Chopsticks

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我是靠谱客的博主迅速画笔，最近开发中收集的这篇文章主要介绍Chopsticks，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

Chopsticks

Time limit: 10 Seconds Memory limit: 32768K
Total Submit: 1706 Accepted Submit: 746

In China, people use a pair of chopsticks to get food on the table, but Mr. L is a bit different. He uses a set of three chopsticks -- one pair, plus an EXTRA long chopstick to get some big food by piercing it through the food. As you may guess, the length of the two shorter chopsticks should be as close as possible, but the length of the extra one is not important, as long as it's the longest. To make things clearer, for the set of chopsticks with lengths A,B,C(A<=B<=C), (A-B)^2 is called the 'badness' of the set.

It's December 2nd, Mr.L's birthday! He invited K people to join his birthday party, and would like to introduce his way of using chopsticks. So, he should prepare K+8 sets of chopsticks(for himself, his wife, his little son, little daughter, his mother, father, mother-in-law, father-in-law, and K other guests). But Mr.L suddenly discovered that his chopsticks are of quite different lengths! He should find a way of composing the K+8 sets, so that the total badness of all the sets is minimized.

Input

The first line in the input contains a single integer T, indicating the number of test cases(1<=T<=20). Each test case begins with two integers K, N(0<=K<=1000, 3K+24<=N<=5000), the number of guests and the number of chopsticks. There are N positive integers Li on the next line in non-decreasing order indicating the lengths of the chopsticks.(1<=Li<=32000).

Output

For each test case in the input, print a line containing the minimal total badness of all the sets.

Sample Input

1
1 40
1 8 10 16 19 22 27 33 36 40 47 52 56 61 63 71 72 75 81 81 84 88 96 98 103 110 113 118 124 128 129 134 134 139 148 157 157 160 162 164

Sample Output

Note

For the sample input, a possible collection of the 9 sets is:
8,10,16; 19,22,27; 61,63,75; 71,72,88; 81,81,84; 96,98,103; 128,129,148; 134,134,139; 157,157,160

容易证明，最好的分组方案中，每组中两根较短的筷子在有序筷子数列中一定是相邻的
best[j][i]表示从前i根筷子中挑出j组（不考虑第三根）
best[j][i]=min{
                 best[j][i-1];(i>j*2)
                 best[j-1][i-2]+(stick[i]-stick[i-1])^2;(n-i>(k-j)*3)
              }

#include<iostream>
#include<cstring>
using namespace std;
const long maxn=2147483647;
long best[1010][5001];
long stick[5001];
int k,n;
int main()
 {
     freopen("in.txt","r",stdin);
     freopen("out.txt","w",stdout);
     int cases,i,j;
     long temp;
     cin>>cases;
     while(cases--)
      {
          cin>>k>>n;
          for(i=1;i<=n;i++)
           cin>>stick[i];
          k+=8;
          memset(best,0,sizeof(best));
          for(j=1;j<=k;j++)
           for(i=j*2;i<=n;i++)
            {
                best[j][i]=maxn;
                if(i>j*2)
                  best[j][i]=best[j][i-1];
                if(n-i>(k-j)*3)
                 {
                     temp=best[j-1][i-2]+(stick[i]-stick[i-1])*(stick[i]-stick[i-1]);
                     if(temp<best[j][i])
                     best[j][i]=temp;
                 }    
            } 
        cout<<best[k][n]<<endl;        
      }    
     
     return 0;
 }