POJ 1836-ALignment 动态规划

题目来源：http://acm.pku.edu.cn/JudgeOnline/problem?id=1836

 

解题报告：

 

设各个成员的身高的数组为h[0...n-1]，n为总人数。要满足题目条件，对0<=i<n，不妨设d[i]代表h[i]左边满足条件（即身高递增）的排列中可以安排的最多的人数，p[i]代表h[i]右边满足条件（即身高递减）的排列中可以安排的最多的人数。

 

则有递推式：

d[i]=max(d[k₁]+1, d[k₂]+1, ...., d[k_t]+1)，其中k_j<i, 且h[k_j]<h[i]，(1<=j<=t)

p[i]=max(p[k₁]+1, p[k₂]+1, ...., p[k_t]+1)，其中k_j>i, 且h[k_j]<h[i]，(1<=j<=t)

 

可以根据d[], p[]求得相应的最优解。

 

这道题一开始WA了，有一个特殊情况没有考虑进去，用以下数据测试：

8
3 4 5 1 2 5 4 3
答案是：2

 

这组数据的排列情况应为3 4 5 5 4 3，虽然5 5的身高一样，但仍能满足条件，我一开始没有考虑到这种情况。

 

 #include <iostream> using namespace std; int main() { int n; cin >> n; double *h=new double[n]; int *d=new int[n]; int *p=new int[n+1]; for(int i=0;i<n;i++) { cin >> h[i]; d[i]=1; p[i]=1; } p[n]=0; for(int i=1;i<n;i++) { for(int k=0;k<i;k++) if(h[i]>h[k]) d[i]=max(d[i],d[k]+1); } for(int i=1;i<n;i++) d[i]=max(d[i],d[i-1]); for(int i=n-1;i>=0;i--) { for(int k=n-1;k>i;k--) if(h[i]>h[k]) p[i]=max(p[i],p[k]+1); } for(int i=n-1;i>=0;i--) p[i]=max(p[i],p[i+1]); int m=p[1]+d[0]; for(int i=1;i<n;i++) { if(m < p[i+1]+d[i]) m=p[i+1]+d[i]; } cout << n-m << endl; }

 

附录：

Alignment

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 4265		Accepted: 1306

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

8
1.86 1.86 1.30621 2 1.4 1 1.97 2.2

Sample Output

4