Submission #224769

#	Time	Username	Problem	Language	Result	Execution time	Memory
224769		urd05	Split the sequence (APIO14_sequence)	C++14	100 / 100	830 ms	5624 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
 
long long psum[110001];
int n;
 
struct Line {
    long long a,b;
};
 
struct Fraction {
    long long up,down;
};
 
Fraction cross(Line one,Line two) {
    if (one.a<two.a) {
        swap(one,two);
    }
    return {two.b-one.b,one.a-two.a};
}
 
bool cmp(Fraction one,Fraction two) {
    return one.up*two.down<one.down*two.up;
}
 
Line arr[110001];
int sz;
 
void insert(Line l) {
    if (sz>=1&&arr[sz-1].a==l.a) {
        if (l.b>arr[sz-1].b) {
            arr[sz-1]=l;
        }
        return;
    }
    while (sz>1) {
        Fraction before=cross(arr[sz-2],arr[sz-1]);
        Fraction now=cross(arr[sz-1],l);
        if (cmp(before,now)) {
            break;
        }
        sz--;
    }
    arr[sz++]=l;
}

vector<int> ret;
long long before[110005];
long long before2[110005];
long long now[110005];

long long getans(int x1,int y1,int x2,int y2) {
    int ind=0;
    if (y1+1==y2) {
        ret.push_back(x2);
        return 0;
    }
    int mid=(y1+y2)/2;
    for(int i=x1;i<=x2;i++) {
        before[i]=-1e18;
        before2[i]=-1e18;
    }
    before[x1]=0;
    before2[x2]=0;
    for(int i=y1+1;i<=mid;i++) {
        sz=0;
        ind=0;
        for(int j=x1;j<=x2;j++) {
            while (ind+1<sz&&cmp(cross(arr[ind],arr[ind+1]),{psum[j],1})) {
                ind++;
            }
            long long val;
            if (ind>=sz) {
                val=-1e18;
            }
            else {
                val=arr[ind].a*psum[j]+arr[ind].b;
            }
            now[j]=val;
            if (before[j]>=0)
            	insert({psum[j],-psum[j]*psum[j]+before[j]});
        }
        for(int j=x1;j<=x2;j++) {
            before[j]=now[j];
        }
    }
    for(int i=y2-1;i>=mid;i--) {
        sz=0;
        ind=0;
        for(int j=x2;j>=x1;j--) {
            while (ind+1<sz&&cmp(cross(arr[ind],arr[ind+1]),{-psum[j],1})) {
                ind++;
            }
            long long val;
            if (ind>=sz) {
                val=-1e18;
            }
            else {
                val=arr[ind].a*(-psum[j])+arr[ind].b-psum[j]*psum[j];
            }
            now[j]=val;
            if (before2[j]>=0)
            	insert({-psum[j],before2[j]});
        }
        for(int j=x1;j<=x2;j++) {
            before2[j]=now[j];
        }
    }
    int opt=-1;
    long long maxi=-1e18;
    for(int i=x1;i<=x2;i++) {
        if (before[i]+before2[i]>maxi) {
            maxi=before[i]+before2[i];
            opt=i;
        }
    }
    getans(x1,y1,opt,mid);
    getans(opt,mid,x2,y2);
    return maxi;
}
 
int main(void) {
    int k;
    scanf("%d %d\n",&n,&k);
    for(int i=0;i<n;i++) {
        long long x;
        scanf("%lld",&x);
        psum[i+1]=psum[i]+x;
    }
    printf("%lld\n",getans(0,0,n,k+1));
    for(int i=0;i<k;i++) {
        printf("%d ",ret[i]);
    }
    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:124:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d\n",&n,&k);
     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:127:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%lld",&x);
         ~~~~~^~~~~~~~~~~

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