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 ll long long
#define ld long double
#define lid id * 2 + 1
#define rid id * 2 + 2
using namespace std;
const ll mod = 1e9 + 7;
ld bestR(ld x1, ld r1, ld x2, ld r2) {
ld l = 0, r = r2 + 1;
while (l < r - 0.0001) {
ld mid = (l + r) / 2;
if (sqrtl((x2 - x1) * (x2 - x1) + abs(r1 - mid) * abs(r1 - mid)) >= r1 + mid) l = mid;
else r = mid - 0.0001;
}
return min(r2, l);
}
int main() {
// ifstream cin("balancing.in");
// ofstream cout("balancing.out");
int n, i;
cin >> n;
vector<ld> x(n), r(n);
for (i = 0; i < n; i++) cin >> x[i] >> r[i];
vector<ld> ans(n);
stack<int> st;
ans[0] = r[0];
st.push(0);
for (i = 1; i < n; i++) {
ld res = r[i];
while (not st.empty()) {
res = min(res, bestR(x[st.top()], ans[st.top()], x[i], r[i]));
if (res > ans[st.top()]) st.pop();
else break;
}
ans[i] = res;
st.push(i);
}
for (i = 0; i < n; i++) cout << fixed << setprecision(3) << ans[i] << endl;
return 0;
}
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