Submission #35826

#	Time	Username	Problem	Language	Result	Execution time	Memory
35826		funcsr	Building Bridges (CEOI17_building)	C++14	30 / 100	3000 ms	42996 KiB

building

#include <iostream>
#include <vector>
#include <queue>
#include <string>
#include <set>
#include <cassert>
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(xs) xs.begin(), xs.end()
#define INF (1LL<<60)
#define _1 first
#define _2 second
using namespace std;
#define MAX_N (1<<20)
int seg[MAX_N*2-1];
int prv[MAX_N*2-1], nxt[MAX_N*2-1];

int sum(int a, int b, int k=0, int l=0, int r=MAX_N) {
  if (b <= l || r <= a) return 0;
  if (a <= l && r <= b) return seg[k];
  return sum(a, b, k*2+1, l, (l+r)/2) + sum(a, b, k*2+2, (l+r)/2, r);
}
int kth(int n, int k=0, int l=0, int r=MAX_N) {
  if (r-l == 1) return l;
  int left = seg[k*2+1];
  if (n <= left) return kth(n, k*2+1, l, (l+r)/2);
  else return kth(n-left, k*2+2, (l+r)/2, r);
}
inline bool is_set(int k) { return seg[k+MAX_N-1]; }
inline int p_left(int x) {
  int s = sum(0, x);
  if (s == 0) return -1;
  return kth(s);
}
inline int p_right(int x) {
  int s = sum(0, x+1);
  if (s == seg[0]) return -1;
  return kth(s+1);
}

void set_val(int k, int v) {
  if (v) {
    int a = p_left(k), b = p_right(k);
    if (a != -1) nxt[a] = k;
    if (b != -1) prv[b] = k;
    nxt[k] = b, prv[k] = a;
  }
  else {
    int a = prv[k], b = nxt[k];
    if (a != -1) nxt[a] = b;
    if (b != -1) prv[b] = a;
    prv[k] = nxt[k] = -1;
  }

  k += MAX_N-1;
  assert(seg[k] != v);
  seg[k] = v;
  while (k) {
    k = (k-1)/2;
    seg[k] = seg[k*2+1] + seg[k*2+2];
  }
}


typedef pair<int, long long> P;

P operator -(const P &a, const P &b) { return P(a._1-b._1, a._2-b._2); }
inline long long det(P a, P b) { return 1LL*a._1*b._2 - 1LL*a._2*b._1; }

int N;
int H[100000], W[100000];
long long dp[1000001];
long long f[1000001];
inline P get(int x) { return P(x, f[x]); }

void update(int x, long long y) {
  if (dp[x] <= y) return;
  if (dp[x] < INF) if (is_set(x)) set_val(x, 0);
  P p = P(x, y+1LL*x*x);
  dp[x] = y;
  f[x] = p._2;
  //if (seg[0]) for (int x=kth(1); x!=-1; x=nxt[x]) cout<<x<<",";cout<<"\n";
  while (true) {
    int right = p_right(x);
    if (right == -1) break;
    P r = get(right);
    if (p._2 >= r._2) return; // erase p
    else {
      right = nxt[right];
      if (right == -1) break;
      P k = get(right);
      if (det(r-p, k-r) > 0) break;
      set_val(prv[right], 0);
    }
  }

  while (true) {
    int left = p_left(x);
    if (left == -1) break;
    P l = get(left);
    if (l._2 >= p._2) set_val(left, 0);
    else {
      if (prv[left] == -1) break;
      left = prv[left];
      P k = get(left);
      if (det(l-k, p-l) > 0) break;
      set_val(nxt[left], 0);
    }
  }
  int right = p_right(x);
  if (right != -1 && prv[right] != -1) {
    P r = get(right);
    P l = get(prv[right]);
    if (det(p-l, r-p) <= 0) return;
  }
  set_val(x, 1);
}

signed main() {
  cin >> N;
  rep(i, N) cin >> H[i];
  long long sum = 0;
  rep(i, N) {
    cin >> W[i];
    sum += W[i];
    W[i] = -W[i];
  }
  rep(h, 1000001) dp[h] = INF, f[h] = INF;
  rep(i, MAX_N*2-1) prv[i] = nxt[i] = -1;
  update(H[0], W[0]);
  for (int i=1; i<N-1; i++) {
    long long m = INF;
    int st = kth(1);
    if (st == -1) continue;
    for (int x=st; x!=-1; x=nxt[x]) m = min(m, f[x] - 2LL*x*H[i]);
    update(H[i], m+1LL*H[i]*H[i]+W[i]);
  }
  long long m = INF;
  rep(h, 1000001) m = min(m, dp[h] + 1LL*(h-H[N-1])*(h-H[N-1]));
  cout << sum + m + W[N-1] << "\n";
  return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 0 / 30
• Subtask 3: 0 / 40