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Submission #491991

# Submission time Handle Problem Language Result Execution time Memory
491991 2021-12-05T09:45:17 Z clams Balloons (CEOI11_bal) C++17
100 / 100
 208 ms 14880 KB 
#pragma GCC optimize(3)
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using db = long double;
#define int long long

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    
    int n;
    cin >> n;
    
    vector<db> x(n + 1), r(n + 1);
    for(int i = 1; i <= n; i++) {
        cin >> x[i] >> r[i];
    }    
    
    // distance between centers of 2 balloons
    // sqrt(abs(x2 - x1)**2 + abs(r2 - r1)**2)
    
    // must be equal to (r1 + r2)
    // => (x2 - x1)**2 + abs(r2 - r1)**2 == (r1 + r2)**2
    // => (x2**2 + x1**2 - 2x1x2) + (r2**2 + r1**2 - 2r1r2) = r1**2 + r2**2 + 2r1r2
    // => (x2 - x1)**2 = 4r1r2
    // => r2 = ((x2 - x1)**2) / (4r1)
    
    vector<db> ans(n + 1);
    stack<pair<db, db>> st;
    
    for(int i = 1; i <= n; i++) {
        if(st.empty()) {
            st.push({x[i], r[i]});
            ans[i] = r[i];
            continue;
        }
        
        while(!st.empty()) {
            pair<db, db> cur = st.top();
            r[i] = min(r[i], (x[i] - cur.first) * (x[i] - cur.first) / (4 * cur.second));
            if(r[i] >= cur.second) st.pop();
            else break;
        }
        
        st.push({x[i], r[i]});
        ans[i] = r[i];
    } 
    
    for(int i = 1; i <= n; i++) {
        cout << fixed << setprecision(3) << ans[i] << '\n';
    }
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB 10 numbers

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB 2 numbers

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB 505 numbers

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 388 KB 2000 numbers

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 21 ms 1440 KB 20000 numbers

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 63 ms 3364 KB 50000 numbers
2 Correct 49 ms 3912 KB 49912 numbers

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 104 ms 6132 KB 100000 numbers

Subtask #8
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 135 ms 7016 KB 115362 numbers
2 Correct 132 ms 9044 KB 119971 numbers

Subtask #9
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 172 ms 9244 KB 154271 numbers
2 Correct 189 ms 14768 KB 200000 numbers

Subtask #10
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 208 ms 11420 KB 200000 numbers
2 Correct 190 ms 14880 KB 199945 numbers