| “Da Bai” (Interactive) |
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| There is an undirected simple graph with 100 vertices. |
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| In each query, you can ask the interactor by choosing three distinct vertices a, b, c. |
| The interactor will tell you how many edges exist among the three vertices {a, b, c}, i.e., the number of edges in the induced sub-graph on {a, b, c}. The answer will be an integer in {0, 1, 2, 3}. |
| You must ensure that a, b, c are pairwise distinct. |
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| Your goal: reconstruct the entire graph. |
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| Implementation details |
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| This is an interactive problem. As usual, you should submit a source code file that can compile. |
| Initially, you should read no input. |
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| You may issue queries by writing to standard output lines of the form |
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| ? a b c |
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| Then you must flush output, and read from standard input one integer in [0, 3], representing the interactor’s response. |
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| When you have determined the graph, output a line |
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| ! |
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| Then output 100 lines, each with a length-100 binary string s_i (i from 1 to 100), describing the graph. Here s_{i,j} = ‘1’ if and only if there is an edge between vertex i and j in the graph. |
| Remember to flush after your output. |
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| Sample |
| For convenience, in this sample we assume the graph has only **4** vertices. (In actual tests the graph has 100 vertices.) |
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| Contestant prints | Interactor replies |
| ---------------------|-------------------- |
| `? 1 2 3` | 0 |
| `? 1 2 4` | 2 |
| `? 1 3 4` | 2 |
| `!` | |
| 0001 |
| 0001 |
| 0001 |
| 1110 |
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| Constraints |
| - All test instances have exactly 100 vertices. |
| - Let Q = the number of queries you make. |
| - If your program exceeds time limit, memory limit, or returns incorrect answer → score=0. |
| - Otherwise, your score depends on Q: |
| - score(Q) = 3400 / (Q + 1) |
| - In other words, a solution with Q < 3400 is awarded the full score. |
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