AGTC (P3356)

状态 dp[i][j]代表字符串前i个和j个的最小操作数。注意边界条件。

#include<iostream>#include<cstdio>#include<algorithm>#include<queue>#include<vector>#include<cmath>#include<set>#include<cstdlib>#include<cstring>#include<stack>#include<string>using namespace std;//freopen("C://i.txt","r",stdin);#define N 1111int lena,lenb;char a[N],b[N];int dp[N][N];int main(){freopen("C://i.txt","r",stdin);int i,j,k;while (cin>>lena){cin>>a;cin>>lenb;cin>>b;for (i=0;i<=lenb;i++)dp[0][i]=i;for (i=1;i<=lena;i++)dp[i][0]=i;for (i=1;i<=lena;i++){for (j=1;j<=lenb;j++){ if (a[i-1]==b[j-1]) { dp[i][j]=dp[i-1][j-1];  dp[i][j]=min(dp[i][j],dp[i-1][j]+1); dp[i][j]=min(dp[i][j],dp[i][j-1]+1);  } else { dp[i][j]=dp[i-1][j-1]+1; dp[i][j]=min(dp[i][j],dp[i-1][j]+1); dp[i][j]=min(dp[i][j],dp[i][j-1]+1); } }}cout<<dp[lena][lenb]<<endl;}}

AGTC

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 7088 Accepted: 2823

Description

Let x and y be two strings over some finite alphabet A. We would like to transformx 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 inx is m and the number of letters in y is n wheren ≥ 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 stringx 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 stringx into a string y.

Sample Input

10 AGTCTGACGC11 AGTAAGTAGGC

Sample Output

4

Source