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注意
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問題文
この問題は「問題 A」と同一の問題であるが、制約が異なる。問題文本文は問題 A のページを、制約は以下を参照のこと。
入力
入力は以下の制約を満たす。
- 3 \leq N \leq 10
- 1 \leq K \leq 2^N
- 0 \leq d_i \leq 6
- 1 \leq \left|c_i \right| \leq 100
- 1 \leq v_{i, j} \leq N
- 全ての j (1 \leq j \lt d_i) について、v_{i, j} < v_{i, j+1}
- i \neq j ならば \left[ v_{i, 1}, \dots , v_{i, d_i} \right] \neq \left[ v_{j, 1}, \dots, v_{j, d_j} \right]
- d_i = 0 となる行は高々 1 度しか登場しない
- 全ての k (1 \leq k \leq N) に対して、k = v_{i, j} を満たす (i, j) が少なくとも 1 つ存在する
Notification
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Problem Setting
The task in problem setting C is almost equivalent to problem setting A. Hence, for details on the task the contestant is refered to problem setting A. The only difference in Problem C is the shape of the higher order pseudo-Boolean function which serves as an input. This input will now have degree at most 6 (d=6), while coefficients are provided for all possible terms of the function. For details of the input problem contestants are referred to the section below.
Input Format
The following requirements shall be imposed on the input problem.
- 3 \leq N \leq 10
- 1 \leq K \leq 2^N
- 0 \leq d_i \leq 6
- 1 \leq \left|c_i \right| \leq 100
- 1 \leq v_{i, j} \leq N
- For all j (1 \leq j \lt d_i) we require v_{i, j} < v_{i, j+1}
- For two lines i,j with i \neq j we require \left[ v_{i, 1}, \dots , v_{i, d_i} \right] \neq \left[ v_{j, 1}, \dots, v_{j, d_j} \right], i.e., two separate lines shall not encode the same type of monomial.
- The line d_i = 0 should not exceed beyond the coefficient.
- All of the variables k (1 \leq k \leq N) should appear in at least one of the term, i.e., there exists at least one v_{i,j} such that k = v_{i, j}.