Submission #30638

#	Time	Username	Problem	Language	Result	Execution time	Memory
30638		Nirjhor	Split the sequence (APIO14_sequence)	C++14	0 / 100	0 ms	1848 KiB

sequence

#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[K][N];
int pre[K][N];
vector <line> v[K];
stack <int> opts;

// dp(i, k) = dp(j, k - 1) + a[j] * a[i] - a[j]^2

// y = m1x + c1, y = m2x + c2, y = m3x + c3
// x = (c1 - c2)/(m2 - m1) 
// x = (c1 - c3)/(m3 - m1) 
// (c1 - c3) * (m2 - m1) < (c1 - c2) * (m3 - m1)

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

Compilation message (stderr)

sequence.cpp: In function 'line query(int, ll)':
sequence.cpp:40:14: 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:47:25: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d", &n, &k);
                         ^
sequence.cpp:49:25: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%lld", a + i);
                         ^

• Subtask 1: 0 / 11
• Subtask 2: 0 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29