Edit Distance Algorithm for String Matching (#10571)

* Edit Distance Algorithm for String Matching

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* Update edit_distance.py

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: 3 people

strings/edit_distance.py

@@ -0,0 +1,32 @@
+def edit_distance(source: str, target: str) -> int:
+    """
+    Edit distance algorithm is a string metric, i.e., it is a way of quantifying how
+    dissimilar two strings are to one another. It is measured by counting the minimum
+    number of operations required to transform one string into another.
+
+    This implementation assumes that the cost of operations (insertion, deletion and
+    substitution) is always 1
+
+    Args:
+    source: the initial string with respect to which we are calculating the edit
+        distance for the target
+    target: the target string, formed after performing n operations on the source string
+
+    >>> edit_distance("GATTIC", "GALTIC")
+    1
+    """
+    if len(source) == 0:
+        return len(target)
+    elif len(target) == 0:
+        return len(source)
+
+    delta = int(source[-1] != target[-1])  # Substitution
+    return min(
+        edit_distance(source[:-1], target[:-1]) + delta,
+        edit_distance(source, target[:-1]) + 1,
+        edit_distance(source[:-1], target) + 1,
+    )
+
+
+if __name__ == "__main__":
+    print(edit_distance("ATCGCTG", "TAGCTAA"))  # Answer is 4