POJ 3356 水LCS
题目链接:
http://poj.org/problem?id=3356
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 13855 | Accepted: 5263 |
Description
Let x and y be two strings over some finite alphabet A. We would like to transform x into y allowing only operations given below:
- Deletion: a letter in x is missing in y at a corresponding position.
- Insertion: a letter in y is missing in x at a corresponding position.
- Change: letters at corresponding positions are distinct
Certainly, we would like to minimize the number of all possible operations.
Illustration
A G T A A G T * A G G C
| | | | | | |
A G T * C * T G A C G CDeletion: * in the bottom line
Insertion: * in the top line
Change: when the letters at the top and bottom are distinct
This tells us that to transform x = AGTCTGACGC into y = AGTAAGTAGGC we would be required to perform 5 operations (2 changes, 2 deletions and 1 insertion). If we want to minimize the number operations, we should do it like
A G T A A G T A G G C
| | | | | | |
A G T C T G * A C G C
and 4 moves would be required (3 changes and 1 deletion).
In this problem we would always consider strings x and y to be fixed, such that the number of letters in x is m and the number of letters in y is n where n ≥ m.
Assign 1 as the cost of an operation performed. Otherwise, assign 0 if there is no operation performed.
Write a program that would minimize the number of possible operations to transform any string x into a string y.
Input
The input consists of the strings x and y prefixed by their respective lengths, which are within 1000.
Output
An integer representing the minimum number of possible operations to transform any string x into a string y.
Sample Input
10 AGTCTGACGC
11 AGTAAGTAGGC
Sample Output
4
Source
#include<cstring>
#include<cstdio>
#include<string>
#include<iostream>
#include<algorithm>
#define max_v 1005
using namespace std;
char x[max_v],y[max_v];
int dp[max_v][max_v];
int l1,l2;
int main()
{
while(~scanf("%d %s",&l1,x))
{
scanf("%d %s",&l2,y);
memset(dp,,sizeof(dp));
for(int i=; i<=l1; i++)
{
for(int j=; j<=l2; j++)
{
if(x[i-]==y[j-])
{
dp[i][j]=dp[i-][j-]+;
}
else
{
dp[i][j]=max(dp[i-][j],dp[i][j-]);
}
}
}
int t=l1;
if(l2>l1)
t=l2;
printf("%d\n",t-dp[l1][l2]);
}
return ;
}
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