Submission #585578

#	Time	Username	Problem	Language	Result	Execution time	Memory
585578		kawaii	Split the sequence (APIO14_sequence)	C++14	100 / 100	591 ms	87740 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second

long long t, n, m, k, a[100005], dp[100005], sum[100005], mod = 1e9 + 7, inf = 1e18;
int trace[100005][205];
string s;
mt19937_64 rng; 

struct lines{
    long long a, b, index;
    lines(long long a = 0, long long b = 0, long long index = 0) : a(a), b(b), index(index){}
    long long f(long long x){ 
        return 1LL * a * x + b; 
    };
};
 
long double slope(lines ln1, lines ln2) {
    return (long double) (ln2.b - ln1.b) / (long double) (ln2.a - ln1.a);
}
 
struct cht{
    vector<lines> lns;
    long long ptr = 0;
    void add(long long a, long long b, long long index){
        lines ln(a, b, index);
        while(lns.size() > 1 && (slope(lns[lns.size() - 2], lns.back()) - slope(lns[lns.size() - 2], ln)) <= 1e-18) lns.pop_back();
        lns.push_back(ln); ptr = min(ptr, (long long) lns.size() - 1);
    }
    pair<long long, long long> get(long long x){
        if(lns.empty()) return {-inf, 0};
        while (ptr + 1 < lns.size() && lns[ptr].f(x) <= lns[ptr + 1].f(x)) ptr++;
        return {lns[ptr].f(x), lns[ptr].index};
    } 
};

cht osu[5]; 

void solve(){  
    osu[0].add(0, 0, 0); 
    for(long long j = 1; j <= k; j++){   
        for(long long i = 1; i <= n; i++){
            long long num = sum[i] * sum[n] - sum[i] * sum[i];
            pair<long long, long long> x = osu[0].get(sum[i] - sum[n]);
            dp[i] = x.fi + num;
            trace[i][j] = x.se;
            osu[1].add(sum[i], dp[i], i);  
            // cout << dp[i] <<" "<< i <<" "<< j <<" "<< trace[i][j] << "\n";
        }
        osu[0] = osu[1];
        osu[1].lns.clear(); osu[1].ptr = 0;  
    }
    long long answer = 0;
    for(long long i = 1; i <= n; i++) answer = max(answer, dp[i]);
    cout << answer << "\n";
    for(long long i = n - 1; i >= 1; i--){
        if(answer != dp[i]) continue;
        vector<long long> v; 
        int x = i;
        for(long long i = k; i >= 1; i--){
            // cout << x <<" ";
            v.push_back(x); 
            x = max(1, min(trace[x][i], x - 1));
        }
        reverse(v.begin(), v.end());
        for(auto i: v) cout << i <<" ";
        return;
    }
}

signed main(){
    ios_base::sync_with_stdio(NULL); cin.tie(nullptr); cout.tie(nullptr);
    rng.seed((long long)main ^ time(0));
    #ifdef Kawaii
        auto starttime = chrono::high_resolution_clock::now();
    #endif

    cin >> n >> k; 
    // n = 1e5, k = 200;
    for(long long i = 1; i <= n; i++){
        cin >> a[i]; 
        // a[i] = rng() % 10001;
        sum[i] = sum[i - 1] + a[i];
    }
    solve();


    #ifdef Kawaii
        auto endtime = chrono::high_resolution_clock::now();
        auto duration = chrono::duration_cast<chrono::milliseconds>(endtime - starttime).count(); 
        cout << "\n=====" << "\nUsed: " << duration << " ms\n";
    #endif
}

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long long int, long long int> cht::get(long long int)':
sequence.cpp:33:24: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<lines>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   33 |         while (ptr + 1 < lns.size() && lns[ptr].f(x) <= lns[ptr + 1].f(x)) ptr++;
      |                ~~~~~~~~^~~~~~~~~~~~

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