#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb(x) push_back(x)
#define mp(x, y) make_pair(x, y)
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define dbg(x...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<" [" << #x << "] = ["; _print(x); cerr << "\e[39m" << endl;
const int N=1e6+10;
//const ll mod=998244353;
const ll mod=1000000007;
const int intinf=2e9;
const ll llinf=9e18;
const ld eps=2e-7;
const ld is_query = -(1LL<<62);
struct line {
ld m, b;
mutable function<const line*()> succ;
bool operator<(const line& rhs) const {
if (rhs.b != is_query) return m < rhs.m;
const line* s = succ();
if (!s) return 0;
ld x = rhs.m;
return b - s->b < (s->m - m) * x;
}
};
struct dynamic_hull : public multiset<line> { // will maintain upper hull for maximum
const ld inf = LLONG_MAX;
bool bad(iterator y) {
auto z = next(y);
if (y == begin()) {
if (z == end()) return 0;
return y->m == z->m && y->b <= z->b;
}
auto x = prev(y);
if (z == end()) return y->m == x->m && y->b <= x->b;
/* compare two lines by slope, make sure denominator is not 0 */
ld v1 = (x->b - y->b);
if (y->m == x->m) v1 = x->b > y->b ? inf : -inf;
else v1 /= (y->m - x->m);
ld v2 = (y->b - z->b);
if (z->m == y->m) v2 = y->b > z->b ? inf : -inf;
else v2 /= (z->m - y->m);
return v1 >= v2;
}
void insert_line(ld m, ld b) {
auto y = insert({ m, b });
y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
if (bad(y)) { erase(y); return; }
while (next(y) != end() && bad(next(y))) erase(next(y));
while (y != begin() && bad(prev(y))) erase(prev(y));
}
ld eval(ld x) {
auto l = *lower_bound((line) { x, is_query });
return l.m * x + l.b;
}
};
dynamic_hull hull;
void solve(){
int n;
cin >> n;
cout << fixed << setprecision(3);
for(int i = 0; i < n; i++){
ld x, r;
cin >> x >> r;
if(i == 0){
cout << r << "\n";
hull.insert_line((ld)-1 / (2 * sqrtl(r)), x / (2 * sqrtl(r)));
}else{
ld ans = hull.eval(x);
cout << min(ans * ans, r) << "\n";
hull.insert_line((ld)-1 / (2 * sqrtl(r)), x / (2 * sqrtl(r)));
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
solve();
return 0;
}
컴파일 시 표준 에러 (stderr) 메시지
bal.cpp: In lambda function:
bal.cpp:76:19: warning: implicit capture of 'this' via '[=]' is deprecated in C++20 [-Wdeprecated]
76 | y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
| ^
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