P3515 [POI2011]Lightning Conductor [决策单调性]

求 \(p\) 使得所有 \(a_j \leq a_i + p - \sqrt |i-j|\)

发现绝对值不好搞，然后就正反做两遍

// powered by c++11
// by Isaunoya
#include<bits/stdc++.h>
#define rep(i , x , y) for(register int i = (x) ; i <= (y) ; ++ i)
#define Rep(i , x , y) for(register int i = (x) ; i >= (y) ; -- i)
using namespace std ;
using db = double ;
using ll = long long ;
using uint = unsigned int ;
#define int long long
using pii = pair < int , int > ;
#define ve vector
#define Tp template
#define all(v) v.begin() , v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back
#define fir first
#define sec second
// the cmin && cmax
Tp < class T > void cmax(T & x , const T & y) { if(x < y) x = y ; }
Tp < class T > void cmin(T & x , const T & y) { if(x > y) x = y ; }
// sort , unique , reverse
Tp < class T > void sort(ve < T > & v) { sort(all(v)) ; }
Tp < class T > void unique(ve < T > & v) { sort(all(v)) ; v.erase(unique(all(v)) , v.end()) ; }
Tp < class T > void reverse(ve < T > & v) { reverse(all(v)) ; }
const int SZ = 0x191981 ;
struct FILEIN {
	~ FILEIN () {} char qwq[SZ] , * S = qwq , * T = qwq , ch ;
	char GETC() { return (S == T) && (T = (S = qwq) + fread(qwq , 1 , SZ , stdin) , S == T) ? EOF : * S ++ ; }
	FILEIN & operator >> (char & c) { while(isspace(c = GETC())) ; return * this ; }
	FILEIN & operator >> (string & s) {
		while(isspace(ch = GETC())) ; s = ch ;
		while(! isspace(ch = GETC())) s += ch ; return * this ;
	}
	Tp < class T > void read(T & x) {
		bool sign = 1 ; while((ch = GETC()) < 0x30) if(ch == 0x2d) sign = 0 ;
		x = (ch ^ 0x30) ; while((ch = GETC()) > 0x2f) x = x * 0xa + (ch ^ 0x30) ;
		x = sign ? x : -x ;
	}
	FILEIN & operator >> (int & x) { return read(x) , * this ; }
	FILEIN & operator >> (signed & x) { return read(x) , * this ; }
	FILEIN & operator >> (unsigned & x) { return read(x) , * this ; }
} in ;
struct FILEOUT { const static int LIMIT = 0x114514 ;
	char quq[SZ] , ST[0x114] ; signed sz , O ;
	~ FILEOUT () { sz = O = 0 ; }
	void flush() { fwrite(quq , 1 , O , stdout) ; fflush(stdout) ; O = 0 ; }
	FILEOUT & operator << (char c) { return quq[O ++] = c , * this ; }
	FILEOUT & operator << (string str) {
		if(O > LIMIT) flush() ; for(char c : str) quq[O ++] = c ; return * this ;
	}
	Tp < class T > void write(T x) {
		if(O > LIMIT) flush() ; if(x < 0) { quq[O ++] = 0x2d ; x = -x ; }
		do { ST[++ sz] = x % 0xa ^ 0x30 ; x /= 0xa ; } while(x) ;
		while(sz) quq[O ++] = ST[sz --] ; return ;
	}
	FILEOUT & operator << (int x) { return write(x) , * this ; }
	FILEOUT & operator << (signed x) { return write(x) , * this ; }
	FILEOUT & operator << (unsigned x) { return write(x) , * this ; }
} out ;

int n ;
ve < int > v ;
ve < double > ans ;
double calc(int x , int y) { return v[x] - v[y] + sqrt(y - x) ; }
void solve(int l , int r , int L , int R) {
	if(l > r) return ;
	int p = L , mid = l + r >> 1 ;
	rep(i , L + 1 , min(mid , R))
		if(calc(p , mid) < calc(i , mid))
			p = i ;
	cmax(ans[mid] , calc(p , mid)) ;
	solve(l , mid - 1 , L , p) ;
	solve(mid + 1 , r , p , R) ;
}
signed main() {
#ifdef _WIN64
	freopen("testdata.in" , "r" , stdin) ;
#else
	ios_base :: sync_with_stdio(false) ;
	cin.tie(nullptr) , cout.tie(nullptr) ;
#endif
// code begin.
	in >> n ;
	v.resize(n) ;
	for(int i = 0 ; i < n ; i ++)
		in >> v[i] ;
	ans.resize(n) ;
	solve(0 , n - 1 , 0 , n - 1) ;
	reverse(v) ;
	reverse(ans) ;
	solve(0 , n - 1 , 0 , n - 1) ;
	reverse(v) ;
	reverse(ans) ;
	for(int i = 0 ; i < n ; i ++)
		out << (int)(ceil(ans[i])) << '\n' ;
	return out.flush() , 0 ;
// code end.
}