String to Palindrome - UVa 10739 dp

String to Palindrome

Input: Standard Input

Output: Standard Output

Time Limit: 1 Second

 

In this problem you are asked to convert a string into a palindrome with minimum number of operations. The operations are described below:

 

Here you’d have the ultimate freedom. You are allowed to:

• Add any character at any position
• Remove any character from any position
• Replace any character at any position with another character

Every operation you do on the string would count for a unit cost. You’d have to keep that as low as possible.

 

For example, to convert “abccda” you would need at least two operations if we allowed you only to add characters. But when you have the option to replace any character you can do it with only one operation. We hope you’d be able to use this feature to your advantage.

 

Input

The input file contains several test cases. The first line of the input gives you the number of test cases, T (1≤T≤10). Then T test cases will follow, each in one line. The input for each test case consists of a string containing lower case letters only. You can safely assume that the length of this string will not exceed 1000 characters.

 

Output

For each set of input print the test case number first. Then print the minimum number of characters needed to turn the given string into a palindrome.

 

Sample Input                               Output for Sample Input

6 tanbirahmed shahriarmanzoor monirulhasan syedmonowarhossain sadrulhabibchowdhury mohammadsajjadhossain

Case 1: 5 Case 2: 7 Case 3: 6 Case 4: 8 Case 5: 8 Case 6: 8

题意：每次可以增加一个字母，删除一个字母，或改变一个字母，问使得原字符串变成回文串的最小的操作数。

思路：dp记录路径避免多次重复，然后具体看代码吧。

AC代码如下：

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
char s[1010];
int dp[1010][1010];
void dfs(int l,int r)
{ if(dp[l][r]>=0)
   return;
  int k=100000;
  dfs(l,r-1);
  dfs(l+1,r);
  dfs(l+1,r-1);
  k=min(dp[l][r-1]+1,dp[l+1][r]+1);
  if(s[l]==s[r])
   k=min(k,dp[l+1][r-1]);
  else
   k=min(k,dp[l+1][r-1]+1);
  dp[l][r]=k;
}
int main()
{ int T,t,i,j,k,len;
  scanf("%d",&T);
  for(t=1;t<=T;t++)
  { scanf("%s",s+1);
    len=strlen(s+1);
    memset(dp,-1,sizeof(dp));
    for(i=1;i<=len;i++)
    { dp[i][i]=0;
      dp[i+1][i]=0;
    }
    dfs(1,len);
    printf("Case %d: %d\n",t,dp[1][len]);
  }
}