#include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>

using namespace std;


int levenShtein(string s1,string s2)
{
	int cel=s1.size();
	int row=s2.size();
	if(cel==0)
		return row;
	if(row==0)
		return cel;
	vector<vector<int>> vec(row+1,vector<int>(cel+1));
	for(int i=0;i<=cel;i++)
		vec[0][i]=i;
	for(int j=0;j<=row;j++)
		vec[j][0]=j;

	for(int r=1;r<=row;r++)
	{
		for(int c=1;c<=cel;c++)
		{
			int cost=0;
			if(s1[r-1]==s2[c-1])
				cost=0;
			else
				cost=2;  //susstitution cost 2
			
			//D[i,j]=min(D[i-1,j]+1,D[i,j-1]+1,D[i,j]+cost)
			vec[r][c]=min(min(vec[r-1][c]+1,vec[r][c-1]+1),vec[r-1][c-1]+cost);
		}
	}
	return vec[row][cel];
}

int main()
{
	string s1("execution");
	string s2("intention");
	cout<<levenShtein(s1,s2)<<endl;

}