Advanced Fruits(链接：http://acm.hdu.edu.cn/showproblem.php?pid=1503）

最新推荐文章于 2019-10-10 16:56:13 发布

LR1741670057

最新推荐文章于 2019-10-10 16:56:13 发布

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分类专栏： LCS最长公共子序列文章标签： LCS 杭电

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本文介绍了一种算法，该算法能够为两种水果基因组合创造的新品种生成最短且包含原有名称的名称。通过使用动态规划求解最长公共子序列问题，确保了新名称既反映了原始水果的特点又能保持最简短。

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Advanced Fruits

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 19 Accepted Submission(s) : 9

Special Judge

Problem Description

The company "21st Century Fruits" has specialized in creating new sorts of fruits by transferring genes from one fruit into the genome of another one. Most times this method doesn't work, but sometimes, in very rare cases, a new fruit emerges that tastes like a mixture between both of them.
A big topic of discussion inside the company is "How should the new creations be called?" A mixture between an apple and a pear could be called an apple-pear, of course, but this doesn't sound very interesting. The boss finally decides to use the shortest string that contains both names of the original fruits as sub-strings as the new name. For instance, "applear" contains "apple" and "pear" (APPLEar and apPlEAR), and there is no shorter string that has the same property.

A combination of a cranberry and a boysenberry would therefore be called a "boysecranberry" or a "craboysenberry", for example.

Your job is to write a program that computes such a shortest name for a combination of two given fruits. Your algorithm should be efficient, otherwise it is unlikely that it will execute in the alloted time for long fruit names.

Input

Each line of the input contains two strings that represent the names of the fruits that should be combined. All names have a maximum length of 100 and only consist of alphabetic characters. Input is terminated by end of file.

Output

For each test case, output the shortest name of the resulting fruit on one line. If more than one shortest name is possible, any one is acceptable.

Sample Input

  
  
   
   apple peach
ananas banana
pear peach

Sample Output

  
  
   
   appleach
bananas
pearch

Source

University of Ulm Local Contest 1999

#include<cstdio>
#include<cstring>
const int max=1010;
char a[max],b[max];
int dp[max][max],p[max][max];
int la,lb;
void lcs()
{
	int i,j;
	memset(dp,0,sizeof(dp));
	for(i=0;i<=la;++i)
	p[i][0]=1;
	for(i=0;i<=lb;++i)
	p[0][i]=2;
	for(i=1;i<=la;++i)
	{
		for(j=1;j<=lb;++j)
		{
			if(a[i-1]==b[j-1])
			{
				dp[i][j]=dp[i-1][j-1]+1;
				p[i][j]=0;
			}
			else if(dp[i-1][j]>=dp[i][j-1])
			{
				dp[i][j]=dp[i-1][j];
				p[i][j]=1;
			}
			else
			{
				dp[i][j]=dp[i][j-1];
				p[i][j]=2;
			}
		}
	}
}

void printlcs(int i,int j)
{
	if(i==0&&j==0)
	return ;
	if(p[i][j]==0)
	{
		printlcs(i-1,j-1);
		printf("%c",b[j-1]);
		//printf("%c",a[i-1]);
	}
	else if(p[i][j]==1)
	{
		printlcs(i-1,j);
		printf("%c",a[i-1]);
	}
	else
	{
		printlcs(i,j-1);
		printf("%c",b[j-1]);
	}
}
int main()
{
	while(~scanf("%s%s",a,b))
	{
		la=strlen(a);
		lb=strlen(b);
		lcs();
		printlcs(la,lb);
		printf("\n");
	}
	return 0;
}