动态规划——C编辑最短距离
2015-08-13 16:52
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C - 编辑距离
时间限制: 1000女士 内存限制: 65536KB 64位输入输出格式: %I64d & %I64u
提交 状态
描述
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.
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
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 yis 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
Sample Output
也是DP中比较经典的问题
d[i][j]表示第一个串到i位置,和第二个串到j位置的最短编辑距离
d[i][j]
如果a[i]==b[j]
d[i][j]=min(d[i-1][j-1],d[i-1][j]+1,d[i][j-1]);
否则d[i][j]=min(d[i-1][j-1]+1,d[i-1][j]+1,d[i][j-1]);
View Code
时间限制: 1000女士 内存限制: 65536KB 64位输入输出格式: %I64d & %I64u
提交 状态
描述
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
Deletion: * in the bottom line
Insertion: * in the top line
Change: when the letters at the top and bottom are distinct
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 yis 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 题目大意: 给出两个字符串X,Y,求出从X——>Y的最小操作次数,只可以删除,添加,修改一个字符。 解题思路:
也是DP中比较经典的问题
d[i][j]表示第一个串到i位置,和第二个串到j位置的最短编辑距离
d[i][j]
如果a[i]==b[j]
d[i][j]=min(d[i-1][j-1],d[i-1][j]+1,d[i][j-1]);
否则d[i][j]=min(d[i-1][j-1]+1,d[i-1][j]+1,d[i][j-1]);
程序代码:
#include <cstdio> #include <iostream> using namespace std; const int M=1100; char a[M],b[M] ; int d[M][M]; int main() { int n,i,j,l,r; while( scanf("%d%s",&l,a+1)!=EOF) { scanf("%d%s",&r,b+1); int len=max(l,r); for(i=0;i<=len;i++) { d[i][0]=i; d[0][i]=i; } for(i=1;i<=l;i++) for(j=1;j<=r;j++) { d[i][j]=min(d[i-1][j]+1,d[i][j-1]+1); if(a[i]==b[j]) d[i][j]=d[i-1][j-1]; else d[i][j]=min(d[i][j],d[i-1][j-1]+1); } printf("%d\n",d[l][r]); } return 0; }
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