2014西安网络预选赛1003（DP+剪枝）hdu5009

Paint Pearls

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 575    Accepted Submission(s): 153

Problem Description

Lee has a string of n pearls. In the beginning, all the pearls have no color. He plans to color the pearls to make it more fascinating. He drew his ideal pattern of the string on a paper and asks for your help. 

In each operation, he selects some continuous pearls and all these pearls will be painted to their target colors. When he paints a string which has k different target colors, Lee will cost k² points. 

Now, Lee wants to cost as few as possible to get his ideal string. You should tell him the minimal cost.

 

Input

There are multiple test cases. Please process till EOF.

For each test case, the first line contains an integer n(1 ≤ n ≤ 5×10⁴), indicating the number of pearls. The second line contains a₁,a₂,...,a_n (1 ≤ a_i ≤ 10⁹) indicating the target color of each pearl.

 

Output

For each test case, output the minimal cost in a line.

 

Sample Input

31 3 3103 4 2 4 4 2 4 3 2 2

 

Sample Output

27

题意：每次可以给一个区间涂色，花费为该区间段不同颜色数量的平方，求涂完整个序列的最小花费

思路：DP[i]表示到从1涂到i的最小花费

            然后从前往后转移

            假设现在由i往后转移，那么转移的时候要枚举从i+1到j的不同颜色的个数x，然后dp[j]=min(dp[j]，dp[i]+x*x)

            但是要加个剪枝，就是当dp[i]+x*x>=dp[n]时就停止