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Submission #30648

# Submission time Handle Problem Language Result Execution time Memory
30648 2017-07-25T20:14:14 Z Nirjhor Split the sequence (APIO14_sequence) C++14
100 / 100
 809 ms 93748 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int K = 205;
const int N = 100005;

struct line {
  int id;
  ll m, c;
};

int n, k, ptr;
ll a[N], f[2][N];
int pre[K][N];
vector <line> v[2];
stack <int> opts;

bool bad (line i, line j, line k) {
  return (i.c - k.c) * (j.m - i.m) <= (i.c - j.c) * (k.m - i.m);
}

void add (int at, line l) {
  v[at].push_back(l);
  while (v[at].size() >= 3 and bad(v[at][v[at].size() - 3], v[at][v[at].size() - 2], v[at][v[at].size() - 1])) {
    v[at].erase(v[at].end() - 2);
  }
}

line query (int at, ll x) {
  while (ptr < v[at].size() - 1 and v[at][ptr].m * x + v[at][ptr].c < v[at][ptr + 1].m * x + v[at][ptr + 1].c) {
    ++ptr;
  }
  ptr = min(ptr, (int) v[at].size() - 1);
  return v[at][ptr];
}

int main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; ++i) {
    scanf("%lld", a + i);
    a[i] += a[i - 1];
  }
  int now = 1, bef = 0;
  for (int i = 1; i <= k; ++i) {
    ptr = 0, v[bef].clear();
    add(bef, {i, a[i], f[bef][i] - a[i] * a[i]});
    for (int j = i + 1; j <= n; ++j) {
      line opt = query(bef, a[j]);
      f[now][j] = opt.m * a[j] + opt.c;
      pre[i][j] = opt.id;
      add(bef, {j, a[j], f[bef][j] - a[j] * a[j]});
    }
    swap(now, bef);
  }
  printf("%lld\n", f[bef][n]);
  for (int i = k, j = n; i; --i) {
    j = pre[i][j];
    assert(0 < j and j < n);
    opts.push(j);
  }
  while (!opts.empty()) {
    printf("%d ", opts.top());
    opts.pop();
  }
  puts("");
  return 0;
}

Compilation message

sequence.cpp: In function 'line query(int, ll)':
sequence.cpp:33:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while (ptr < v[at].size() - 1 and v[at][ptr].m * x + v[at][ptr].c < v[at][ptr + 1].m * x + v[at][ptr + 1].c) {
              ^
sequence.cpp: In function 'int main()':
sequence.cpp:41:25: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d", &n, &k);
                         ^
sequence.cpp:43:25: 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 84448 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 84448 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 84448 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 84448 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 84448 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 84448 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 84448 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 84448 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 84448 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 84448 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 84448 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 84448 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 84448 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 84448 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 84448 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 84448 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 84448 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84448 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 84448 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 84448 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 84448 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 84448 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 84448 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 84448 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 84448 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 84448 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 84448 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84448 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 84448 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 0 ms 84448 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 84448 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 0 ms 84448 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 0 ms 84448 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 0 ms 84448 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 0 ms 84448 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 84448 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 0 ms 84448 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 84596 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 84596 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 3 ms 84596 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 84596 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 84596 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 3 ms 84596 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 3 ms 84596 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 3 ms 84596 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 0 ms 84596 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 84596 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 85108 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 0 ms 85108 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 43 ms 85684 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 0 ms 85684 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 33 ms 85108 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 43 ms 85108 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 49 ms 85684 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 29 ms 85684 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 39 ms 85684 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 56 ms 85684 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 93748 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 29 ms 93748 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 529 ms 93748 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 26 ms 93748 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 809 ms 93748 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 553 ms 90672 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 576 ms 93748 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 363 ms 93748 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 433 ms 93748 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 556 ms 93748 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845