Levenshtein Distance

• Time : O(nm)
• Space : O(min(n,m))

c++

using namespace std;

int levenshteinDistance(string str1, string str2) {
  if(str1.length() < str2.length()) return levenshteinDistance(str2, str1);
	
	int n = str1.length(), m = str2.length();
	vector<int> dp(m + 1, 0);
	for(int i = 0; i <= m; i++) dp[i] = i;
	
	for(int i = 1; i <= n; i++) {
		vector<int> ndp(m + 1, i);
		for(int j = 1; j <= m; j++) {
			if(str1[i-1] == str2[j-1]) {
				ndp[j] = dp[j-1];
			} else {
				ndp[j] = 1 + min({ndp[j-1], dp[j-1], dp[j]});
			}
		}
		swap(dp, ndp);
	}
	
  return dp.back();
}