《Cracking the Coding Interview》——第6章：智力题——题目2

2014-03-19 06:57

题目：对于8x8的棋盘，如果拿掉对角位置的两个小块儿，能否用1x2的多米诺牌拼成剩下的棋盘？

解法：不可能。且不说8x8，NxN都是不可能的。如果N是奇数，NxN-2是奇数，自然不可能用偶数的面积拼成。如果N为偶数，根据小学学过的染色问题，将1x2的骨牌染成1黑1白，那么最后拼成的棋盘肯定有31黑31白。问题是，摘掉的两个对角位置的颜色是一样的，所以得出矛盾，也不可能完成。

代码：

 // 6.2 There is an 8x8 chessboard, if we remove the two pieces at diagonal corners, can you cover the rest of the board with 2x1 dominoes?
 // Answer:
 //    It is impossible. Let's supposed it is feasible, we can color each domino into black and white halves.
 //    When the board is completely covered, there'll be 62 1x1 squares, exactly 31 white and 31 black.
 //    Actually the two squares removed are in same color, thus you can't turn (30, 32) into (31, 31), however you tile them up.
 int main()
 {
     return ;
 }