Description
Inspired by a “Little Bishops” problem, Petya now wants to solve problem for rooks.
A rook is a piece used in the game of chess which is played on a board of square grids. A rook can only move horizontally and vertically from its current position and two rooks attack each other if one is on the path of the other.
Given two numbers $n$ and $k$, your job is to determine the number of ways one can put $k$ rooks on an $n\times n$ chessboard so that no two of them are in attacking positions.
Input
The input file contains two integers $n$ ($1\leq n\leq 10$) and $k$ ($0\leq k\leq n^2$).
Output
Write index $I$ for given number as the first number in line. Write $I$ super-primes numbers that are items in optimal presentation for given number. Write these $I$ numbers in order of non-increasing.
Sample Input
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Sample Output
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Analysis
由于 $K$ 个车每行只能放一个,所以一共有 $K!$ 种情况,一共有 $N\times N$ 的棋盘,行列选择共 $\binom{N}{k}\cdot \binom{N}{k}$ 种情况。因此,通过排列组合,我们有 $$\mathrm{ans} = \binom{N}{k}\cdot \binom{N}{k}\cdot K!$$ 化简可得 $$\mathrm{ans} = \frac{N!}{K!\cdot (N - K)!}\cdot\frac{N!}{(N - K)!}$$
Solution
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还以为类似八皇后,准备写 Check
函数,后来发现只是简单的排列组合而已。