打表法


https://www.cnblogs.com/hxtblogs/p/7654635.html
打表是一种典型的用空间换时间的技巧,一般指将所有可能需要用到的结果事先计算出来,这样后面需要用到时就可以直接查表获得。打表常见的用法有如下几种:
  1、在程序中一次性计算出所有需要用到的结果,之后的查询直接取这些结果。
   这个是最常用到的用法,例如在一个需要查询大量Fibonacci数F(n)的问题中,显然每次从头开始计算是非常耗时的,对Q次查询会产生O(nQ)的时间复杂度;而如果进行预处理,即把所有Fibonacci数预先计算并存在数组中,那么每次查询就只需O(1)的时间复杂度,对Q次查询就值需要O(n+Q)的时间复杂度(其中O(n)是预处理的时间)。
  2、在程序B中分一次或多次计算出所有需要用到的结果,手工把结果写在程序A的数组中,然后在程序A中就可以直接使用这些结果。
  这种用法一般是当程序的一部分过程小号的时间过多,或是没有想到好的算法,因此在另一个程序中使用暴力算法去i出结果,这样就能直接在源程序中使用这些结果。例如对n皇后问题来说,如果使用的算法不够好,就容易超时,而可以在本地用程序计算付出对所有n来说n皇后问题的方案数,然后把算出的结果直接卸载数组中,就可以根据题目输入的n来直接输出结果。
  3、对一些感觉不会做的题目,先用暴力程序计算小范围数据的结果,然后找规律,或许就能发现一些“蛛丝马迹”。
  这种用法在数据范围非常大时候容易用到,因为这样的题目可能不是用直接能想到的算法来解决的,而需要寻找一些规律才能得到结果。



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