Submission #891220

#	Time	Username	Problem	Language	Result	Execution time	Memory
891220		Kutan	Split the sequence (APIO14_sequence)	C++14	100 / 100	416 ms	86992 KiB

sequence

// Cao Quang Hung
#include <cassert>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
 
using namespace std;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define pii pair<int,int>
#define pll pair<long long , long long>
#define vi vector<int>
#define vpii vector<pii>
#define SZ(x) ((int)(x.size()))
#define fi first
#define se second
#define IN(x,y) ((y).find((x))!=(y).end())
#define ALL(t) t.begin(),t.end()
#define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++)
#define REP(i,a,b) for(int (i)=(a);(i)<=(b);++i)
#define REPD(i,a,b) for(int (i)=(a); (i)>=(b);--i)
#define FOR(i, n) for (int (i) = 0; (i) < (n); ++(i))
#define dem(x) __builtin_popcount(x)
#define Mask(x) (1LL << (x))
#define BIT(x, i) ((x) >> (i) & 1)
#define ln '\n'
#define io_faster ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
///mt19937 rnd(time(0));
 
const int INF = 1e9 , mod = 1e9 + 7;
 
template <class T1, class T2>
inline T1 mul(T1& x, const T2 &k){ return x = (1LL * x * k) % mod; }
 
template <class T1 , class T2>
inline T1 pw(T1 x, T2 k){T1 res = 1; for (; k ; k >>= 1){ if (k & 1) mul(res, x); mul(x, x); } return res;}
 
template <class T>
inline bool minimize(T &x, const T &y){ if (x > y){x = y; return 1;} return 0; }
 
template <class T>
inline bool maximize(T &x, const T &y){ if (x < y){x = y; return 1;} return 0; }
 
template <class T>
inline void add(T &x , const T &y){ if ((x += y) >= mod) x -= mod; }
 
template <class T>
inline T product (const T &x , const T &y) { return 1LL * x * y % mod; }
 
#define PROB "a"
void file(){
    if(fopen(PROB".inp", "r")){
        freopen(PROB".inp","r",stdin);
        freopen(PROB".out","w",stdout);
    }
}
void sinh_(){
//    srand(time(0));
//    freopen(PROB".inp" , "w" , stdout);
//    int n;
}
 
typedef long long ll;
typedef long double db;
const int N = 1e5 + 2;
 
ll dp[N];
int n, k, a[N], pre[N], pf[N][205];
void readip(){
    cin >> n >> k; ++k;
    REP(i, 1, n) cin >> a[i];
    pre[0] = 0;
    REP(i, 1, n) pre[i] = pre[i - 1] + a[i];
}
 
struct line{
    ll a, b;
    line(ll _a = 0, ll _b = 0) {
        a = _a, b = _b;
    }
 
    ll gety(int x) {
        return a * x + b;
    }
 
    db getintersect(const line &other) {
        return 1.0 * db(b - other.b) / db(other.a - a);
    }
};
 
struct convex_hull_trick{
    vector<pair<line, int>> dq;
    int pt = 0;
 
    void addLine(line newline, int id) {
        if (!dq.empty() && newline.a == dq.back().first.a) {
            if (newline.b <= dq.back().first.b) return;
            dq.pop_back();  
        }
 
        while(dq.size() >= 2 && dq[SZ(dq) - 2].first.getintersect(newline) 
                             <= dq[SZ(dq) - 2].first.getintersect(dq.back().first))
            dq.pop_back();
        
        dq.eb(newline, id);
        minimize(pt, SZ(dq) - 1);
    }
 
    ll get(int x) {
        if (dq.empty()) return -1e18;
        while(pt + 1 < SZ(dq) && dq[pt + 1].first.gety(x) > dq[pt].first.gety(x))
            ++pt;
        return dq[pt].first.gety(x);
    }
 
    int getpos() {
        return dq[pt].second;
    }
 
    void init() {
        dq.clear();
        pt = 0;
    }
 
} CHT;
 
void solve(){   
    memset(dp, -0x3f, sizeof dp);
    dp[0] = 0;
    REP(T, 1, k) {
        CHT.init();
        if (T == 1) CHT.addLine(line(0, 0), 0);
        REP(i, 1, n) {
            ll dpi = dp[i];
            dp[i] = 1LL * pre[n] * pre[i] 
                  - 1LL * pre[i] * pre[i] 
                  + CHT.get(pre[i] - pre[n]);
 
            pf[i][T] = CHT.getpos();
            if (i >= T - 1) CHT.addLine(line(pre[i], dpi), i);
        }   
    }
 
    vi ans;
    int i = n;
    REPD(j, k, 2) {
        int nxt = pf[i][j];
        ans.eb(nxt);
        i = nxt;
    }
    cout << dp[n] << ln;
    reverse(ALL(ans));
    for (int x : ans) cout << x << ' '; cout << ln;
}
 
int main(){
    sinh_();
    io_faster
    file();
    int t = 1;
//    cin >> t;
    while (t--){
        readip();
        solve();
    }
}

Compilation message (stderr)

sequence.cpp: In function 'void readip()':
sequence.cpp:92:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   92 | #define REP(i,a,b) for(int (i)=(a);(i)<=(b);++i)
      |                            ^
sequence.cpp:143:5: note: in expansion of macro 'REP'
  143 |     REP(i, 1, n) cin >> a[i];
      |     ^~~
sequence.cpp:92:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   92 | #define REP(i,a,b) for(int (i)=(a);(i)<=(b);++i)
      |                            ^
sequence.cpp:145:5: note: in expansion of macro 'REP'
  145 |     REP(i, 1, n) pre[i] = pre[i - 1] + a[i];
      |     ^~~
sequence.cpp: In function 'void solve()':
sequence.cpp:92:28: warning: unnecessary parentheses in declaration of 'T' [-Wparentheses]
   92 | #define REP(i,a,b) for(int (i)=(a);(i)<=(b);++i)
      |                            ^
sequence.cpp:202:5: note: in expansion of macro 'REP'
  202 |     REP(T, 1, k) {
      |     ^~~
sequence.cpp:92:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   92 | #define REP(i,a,b) for(int (i)=(a);(i)<=(b);++i)
      |                            ^
sequence.cpp:205:9: note: in expansion of macro 'REP'
  205 |         REP(i, 1, n) {
      |         ^~~
sequence.cpp:93:29: warning: unnecessary parentheses in declaration of 'j' [-Wparentheses]
   93 | #define REPD(i,a,b) for(int (i)=(a); (i)>=(b);--i)
      |                             ^
sequence.cpp:218:5: note: in expansion of macro 'REPD'
  218 |     REPD(j, k, 2) {
      |     ^~~~
sequence.cpp:225:5: warning: this 'for' clause does not guard... [-Wmisleading-indentation]
  225 |     for (int x : ans) cout << x << ' '; cout << ln;
      |     ^~~
sequence.cpp:225:41: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'for'
  225 |     for (int x : ans) cout << x << ' '; cout << ln;
      |                                         ^~~~
sequence.cpp: In function 'void file()':
sequence.cpp:125:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  125 |         freopen(PROB".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:126:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  126 |         freopen(PROB".out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~

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