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COLOCON -Colopl programming contest 2018- Final C - スペースエクスプローラー高橋君

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C - スペースエクスプローラー高橋君

CHTで解いてたけどmonotone minimaで解けるらしいので解くことにした

考えたこと

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
#define int ll
using VI = vector<int>;
using VVI = vector<VI>;
using PII = pair<int, int>;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
#define PB push_back

const ll LLINF = (1LL<<60);
const int INF = (1LL<<30);
const int MOD = 1000000007;

template <typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template <typename T> bool IN(T a, T b, T x) { return a<=x&&x<b; }
template<typename T> T ceil(T a, T b) { return a/b + !!(a%b); }
template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a){
  out<<'('<<a.first<<','<<a.second<<')';
  return out;
}
template<class T>
ostream &operator <<(ostream& out,const vector<T>& a){
  out<<'[';
  REP(i, a.size()) {out<<a[i];if(i!=a.size()-1)out<<',';}
  out<<']';
  return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};

// monotone minima
// O(NlogN)
// verify: https://beta.atcoder.jp/contests/colopl2018-final-open/tasks/colopl2018_final_c
const int MAX_N = 200010;
int minima[MAX_N];
int a[MAX_N];

int f(int i, int j) { return a[j] + (j-i)*(j-i); }
void monotoneMinima(int ib, int ie, int jb, int je) {
  if(ib > ie) return;
  if(ib == ie) {
    int jm = jb;
    int fm = f(ib, jm), fj;
    for(int j=jb+1; j<=je; ++j) {
      if(fm > (fj = f(ib, j))) {
        fm = fj;
        jm = j;
      }
    }
    minima[ib] = jm;
    return;
  }
  int im = (ib+ie)/2;
  monotoneMinima(im, im, jb, je);
  monotoneMinima(ib, im-1, jb, minima[im]);
  monotoneMinima(im+1, ie, minima[im], je);
}

signed main(void)
{
  int n;
  cin >> n;
  REP(i, n) cin >> a[i];

  monotoneMinima(0, n-1, 0, n-1);
  REP(i, n) cout << f(i, minima[i]) << endl;

  return 0;
}