Submission #112817

#	Time	Username	Problem	Language	Result	Execution time	Memory
112817		Kamisama	Split the sequence (APIO14_sequence)	C++14	71 / 100	2023 ms	84940 KiB

sequence

#include <iostream>
#include <cstdio>
#include <iomanip>
#include <chrono>
//#define Kami
#define taskname "APIO14_sequence"
using namespace std;
const int maxn=1e5+3;
const int maxk=2e2+3;

template<typename T> inline void Read(T &x){
    register char c;
    bool neg=false;
    for(c=getchar();c<'0'||c>'9';c=getchar()) if(c=='-') neg=true;
    for(x=0;'0'<=c&&c<='9';c=getchar()) x=x*10+c-'0';
    if(neg) x=-x;
}template<typename T,typename... Args> inline void Read(T &x,Args&... args){
    Read(x);
    Read(args...);
}template<typename T> inline void Write(T x){
    if(x<0) putchar('-'),x=-x;
    if(x>9) Write(x/10);
    putchar(x%10+'0');
}template<typename T> inline void Write(T x, const char &c){
    if(x<0) putchar('-'),x=-x;
    Write(x);
    putchar(c);
}template <typename T,typename... Args> inline void Write(const T &a, const char &c, Args... args){
    Write(a,c);
    Write(args...);
}

struct TLines{
    long long a, b; int id;
    inline TLines(long long _a=0, long long _b=0, int _id=0){a=_a;b=_b;id=_id;}
    inline long long Value(const long long &x){return a*x+b;}
    friend inline bool isBad(const TLines &d1, const TLines &d2, const TLines &d3){
        return (d2.b-d1.b)*(d1.a-d3.a)>=(d3.b-d1.b)*(d1.a-d2.a);
    }
};

int n,k,a[maxn],trace[maxn][maxk];
long long s[maxn],f[maxn],g[maxn];
TLines convex[maxn];

inline void Enter(){
    Read(n,k);
    for(int i=1;i<=n;i++) Read(a[i]), s[i]=s[i-1]+a[i];
}

inline void Solve(){ // f[i] = max{ s[j]*s[i] + f[j] - s[j]^2 }
    for(int t=1;t<=k;t++){
        int best=1;
        int nConvex=0;
        swap(f,g);
        for(int i=1;i<=n;i++){
            long long x=s[i];
            while(best<nConvex && convex[best].Value(x)<=convex[best+1].Value(x)) best++;
            f[i]=convex[best].Value(x);
            trace[i][t]=convex[best].id;
            TLines newline(s[i],g[i]-s[i]*s[i],i);
            while(nConvex>1 && isBad(convex[nConvex-1],convex[nConvex],newline)){
                best-=(best==nConvex);
                nConvex--;
            } convex[++nConvex]=newline;
        }
    }
    Write(f[n],'\n');
    for(int x=n,i=k;i>=1;i--) Write(x=trace[x][i],' ');
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL); if(fopen(taskname".INP","r"))
    freopen(taskname".INP","r",stdin),
    freopen(taskname".OUT","w",stdout);
    #ifdef Kami
    auto start=chrono::steady_clock::now();
    #endif

    Enter();
    Solve();

    #ifdef Kami
    auto end=chrono::steady_clock::now();
    cerr<<"\nIn milliseconds : "
        <<chrono::duration_cast<chrono::milliseconds>(end-start).count();
    cerr<<'\n'<<"In seconds : "<<fixed<<setprecision(3)
        <<(double)chrono::duration_cast<chrono::milliseconds>(end-start).count()/1000<<'\n';
    #endif

    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:75:38: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(taskname".INP","r",stdin),
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~
     freopen(taskname".OUT","w",stdout);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:75:38: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]

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