class Solution {
    /**
     * Find the LCS of both strings
     * Once LCS length is found, we can remove the length of LCS from both the strings
     * and then we can sum up the remaining length of both strings
     */
    public int minDistance(String word1, String word2) {
        int n = word1.length();
        int m = word2.length();

        int[][] t = new int[n+1][m+1];

        for(int i=0; i<n+1; i++)
        {
            for(int j=0; j<m+1; j++)
            {
                if(i == 0 || j == 0)
                    t[i][j] = 0;
            }
        }

        for(int i=1; i<n+1; i++)
        {
            for(int j=1; j<m+1; j++)
            {
                if(word1.charAt(i-1) == word2.charAt(j-1))
                {
                    t[i][j] = 1 + t[i-1][j-1];
                }
                else
                    t[i][j] = Math.max(t[i-1][j], t[i][j-1]);
            }
        }

        int lcsLength = t[n][m];

        return (n-lcsLength) + (m-lcsLength);
    }
}

// lcs: etco = 4
// n = 8
// m = 4