poj 1836(简单DP+两边lis)

Alignment

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 11750 Accepted: 3746

Description

In the army, a platoon is composed by n soldiers. During the morning inspection, the soldiers are aligned in a straight line in front of the captain. The captain is not satisfied with the way his soldiers are aligned; it is true that the soldiers are aligned in order by their code number: 1 , 2 , 3 , . . . , n , but they are not aligned by their height. The captain asks some soldiers to get out of the line, as the soldiers that remain in the line, without changing their places, but getting closer, to form a new line, where each soldier can see by looking lengthwise the line at least one of the line's extremity (left or right). A soldier see an extremity if there isn't any soldiers with a higher or equal height than his height between him and that extremity. 

Write a program that, knowing the height of each soldier, determines the minimum number of soldiers which have to get out of line. 

Input

On the first line of the input is written the number of the soldiers n. On the second line is written a series of n floating numbers with at most 5 digits precision and separated by a space character. The k-th number from this line represents the height of the soldier who has the code k (1 <= k <= n). 

There are some restrictions: 
• 2 <= n <= 1000 
• the height are floating numbers from the interval [0.5, 2.5] 

Output

The only line of output will contain the number of the soldiers who have to get out of the line.

Sample Input

81.86 1.86 1.30621 2 1.4 1 1.97 2.2

Sample Output

4

Source

Romania OI 2002

 

拿到这个题目后，用了5分钟想到，满足条件的解一定构成一个三角形（即先增后减，不会有波谷）。

而且这个三角形只有顶点（最高值）可以是两个相同的值，在上升期间或者下降期间都必须是严格单调的。

因此明显是枚举最高点+双边lis。

可是贡献了三次wrong answer。第一次WA是因为没有考虑最高点其实是可以有2个相同取值的，比如：

1 2 3 3 2 1 这就是一个满足要求的序列。因此在lis的时候，上界（程序中的bound）事实上是可以取等号的。

第二次WA是因为没有判断最高点重复的个数，如果左面的lis和右面的lis的最大值与data[i]都相同，那中间峰值处就会有3个一样的身高，这种情况需要减1。因此在main程序中加入了left_high 和 right_high的判断。

第三次WA一直没有找到，最后才发现是cmp函数中，类型是double而不是int！！！！

 

提交记录：

1、WA， 修改work1和work2中，使得bound可以取等号。

2、WA， 修改对left_high 和 right_high的判断，使得不会有3个峰值。

3、WA，修改比较函数的输入类型a 和 b的类型为double！！！

4、Accepted。