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Submission #158407

# Submission time Handle Problem Language Result Execution time Memory
158407 2019-10-17T00:43:20 Z mhy908 Split the sequence (APIO14_sequence) C++14
100 / 100
 608 ms 87088 KB 
#include <bits/stdc++.h>
#define F first
#define S second
#define pb push_back
#define llinf 8987654321987654321
using namespace std;
typedef long long LL;
typedef pair<int, int> pii;
typedef pair<LL, LL> pll;
int n, k;
LL arr[100010], sum[100010], dp[2][100010];
int pass[210][100010];
struct LinearFunc{
    LL a, b;
    int c;
    long double s;
    LinearFunc(): LinearFunc(1, 0, 0){}
    LinearFunc(LL a1, LL b1, int c1): a(a1), b(b1), s(0), c(c1){}
}f[100010];
long double cross(LinearFunc &f, LinearFunc &g){
    return (long double)(g.b-f.b)/(long double)(f.a-g.a);
}
void print(int num, int x){
    if(num<=1)return;
    print(num-1, pass[num][x]);
    printf("%d ", pass[num][x]);
}
int main()
{
    scanf("%d %d", &n, &k);
    for(int i=1; i<=n; i++)scanf("%lld", &arr[i]), sum[i]=sum[i-1]+arr[i];
    for(int i=1; i<=n; i++)dp[0][i]=llinf;
    for(int j=1; j<=k+1; j++){
        int top=0, fpos=0;
        for(int i=j; i<=n; i++){
            LinearFunc g(-2*sum[i-1], dp[(j+1)%2][i-1]+sum[i-1]*sum[i-1], i-1);
            bool flag=true;
            while(top>0){
                if(f[top-1].a!=g.a){
                    g.s=cross(f[top-1], g);
                    if(f[top-1].s<g.s)break;
                    if(--top==fpos)fpos--;
                }
                else{
                    if(f[top-1].b<=g.b){
                        flag=false;
                        break;
                    }
                    if(--top==fpos)fpos--;
                }
            }
            if(flag)f[top++]=g;
            LL x=sum[i];
            while(fpos+1<top&&f[fpos+1].s<x)fpos++;
            dp[j%2][i]=f[fpos].a*x+f[fpos].b+sum[i]*sum[i];
            pass[j][i]=f[fpos].c;
        }
    }
    printf("%lld\n", (sum[n]*sum[n]-dp[(k+1)%2][n])/2);
    print(k+1, n);
}
/*
5 1
0 1 0 0 1
*/

Compilation message

sequence.cpp: In constructor 'LinearFunc::LinearFunc(LL, LL, int)':
sequence.cpp:16:17: warning: 'LinearFunc::s' will be initialized after [-Wreorder]
     long double s;
                 ^
sequence.cpp:15:9: warning:   'int LinearFunc::c' [-Wreorder]
     int c;
         ^
sequence.cpp:18:5: warning:   when initialized here [-Wreorder]
     LinearFunc(LL a1, LL b1, int c1): a(a1), b(b1), s(0), c(c1){}
     ^~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:30:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d", &n, &k);
     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:31:50: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(int i=1; i<=n; i++)scanf("%lld", &arr[i]), sum[i]=sum[i-1]+arr[i];
                            ~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 5112 KB contestant found the optimal answer: 108 == 108
2 Correct 6 ms 5112 KB contestant found the optimal answer: 999 == 999
3 Correct 6 ms 5012 KB contestant found the optimal answer: 0 == 0
4 Correct 7 ms 5112 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 6 ms 5080 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 6 ms 5112 KB contestant found the optimal answer: 1 == 1
7 Correct 6 ms 4984 KB contestant found the optimal answer: 1 == 1
8 Correct 6 ms 5116 KB contestant found the optimal answer: 1 == 1
9 Correct 6 ms 5112 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 6 ms 5112 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 6 ms 4984 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 6 ms 5112 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 6 ms 5112 KB contestant found the optimal answer: 140072 == 140072
14 Correct 6 ms 4984 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 6 ms 4984 KB contestant found the optimal answer: 805 == 805
16 Correct 6 ms 5112 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 6 ms 4984 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 4984 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 6 ms 4984 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 6 ms 5240 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 7 ms 5112 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 7 ms 5072 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 6 ms 5112 KB contestant found the optimal answer: 933702 == 933702
7 Correct 6 ms 5112 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 6 ms 5112 KB contestant found the optimal answer: 687136 == 687136
9 Correct 6 ms 5112 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 6 ms 5116 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 5112 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 6 ms 5112 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 7 ms 6008 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 6 ms 5112 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 7 ms 5752 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 7 ms 5880 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 7 ms 6008 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 6 ms 5240 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 6 ms 5240 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 6 ms 5368 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 5112 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 5112 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 10 ms 6776 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 5076 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 6776 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 6520 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 6776 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 6904 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 7 ms 5368 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 5752 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 5496 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 8 ms 5496 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 48 ms 14116 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 8 ms 5496 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 43 ms 10620 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 45 ms 11512 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 52 ms 11964 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 37 ms 10776 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 41 ms 11512 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 50 ms 13192 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 9720 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 27 ms 9720 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 412 ms 86776 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 27 ms 10232 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 608 ms 87088 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 394 ms 63636 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 463 ms 67704 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 331 ms 56824 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 337 ms 63736 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 439 ms 79480 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845