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Submission #23168

# Submission time Handle Problem Language Result Execution time Memory
23168 2017-05-04T06:20:35 Z ruhanhabib39 Split the sequence (APIO14_sequence) C++14
62 / 100
 623 ms 91876 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long Long;

const int MAXN = 1e5;
const int MAXK = 200;

int N, K;
Long A[MAXN + 10], S[MAXN + 10];

Long dp[2][MAXN + 10];
int pos[MAXK + 10][MAXN + 10];

struct dat {
   Long m, b; int i;
   Long f(Long x) const {
      return m*x + b;
   }
};

bool bad(dat l1, dat l2, dat l3) {
   return (l1.b - l3.b)*(l2.m - l1.m) < (l1.b-l2.b)*(l3.m-l1.m);
}

vector<dat> L;

void add(dat l) {
   L.push_back(l);
   while(L.size() >= 3 && bad(L[L.size()-3], L[L.size()-2], L[L.size()-1])) {
      L.erase(L.end() - 2);
   }
}

int ii = 0;

int get(Long x) {
   if(ii >= (int)L.size()) ii = L.size()-1;
   while(ii+1 < (int)L.size() && L[ii+1].f(x) >= L[ii].f(x)) {
      ii++;
   }
   return L[ii].i;
}

void add(int x, int j) {
   Long m = S[j];
   Long b = - S[j] * S[j] + dp[x][j];
   add(dat{m, b, j});
}

void calc_dp() {
   for(int k = 1; k <= K; k++) {
      int x = k & 1;
      L.clear(); ii = 0;
      if(k > 0) add(x ^ 1, k-1);
      for(int i = k; i <= N; i++) {
         int j = get(S[i]);
         pos[k][i] = j;
         dp[x][i] = S[j]*S[i] - S[j]*S[j] + dp[x^1][j];
         add(x ^ 1, i);
      }
   }
}

int main() {
   scanf("%d%d", &N, &K);
   S[0] = 0;
   for(int i = 1; i <= N; i++) {
      scanf("%lld", &A[i]);
      S[i] = A[i] + S[i-1];
   }
   calc_dp();
   printf("%lld\n", dp[K&1][N]);
   int i = N, k = K;
   while(k > 0) {
      i = pos[k][i];
      printf("%d ", i);
      k--;
   }
   printf("\n");
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:66:25: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
    scanf("%d%d", &N, &K);
                         ^
sequence.cpp:69:27: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
       scanf("%lld", &A[i]);
                           ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 87184 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 87184 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 87184 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 87184 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 87184 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 87184 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 87184 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 87184 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 87184 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 87184 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 87184 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 87184 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 87184 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 87184 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 87184 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 87184 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 87184 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 87184 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 87184 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 87184 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 87184 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 87184 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 87184 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 87184 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 87184 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 87184 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 87184 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 87184 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 87184 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 0 ms 87184 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 87184 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 0 ms 87184 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 0 ms 87184 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 0 ms 87184 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 0 ms 87184 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 87184 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 0 ms 87184 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 87184 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 87184 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 3 ms 87184 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 87184 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 3 ms 87184 KB contestant found the optimal answer: 679388326 == 679388326
6 Incorrect 3 ms 87184 KB contestant didn't find the optimal answer: 4699030135 < 4699030287
7 Halted 0 ms 0 KB -

Subtask #5
0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 87844 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 0 ms 87844 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 53 ms 87844 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 0 ms 87844 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 33 ms 87844 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Incorrect 43 ms 87844 KB contestant didn't find the optimal answer: 514786325281 < 514790755404
7 Halted 0 ms 0 KB -

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 91876 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 19 ms 91876 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 473 ms 91876 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 19 ms 91876 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 623 ms 91876 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 389 ms 91876 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 433 ms 91876 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 346 ms 91876 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 333 ms 91876 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 429 ms 91876 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845