Submission #227809

#	Time	Username	Problem	Language	Result	Execution time	Memory
227809		caoash	Split the sequence (APIO14_sequence)	C++14	22 / 100	743 ms	131076 KiB

sequence

#pragma GCC target ("sse4")

#include <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef pair<int, pi> pii;

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define fax(i, a) for (int i = 0; i < (a); i++)
#define f0x(i, a, b) for (int i = (a); i < (b); i++)
#define f0xd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define faxd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
#define memeset memset

#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rsz resize

template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }

template <class T, int ...Ns> struct BIT {
    T val = 0;
    void upd(T v) { val += v; }
    T query() { return val; }
};
 
template <class T, int N, int... Ns> struct BIT<T, N, Ns...> {
    BIT<T,Ns...> bit[N + 1];
    template<typename... Args> void upd(int pos, Args... args) {
        for (; pos <= N; pos += (pos&-pos)) bit[pos].upd(args...);
    }
    template<typename... Args> T sum(int r, Args... args) {
        T res = 0; for (; r; r -= (r&-r)) res += bit[r].query(args...); 
        return res;
    }
    template<typename... Args> T query(int l, int r, Args... args) {
        return sum(r,args...)-sum(l-1,args...);
    }
};

namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);

    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class T, class... Ts> void re(T& t, Ts&... ts) { 
        re(t); re(ts...); 
    }

    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { fax(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { fax(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
    void pr(int x) { cout << x; }
    void pr(long x) { cout << x; }
    void pr(ll x) { cout << x; }
    void pr(unsigned x) { cout << x; }
    void pr(unsigned long x) { cout << x; }
    void pr(unsigned long long x) { cout << x; }
    void pr(float x) { cout << x; }
    void pr(double x) { cout << x; }
    void pr(ld x) { cout << x; }
    void pr(char x) { cout << x; }
    void pr(const char* x) { cout << x; }
    void pr(const string& x) { cout << x; }
    void pr(bool x) { pr(x ? "true" : "false"); }
    
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T> void pr(const T& x);
    
    template<class T, class... Ts> void pr(const T& t, const Ts&... ts) { 
        pr(t); pr(ts...); 
    }
    template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
        pr("{",x.f,", ",x.s,"}"); 
    }
    template<class T> void pr(const T& x) { 
        pr("{"); // const iterator needed for vector<bool>
        bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; 
        pr("}");
    }
    
    void ps() { pr("\n"); } // print w/ spaces
    template<class T, class... Ts> void ps(const T& t, const Ts&... ts) { 
        pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); 
    }
    
    void pc() { pr("]\n"); } // debug w/ commas
    template<class T, class... Ts> void pc(const T& t, const Ts&... ts) { 
        pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); 
    }
    #define dbg(x...) pr("[",#x,"] = ["), pc(x);
}

using namespace output;

namespace io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
    }
}

using namespace io;

mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());

const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 100005;
const ld PI = 4*atan((ld)1);

int N,K; ll a[MX], pre[MX]; vector<pl> ranges; ll dp[MX][205]; int fr[MX][205];

struct Line{
   ll m,c; int ind;
   ll f(ll x){
      return m*x+c;
   }
   ll isect(Line l){
      return floor(c-l.c)/(l.m-m);
   }
};

vector<Line> vals; set<pl> used; 

bool cmp(Line a, Line b){
   return (a.m == b.m) ? (a.c < b.c) : (a.m < b.m);
}

void precomp(){
   sort(all(vals), cmp);
   int S = sz(vals);
   ranges.rsz(S);
   ll prev = -INF;
   f0x(i,1,S){
      ll x = vals[i-1].isect(vals[i]);
      ranges[i-1] = mp(prev, x);
      prev = x+1;
   }
   ranges[S-1] = mp(prev, INF);
}

pair<ll, int> query(ll x){
   //dbg(x);
   int lo = 0; int hi = sz(ranges)-1; int ans = -1;
   while(lo <= hi){
      int mid = lo + (hi-lo)/2;
      //dbg(mid, ranges[mid]);
      if(ranges[mid].f <= x && ranges[mid].s >= x){
         ans = mid;
         break;
      }
      else if(ranges[mid].f > x){
         hi = mid-1;
      }
      else if(ranges[mid].s < x){
         lo = mid+1;
      }
   }
   //dbg(ans);
   if(ans == -1){
      return mp(0,-1);
   }
   return mp(vals[ans].f(x), vals[ans].ind);
}

int main() {
   setIO(); 
   re(N,K); 
   fax(i,N) {
      re(a[i]);
   }
   fax(i,N){
      fax(j,K+2){
         dp[i][j] = -INF;
      }
   }
   pre[0] = a[0];
   fax(i,N){
      pre[i] = pre[i-1] + a[i];
   }
   fax(i,N){
      dp[i][1] = 0; 
      fr[i][1] = -1;
      //dbg(i,1,dp[i][1]);
      Line tri = {pre[i], -(pre[i]*pre[i]), i};
      if(!used.count(mp(tri.m, tri.c))){
         used.insert(mp(tri.m, tri.c));
         vals.pb(tri);
         //dbg("INSERTING", pre[i], -(pre[i]*pre[i]));
      }
   }
   f0x(j,2,K+2){
      precomp();
      
      //dbg(ranges);
      /*
      trav(curr, vals){
         dbg(curr.m, curr.c);
      }
      */
      //dbg(vals[1].isect(vals[2]));
     
      fax(i,N){
        pair<ll,int> ret = query(pre[i]);
        dp[i][j] = ret.f;
        fr[i][j] = ret.s;
        //dbg(i,j,pre[i], dp[i][j]);
      }
      vals.clear();
      ranges.clear();
      fax(i,N){
         Line tri = {pre[i], dp[i][j]-(pre[i]*pre[i]), i};      
         if(!used.count(mp(tri.m, tri.c))){
            used.insert(mp(tri.m, tri.c));
            vals.pb(tri);
            //dbg("INSERTING", pre[i], dp[i][j]-(pre[i]*pre[i]));
         }
      }
   }
   /*
   trav(curr, vals){
      dbg(curr.m, curr.c);
   }
   */
   pr(dp[N-1][K+1]);
   ps();
   vi fin;
   int pos = N-1; int ci = K+1;
   while(pos >= 0 && ci >= 0){
      if(pos != N-1) fin.pb(pos+1);
      pos = fr[pos][ci];
      ci--;
   }
   reverse(all(fin));
   trav(curr, fin) pr(curr, " ");
}

Compilation message (stderr)

sequence.cpp: In function 'void io::setIn(std::__cxx11::string)':
sequence.cpp:133:35: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     void setIn(string s) { freopen(s.c_str(),"r",stdin); }
                            ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void io::setOut(std::__cxx11::string)':
sequence.cpp:134:36: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     void setOut(string s) { freopen(s.c_str(),"w",stdout); }
                             ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

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