Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 12240 | Accepted: 4594 |
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 C
Deletion: * 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 <stdio.h>
#define MAXN 1024
int dp[MAXN][MAXN];
char str1[MAXN],str2[MAXN];
int min3(int a,int b,int c){
int min=a;
if(min>b) min=b;
if(min>c) min=c;
return min;
}
int main()
{
int n,m;
while(scanf("%d%s",&n,str1)!=EOF){
scanf("%d%s",&m,str2);
for(int i=0;i<=n;i++)
dp[i][0]=i;
for(int j=0;j<=m;j++)
dp[0][j]=j;
int count;
for(int i=1;i<=n;i++){
for(int j=1;j<=m;j++){
str1[i-1]==str2[j-1]?count=0:count=1;
dp[i][j]=min3(dp[i-1][j-1]+count,dp[i-1][j]+1,dp[i][j-1]+1);
}
}
printf("%d\n",dp[n][m]);
}
return 0;
}
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