算法导论-15-3-编辑距离

题目：









思考：

（1）初始化：

s[0,0]=0

s[i,0] = i * cost(delete)

s[0,j] = j * cost[insert]

（2）递推



（3）最后的操作kill

c[i][j] = MIN(c[m,n], MIN(c[i,n]+cost(kill)))， 其中0<=i<m

代码：

#include <iostream>
using namespace std;
//6种操作的代价，依次是copy,replace,delete,insert,twiddle,kill
int cost[6] = {1,1,1,1,1,1};
int s[15][15] = {0};
//字符从0开始计数，s[][]从1开始
int DP(char *x, char *z, int lx, int lz)
{
int i = 0, j = 0,temp;
//初始化s[0][0]=0
//s[i,0] = i * cost(delete)
for(i = 1; i <= lx; i++)
s[i][0] = i * cost[2];
//s[0,j] = j * cost[insert]
for(j = 1; j <= lz; j++)
s[0][j] = i * cost[3];
//DP
for(i = 0; i < lx; i++)
{
for(j = 0; j < lz; j++)
{
s[i+1][j+1] = 0x7fffffff;
//copy
if(x[i] == z[j])
{
temp = s[i][j] + cost[0];
if(temp < s[i+1][j+1])
s[i+1][j+1] = temp;
}
//replace
if(x[i] != z[j])
{
temp = s[i][j] + cost[1];
if(temp < s[i+1][j+1])
s[i+1][j+1] = temp;
}
//delete
temp = s[i][j+1] + cost[2];
if(temp < s[i+1][j+1])
s[i+1][j+1] = temp;
//insert
temp = s[i+1][j] + cost[3];
if(temp < s[i+1][j+1])
s[i+1][j+1] = temp;
//twidle
if(i && j && x[i] == z[j-1] && x[i-1] == z[j])
{
temp = s[i-1][j-1] + cost[4];
if(temp < s[i+1][j+1])
s[i+1][j+1] = temp;
}
}
}
//kill
int ret = s[lx][lz];
for(i = 1; i < lx; i++)
if(s[i][lz] + cost[5] < ret)
ret = s[i][lz] + cost[5];
return ret;
}
void Print(int lx, int lz)
{
int i, j;
for(i = 1; i <= lx; i++)
{
for(j = 1; j <= lz; j++)
cout<<s[i][j]<<' ';
cout<<endl;
}
}
int main()
{
char a[] = "algorithm";
char b[] = "altruistic";
int la = strlen(a), lb = strlen(b);
cout<<DP(a, b, la, lb)<<endl;
Print(la, lb);
return 0;
}