我贴到WXC 去吧, 好不好? |
We use induction. Suppose it is true for any number < N. Pick a point P inside the polygon formed by the points so that no two points in the original sets are colinear with P. Draw a line thru P, and rotate the line, to a place where there are equal numbers of blue and red points on each side of the line. By the inductive assumption we can do it for each side. |
出 过 吗 ?对 不 起 ! 贴 到 WXC, no problem. |
让距离最近的两个红蓝点配成一对,其他点无论怎么连, 都不会与他们相交 (证明同野菜花的)。 可以把他们拿开了。剩下的以此类推。 这题在WXC 贴出后,有人指出在一些退化情形题目是不对的,比如说都在一条直线上, 并且红蓝各在一端的时候。不过WXC还没有人正确解答,虽然有一个有正确的思路。 |
不太明白为什么"让距离最近的两个红蓝点配成一对,其他点无论怎么连, 都不会与他们相交 " 能否解释一下? Thanks |
It is not my idea, I only rewrite it. Since there are finitely many points, there are only finitely many ways to draw N lines such that each line has two ends in different colors. |
but no very intuitive. I hate induction, and don't use it unless could not think of another way. |
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