构造

CF2048E

二分图，左部 $2N$ 个点，右部 $M$ 个点。能否用至多 $N$ 种颜色为 $2MN$ 条边着色，满足图中没有单色环。

每种颜色构成一个森林，边数最多 $2N+M-1$。

Problem - 2094F - Codeforces（shift）

Problem - 2101A - Codeforces（蛇形）

【12E】构造 $N\times N$ 的矩阵（$N$ 为偶数），只能使用 $N$ 种不同的数字，且满足任一行（列）的数字互不相同，主对角线都是 0，且整体关于主对角线对称。

Trulicina gives you integers $n$, $m$, and $k$. It is guaranteed that $k\geq 2$ and $n\cdot m\equiv 0 \pmod{k}$.

Output a $n$ by $m$ grid of integers such that each of the following criteria hold:

• Each integer in the grid is between $1$ and $k$, inclusive.
• Each integer from $1$ to $k$ appears an equal number of times.
• No two cells that share an edge have the same integer.

It can be shown that such a grid always exists. If there are multiple solutions, output any.

1628C. Grid Xor

$1\times3$ 或 $2\times 2$

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