                jump[i][k] = gg.idx;
            }
            int m = 0;
            if(i >= 2){
                m = pref.vals[i - 2];
            }
            line nw = {-m, dp[i - 1][k], i - 1};
            hulls[k].add(nw);
        }
    }
    for(int i = 0;i<=n;i++){
        deb(dp[i]);
    }
    int MX = -1;
    ll val = -1;
    for(int i = 0;i<=n;i++){
        if(dp[i][K] > val){
            val = dp[i][K];
            MX = i;
        }
    }
    cout << val << "\n";
    vector<int> temp;
    int c = K;
    while(MX != 0 && MX != -1 &&  c > 0){
        temp.push_back(MX);
        MX = jump[MX][c];
        --c;
    }
    reverse(temp.begin(), temp.end());
    for(int e : temp)cout << e << " ";
    cout << "\n";
}

Compilation message (stderr)

sequence.cpp: In member function 'line hull::get(ll)':
sequence.cpp:46:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::deque<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   46 |         for(int i = 0;i<size();i++){
      |                       ~^~~~~~~

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