减治法概念

 

1、减治法的定义？

   答：The decrease-and-conquer technique is based on exploring the relationship between a solution to a given instance of a problem and a solution to a smaller instance or of the same problem.

 

2、减法法的三种类型是什么，分别举例说明？

   答：there are three major variations of decrease-and-conquer:

（1）Decrease by a constant:

   the size of the problem is reduced by the same constant on each iteration/recursion of the algorithm.

For example :

Insertion sort (插入排序)、DFS（有向图的深度优先遍历）、BFS（有向图的广度优先遍历）

（2）Decrease by a constant factor:

   the size of the problem is reduced by the same constant factor on each iteration/recursion of the algorithm.

For example :

Binary search （折半查找算法）、Fake-coin problems（假币问题）

（3）Variable-size decrease:

   the size reduction pattern varies from one iteration of an algorithm to another.

For example :

Euclid’s algorithm（欧几里得求最大公约数算法）

 

3、减治法和分治法的区别是什么，可举例说明？

   答：The divide-and-conquer has three steps: divide,conquer and combine.It must deal with each problems,and combine them finally.But the decrease-and-conquer technique is based on exploring the relationship between a solution to a given instance of a problem and a solution to a smaller instance or of the same problem. It do not combine them and do not solve each of them.

   For example: compute  a ⁿ

The divide-and-conquer ：compute  a ⁿ=a ^n/2  * a ^n/2   if a>1;

                                 =a          if a=1.

The decrease-and-conquer ：compute  a ⁿ=(a ^n/2 )*2         if n is even and positive;

                                   = (a^(n-1)/2 ) ² * a   if n is odd and > 1;

                                   =a                if a=1.

 

转载于:https://www.cnblogs.com/qilinart/articles/4982856.html