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+---
+title: levenshtein_distance
+tags: string,algorithm,intermediate
+firstSeen: 2021-10-07T20:34:00-04:00
+---
+
+Uses dynamic programming to calculate the difference between two strings according to the Levenshtein distance algorithm.
+
+- If either of the two strings has a `length` of zero, return the `length` of the other one.
+- Create a 2D array (list of lists) to be populated with the Levenshtein distances between each pair of prefixes of the source and target strings.
+- Use a `for` loop to iterate over the letters of the target string and a nested `for` loop to iterate over the letters of the source string.
+- Calculate the cost of substituting the letters corresponding to `i - 1` and `j - 1` in the target and source respectively (`0` if they are the same, `1` otherwise).
+- Use `Math.min()` to populate each element in the 2D array with the minimum of:
+    - The cell above incremented by one
+    - The cell to the left incremented by one
+    - The cell to the top left incremented by the previously calculated cost.
+- Return the last element of the last row of the produced array.
+
+```py
+def levenshteinDistance(s, t):
+    m = len(s)
+    n = len(t)
+    if m == 0 return n
+    if n == 0 return m
+    dists = [[i] for i in range(1, m + 1)]
+    dists.insert(0, list(range(0, n + 1)))
+    for j in range(1, n + 1):
+        for i in range(1, m + 1):
+            cost = 0
+            if s[i - 1] != t[j - 1]:
+                cost = 1
+            dists[i].insert(j, min(dists[i - 1][j] + 1,
+                               dists[i][j - 1] + 1,
+                               dists[i - 1][j - 1] + cost))
+    return d[-1][-1]
+```
+
+```py
+levenshtein('duck','dark') # 2
+```