演算法導論-15-3-編輯距離

題目：

思考：

（1）初始化：

s[0,0]=0

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

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

（2）遞推

（3）最後的操作kill

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

代碼：

#include <iostream>using namespace std;//6種操作的代價，依次是copy,replace,delete,insert,twiddle,killint cost[6] = {1,1,1,1,1,1};int s[15][15] = {0};//字元從0開始計數，s[][]從1開始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];//DPfor(i = 0; i < lx; i++){for(j = 0; j < lz; j++){s[i+1][j+1] = 0x7fffffff;//copyif(x[i] == z[j]){temp = s[i][j] + cost[0];if(temp < s[i+1][j+1])s[i+1][j+1] = temp;}//replaceif(x[i] != z[j]){temp = s[i][j] + cost[1];if(temp < s[i+1][j+1])s[i+1][j+1] = temp;}//deletetemp = s[i][j+1] + cost[2];if(temp < s[i+1][j+1])s[i+1][j+1] = temp;//inserttemp = s[i+1][j] + cost[3];if(temp < s[i+1][j+1])s[i+1][j+1] = temp;//twidleif(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;}}}//killint 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;}