52 lines
2.7 KiB
Markdown
52 lines
2.7 KiB
Markdown
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## Bathroom Stalls
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A certain bathroom has **N** + 2 stalls in a single row; the stalls on the left and right ends are permanently occupied by the bathroom guards. The other **N** stalls are for users.
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Whenever someone enters the bathroom, they try to choose a stall that is as far from other people as possible. To avoid confusion, they follow deterministic rules: For each empty stall S, they compute two values LS and RS, each of which is the number of empty stalls between S and the closest occupied stall to the left or right, respectively. Then they consider the set of stalls with the farthest closest neighbor, that is, those S for which min(LS, RS) is maximal. If there is only one such stall, they choose it; otherwise, they choose the one among those where max(LS, RS) is maximal. If there are still multiple tied stalls, they choose the leftmost stall among those.
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**K** people are about to enter the bathroom; each one will choose their stall before the next arrives. Nobody will ever leave.
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When the last person chooses their stall S, what will the values of max(LS, RS) and min(LS, RS) be?
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### Input
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The first line of the input gives the number of test cases, **T. T** lines follow. Each line describes a test case with two integers **N** and **K**, as described above.
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### Output
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For each test case, output one line containing Case #x: y z, where x is the test case number (starting from 1), y is max(LS, RS), and z is min(LS, RS) as calculated by the last person to enter the bathroom for their chosen stall S.
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### Limits
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1 ≤ **T** ≤ 100.
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1 ≤ **K** ≤ **N**.
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Time limit: 30 seconds per test set.
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Memory limit: 1GB.
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#### Test set
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1 ≤ N ≤ 1018.
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### Sample
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```
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Input Output
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5
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4 2 Case #1: 1 0
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5 2 Case #2: 1 0
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6 2 Case #3: 1 1
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1000 1000 Case #4: 0 0
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1000 1 Case #5: 500 499
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```
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In Sample Case #1, the first person occupies the leftmost of the middle two stalls, leaving the following configuration (O stands for an occupied stall and . for an empty one): O.O..O. Then, the second and last person occupies the stall immediately to the right, leaving 1 empty stall on one side and none on the other.
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In Sample Case #2, the first person occupies the middle stall, getting to O..O..O. Then, the second and last person occupies the leftmost stall.
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In Sample Case #3, the first person occupies the leftmost of the two middle stalls, leaving O..O...O. The second person then occupies the middle of the three consecutive empty stalls.
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In Sample Case #4, every stall is occupied at the end, no matter what the stall choices are.
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In Sample Case #5, the first and only person chooses the leftmost middle stall.
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