hdu1074（狀壓dp）

題目連結：http://acm.hdu.edu.cn/showproblem.php?pid=1074

Doing Homework

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 11457    Accepted Submission(s): 5471

Problem Description Ignatius has just come back school from the 30th ACM/ICPC. Now he has a lot of homework to do. Every teacher gives him a deadline of handing in the homework. If Ignatius hands in the homework after the deadline, the teacher will reduce his score of the final test, 1 day for 1 point. And as you know, doing homework always takes a long time. So Ignatius wants you to help him to arrange the order of doing homework to minimize the reduced score.

Input The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.

Each test case start with a positive integer N(1<=N<=15) which indicate the number of homework. Then N lines follow. Each line contains a string S(the subject's name, each string will at most has 100 characters) and two integers D(the deadline of the subject), C(how many days will it take Ignatius to finish this subject's homework).

Note: All the subject names are given in the alphabet increasing order. So you may process the problem much easier.

Output For each test case, you should output the smallest total reduced score, then give out the order of the subjects, one subject in a line. If there are more than one orders, you should output the alphabet smallest one.

Sample Input

23Computer 3 3English 20 1Math 3 23Computer 3 3English 6 3Math 6 3  

Sample Output

2ComputerMathEnglish3ComputerEnglishMath Hint In the second test case, both Computer->English->Math and Computer->Math->English leads to reduce 3 points, but the word "English" appears earlier than the word "Math", so we choose the first order. That is so-called alphabet order.  

思路：參考了https://www.cnblogs.com/kuangbin/archive/2013/04/12/3016987.html

首先用二進制表示，枚舉每一個狀态，第二層循環表示該狀态由這本書沒完成時的狀态轉移而來，同時記錄前驅。最後輸出書名的時候用一個棧（遞歸）即可，見代碼。

#include<cstdio>
#include<algorithm>
#include<cstring>
#define INF 10000000
using namespace std;
const int maxn=16;
typedef struct
{
	char name[110];
	int dl;
	int red;
}  sub;
sub a[20];
int dp[1<<maxn];
int pre[1<<maxn];
int n;
void output(int sta)
{
	if(sta==0)
	return ;
	int t=0;
	for(int i=0;i<n;i++)
	{
		if(((1<<i)&sta)!=0 && (pre[sta]&(1<<i))==0)
		{
			t=i;
			break;
		}
	}
	output(pre[sta]);
	printf("%s\n",a[t].name);
}
int main()
{
   int t;
   scanf("%d",&t);
   while(t--)
   {
   	   scanf("%d",&n);
   	   fill(dp,dp+(1<<n),INF);
   	   dp[0]=0;
   	   memset(pre,0,sizeof(pre));
   	   for(int i=0;i<n;i++)
   	   {
   	   	  scanf("%s%d%d",a[i].name,&a[i].dl,&a[i].red);
	   }
       for(int i=0;i<(1<<n);i++)
       {
			  for(int j=0;j<n;j++)
       	   {
       	      if((1<<j)&i)
			  continue;
			  int tottime=0;
			  for(int k=0;k<n;k++)
			  {
			      if((1<<k)&i)
				  tottime+=a[k].red;	
			  }	
			  int s=tottime+a[j].red;
			  if(s>a[j].dl)
			  s-=a[j].dl;
			  else
			  s=0;
			  if(dp[i|(1<<j)]>dp[i]+s)
			  {
			     dp[i|(1<<j)]=dp[i]+s;
			     pre[i|(1<<j)]=i;
			  }
		   }
	   }
	   printf("%d\n",dp[(1<<n)-1]);
	   output((1<<n)-1);
   }
   return 0;
}