Minimum editing distance (linear DP writing method)

Topic linking ：902. The shortest editing distance - AcWing Question bank

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  Code ：

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1010;
ll n,m;
char a[N],b[N];
int f[N][N];
int main()
{
    cin>>n;
    cin>>a+1;
    cin>>m;
    cin>>b+1;
    // Boundary treatment f[n][0] The required step is to delete n Step a Some elements 
    // Empathy f[0][m] The required step is to delete m Step b Some elements 
    for(int i=0;i<=n;i++) f[i][0]=i;
    for(int i=0;i<=m;i++) f[0][i]=i;

    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=m;j++)
        {
            f[i][j]=min(f[i-1][j]+1,f[i][j-1]+1);// Compare the added and deleted operands to get the smaller value 
            
            // Here is the replacement operation , Judge whether it is the same ;

            if(a[i]==b[j]) f[i][j]=min(f[i][j],f[i-1][j-1]);// In the same way, this does not require operands +1（ There is no need to replace ）
            // Different operands need to be replaced 1
            else f[i][j]=min(f[i][j],f[i-1][j-1]+1);
        }
    }
    cout<<f[n][m]<<endl;
    return 0;
}