This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define sz(x) (int)(x.size())
using namespace std;
inline namespace IO {
const int BUFFER_SIZE = 1 << 15;
char input_buffer[BUFFER_SIZE];
int input_pos = 0, input_len = 0;
char output_buffer[BUFFER_SIZE];
int output_pos = 0;
char number_buffer[100];
uint8_t lookup[100];
void _update_input_buffer() {
input_len = fread(input_buffer, sizeof(char), BUFFER_SIZE, stdin);
input_pos = 0;
if (input_len == 0)
input_buffer[0] = EOF;
}
inline char next_char(bool advance = true) {
if (input_pos >= input_len)
_update_input_buffer();
return input_buffer[advance ? input_pos++ : input_pos];
}
template<typename T>
inline void read_int(T &number) {
bool negative = false;
number = 0;
while (!isdigit(next_char(false)))
if (next_char() == '-')
negative = true;
do {
number = 10 * number + (next_char() - '0');
} while (isdigit(next_char(false)));
if (negative)
number = -number;
}
template<typename T, typename... Args>
inline void read_int(T &number, Args &... args) {
read_int(number);
read_int(args...);
}
void _flush_output() {
fwrite(output_buffer, sizeof(char), output_pos, stdout);
output_pos = 0;
}
inline void write_char(char c) {
if (output_pos == BUFFER_SIZE)
_flush_output();
output_buffer[output_pos++] = c;
}
template<typename T>
inline void write_int(T number, char after = '\0') {
if (number < 0) {
write_char('-');
number = -number;
}
int length = 0;
while (number >= 10) {
uint8_t lookup_value = lookup[number % 100];
number /= 100;
number_buffer[length++] = (lookup_value & 15) + '0';
number_buffer[length++] = (lookup_value >> 4) + '0';
}
if (number != 0 || length == 0)
write_char(number + '0');
for (int i = length - 1; i >= 0; i--)
write_char(number_buffer[i]);
if (after)
write_char(after);
}
void init() {
// Make sure _flush_output() is called at the end of the program.
bool exit_success = atexit(_flush_output) == 0;
assert(exit_success);
for (int i = 0; i < 100; i++)
lookup[i] = (i / 10 << 4) + i % 10;
}
}
int n, L;
vector<pair<double, double>> a;
void solve() {
read_int(n, L);
a.clear();
for (int i=0; i<n; i++) {
int x, y; read_int(x, y);
if (!a.empty() && x==a.back().first) {
if (abs(y)<abs(a.back().second)) a.back().second=y;
}
else a.push_back({x, y});
}
n=sz(a);
double l=0, r=1e9;
while (r-l>0.0009) {
double mid=(l+r)/2;
double borne=0;
double popo=pow(mid, 2);
for (int i=0; i<n; i++) {
if (abs(a[i].second)>mid) continue;
double x=a[i].first, y=a[i].second;
double dist=sqrt(popo-pow(y, 2));
if (x-dist<=borne && x+dist>borne) borne=x+dist;
}
if (borne>=L) r=mid;
else l=mid;
}
cout << fixed << setprecision(3) << l << '\n';
return;
}
signed main() {
ios::sync_with_stdio(0);
cin.tie(0);
solve();
return 0;
}
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