Wooden Sticks
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 14809 | Accepted: 6081 |
Description
There is a pile of n wooden sticks. The length and weight of each stick are known in advance. The sticks are to be processed by a woodworking machine in one by one fashion. It needs some time, called setup time, for the machine to prepare processing a stick. The setup times are associated with cleaning operations and changing tools and shapes in the machine. The setup times of the woodworking machine are given as follows: (a) The setup time for the first wooden stick is 1 minute. (b) Right after processing a stick of length l and weight w , the machine will need no setup time for a stick of length l' and weight w' if l <= l' and w <= w'. Otherwise, it will need 1 minute for setup. You are to find the minimum setup time to process a given pile of n wooden sticks. For example, if you have five sticks whose pairs of length and weight are ( 9 , 4 ) , ( 2 , 5 ) , ( 1 , 2 ) , ( 5 , 3 ) , and ( 4 , 1 ) , then the minimum setup time should be 2 minutes since there is a sequence of pairs ( 4 , 1 ) , ( 5 , 3 ) , ( 9 , 4 ) , ( 1 , 2 ) , ( 2 , 5 ) .
Input
The input consists of T test cases. The number of test cases (T) is given in the first line of the input file. Each test case consists of two lines: The first line has an integer n , 1 <= n <= 5000 , that represents the number of wooden sticks in the test case, and the second line contains 2n positive integers l1 , w1 , l2 , w2 ,..., ln , wn , each of magnitude at most 10000 , where li and wi are the length and weight of the i th wooden stick, respectively. The 2n integers are delimited by one or more spaces.
Output
The output should contain the minimum setup time in minutes, one per line.
Sample Input
3 5 4 9 5 2 2 1 3 5 1 4 3 2 2 1 1 2 2 3 1 3 2 2 3 1
Sample Output
213
Source
思路：有一堆棍子，棍子有长度（L）和重量（W）。机器处理第一根棍子花费1秒。如果后一根棍子的长度（L`)和重量（W`)都比前一根的大，则后一根棍子不需要花费时间（L`>=L&&W`>=W)。求怎样处理这一堆棍子，所花费的时间最少。
本题可以运用贪心策略，首先按照L进行递增排序，如果L相等则按照W递增进行排序（当然也可以把W当做第一关键字，L当做第二关键字）。排序后，从前往后，找出每一根棍子的后继棍子（条件为后一根棍子的L和W都>=前一根的）。最后可以找出都少条这样的链即为所求。
注意：本题表面上看可以依据L*W的递增进行排序，但是，实际上是不行的。反例：(5,2) (4,3) (4,1) (1,3)。如果按照L,W排序为：（1,3），（4,1），（4,3），（5,2）。结果为2。如果按照面积排序为（1,3），（4,1），（5,2），（4,3）。结果为3。
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