学步园

简单dp

res[i][j]表示i长度的前a个字符的串与前j个长度的b字符串的编辑距离

当stra[i-1]等于strb[j-1]时，状态转移为res[i][j]=res[i-1][j-1]

否则,res[i][j]=MIN(res[i-1][j-1]+1,res[i][j-1]+1,res[i-1][j]+1)

#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
char stra[1010];
char strb[1010];
int res[1010][1010];
//res[i][j]表示i长度的前a个字符的串与前j个长度的b字符串的编辑距离
//最后结果为res[la][lb]
int main()
{
	int la,lb;
	while (~scanf("%d %d",&la,&lb))
	{
		scanf("%s",stra);
		scanf("%s",strb);
		//求res[i][j]
		//res[i-1][j]+1          res[i][j-1]+1    res[i-1][j-1]
		for (int i= 0; i <=lb; i++)
		{
			res[0][i]=i;
		}
		for (int i = 0; i <=la; i++)
		{
			res[i][0]=i;
		}
		for(int i=1;i<=la;i++)
		{
			for(int j=1;j<=lb;j++)
			{
				res[i][j]=INT_MAX;
			}
		}
		for(int i=1;i<=la;i++)
		{
			for (int j = 1; j <=lb; j++)
			{
				if(stra[i-1]==strb[j-1])
				{
					res[i][j]=res[i-1][j-1];
				}
				if(res[i-1][j]>res[i][j-1])
				{
					if (res[i][j]>res[i][j-1]+1)
					{
						res[i][j]=res[i][j-1]+1;
					}
				}
				else
				{
					if (res[i][j]>res[i-1][j]+1)
					{
						res[i][j]=res[i-1][j]+1;
					}
				}
				if(res[i][j]>res[i-1][j-1]+1)
				{
					res[i][j]=res[i-1][j-1]+1;
				}
			}
		}
		printf("%d\n",res[la][lb]);
	}
	return 0;
}