Codeforces 56D Changing a String

http://codeforces.com/contest/56/problem/D

题目大意：

一个字符串变为目标字符串，可以执行插入，置换和删除3种操作，求最少操作数。

思路:dp[i][j]代表当前串前i个变成目标串前j个的最小花费。

 

#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<iostream>
#define ll long long
char a[200005],b[200005];
int n,m;
ll f[1005][1005];
int read(){
    int t=0,f=1;char ch=getchar();
    while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
    while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();}
    return t*f;
}
void dfs(int n,int m){
    if (n==0&&m==0){
        return;
    }
    if (n>=1&&f[n][m]==f[n-1][m]+1){
        dfs(n-1,m);
        printf("DELETE %d\n",m+1);
    }else
    if (m>=1&&f[n][m]==f[n][m-1]+1){
        dfs(n,m-1);
        printf("INSERT %d %c\n",m,b[m]);
    }else{
        dfs(n-1,m-1);
        if (a[n]!=b[m])
        printf("REPLACE %d %c\n",m,b[m]);
    }
}
int main(){
    scanf("%s",a+1);n=strlen(a+1);
    scanf("%s",b+1);m=strlen(b+1);
    for (int i=0;i<=n;i++)
     for (int j=0;j<=m;j++)
      f[i][j]=0;
    f[0][0]=0;
    for (int i=1;i<=n;i++)
     f[i][0]=i;
    for (int i=1;i<=m;i++)
     f[0][i]=i;
    for (int i=1;i<=n;i++)
     for (int j=1;j<=m;j++)
      f[i][j]=std::min(std::min(f[i-1][j],f[i][j-1])+1,f[i-1][j-1]+(a[i]!=b[j]));
    printf("%I64d\n",f[n][m]); 
    dfs(n,m); 
}