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Submission #29756

# Submission time Handle Problem Language Result Execution time Memory
29756 2017-07-20T14:23:29 Z sampriti Split the sequence (APIO14_sequence) C++14
100 / 100
 659 ms 88532 KB 
#include <cstdio>
#include <algorithm>
#include <climits>

using namespace std;

struct line {
  long long m, c;

  line(long long _m, long long _c) : m(_m), c(_c) {};

  long long at(long long x) {
    return m * x + c;
  }

  double intersect(line other) {
    return double(other.c - c)/(m - other.m);
  }
};

int N, K;
int A[100001];
long long P[100001];
long long dp[2][100002];
int nxt[202][100002];

vector<pair<line, int> > lines;
vector<double> inter;

void insert(line x, int k) {
  while(!lines.empty() && lines.back().first.m == x.m) {
    if(lines.back().first.c >= x.c) return;
    lines.pop_back();
    if(!inter.empty()) inter.pop_back();
  }

  while(!inter.empty() && x.intersect(lines.back().first) <= inter.back()) {
    inter.pop_back();
    lines.pop_back();
  }

  if(!lines.empty()) {
    inter.push_back(x.intersect(lines.back().first));
  }

  lines.push_back({x, k});
}

int inter_ptr;
pair<line, int> get_best(long long x) {
  inter_ptr = min(inter_ptr, (int)inter.size());
  while(inter_ptr < inter.size() && x > inter[inter_ptr]) inter_ptr++;
  return lines[inter_ptr];
}

int main() {
  scanf("%d %d", &N, &K);
  for(int i = 1; i <= N; i++) scanf("%d", &A[i]);
  for(int i = 1; i <= N; i++) P[i] = P[i - 1] + A[i];

  dp[0][0] = LLONG_MIN/10;
  int t = 1;

  for(int _k = 2; _k <= K + 1; _k++) {
    dp[t][0] = LLONG_MIN/10;

    lines.clear();
    inter.clear();
    inter_ptr = 0;

    for(int i = 1; i <= N; i++) {
      insert(line(P[i - 1], dp[t ^ 1][i - 1] - P[i - 1] * P[i - 1]), i);

      auto it = get_best(P[i]);
      dp[t][i] = it.first.at(P[i]);
      nxt[_k][i] = it.second;
    }

    t ^= 1;
  }

  printf("%lld\n", dp[t ^ 1][N]);

  int i = N, j = K + 1;
  while(j > 1) {
    printf("%d ", nxt[j][i] - 1);
    i = nxt[j][i] - 1;
    j--;
  }
  printf("\n");
}

Compilation message

sequence.cpp: In function 'std::pair<line, int> get_best(long long int)':
sequence.cpp:52:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(inter_ptr < inter.size() && x > inter[inter_ptr]) inter_ptr++;
                   ^
sequence.cpp: In function 'int main()':
sequence.cpp:57:25: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d", &N, &K);
                         ^
sequence.cpp:58:49: 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("%d", &A[i]);
                                                 ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 82816 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 82816 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 82816 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 82816 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 82816 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 82816 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 82816 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 82816 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 82816 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 82816 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 82816 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 82816 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 82816 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 82816 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 82816 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 82816 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 82816 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 82816 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 82816 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 82816 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 82816 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 82816 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 82816 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 82816 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 82816 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 82816 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 82816 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 82816 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 82816 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 0 ms 82816 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 82816 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 0 ms 82816 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 0 ms 82816 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 0 ms 82816 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 0 ms 82816 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 82816 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 0 ms 82816 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 82816 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 82816 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 82816 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 82816 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 3 ms 82816 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 3 ms 82816 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 82816 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 3 ms 82816 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 0 ms 82816 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 82816 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 83184 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 83184 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 56 ms 83540 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 0 ms 83540 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 36 ms 83184 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 36 ms 83184 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 46 ms 83540 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 33 ms 83540 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 36 ms 83540 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 46 ms 83540 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 26 ms 88532 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 16 ms 88532 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 489 ms 88532 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 29 ms 88532 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 659 ms 88532 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 443 ms 88532 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 429 ms 88532 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 396 ms 88532 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 373 ms 88532 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 493 ms 88532 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845