In standard Edit Distance where we are allowed 3 operations, insert, delete and replace. Consider a variation of edit distance where we are allowed only two operations insert and delete, find edit distance in this variation.
Input : str1 = "cat", st2 = "cut" Output : 2 We are allowed to insert and delete. We delete 'a' from "cat" and insert "u" to make it "cut". Input : str1 = "acb", st2 = "ab" Output : 1 We can convert "acb" to "ab" by removing 'c'.
One solution is to simply modify Edit Distance Solution by making two recursive call instead of three. An interesting solution is based on LCS.
1) Find LCS of two strings. Let length of LCS be x.
2) Let length of first string be m and length of second string be n. Our result is (m – x) + (n – x). We basically need to do (m – x) delete operations and (n – x) insert operations.
# Python 3 program to find Edit Distance
# (when only two operations are allowed,
# insert and delete) using LCS.
def editDistanceWith2Ops(X, Y):
# Find LCS
m = len(X)
n = len(Y)
L = [[0 for x in range(m + 1)]
for y in range(n + 1)]
for i in range(m + 1):
for j in range(n + 1):
if (i == 0 or j == 0):
L[i][j] = 0
elif (X[i – 1] == Y[j – 1]):
L[i][j] = L[i – 1][j – 1] + 1
L[i][j] = max(L[i – 1][j],
L[i][j – 1])
lcs = L[m][n]
# Edit distance is delete operations +
# insert operations.
return (m – lcs) + (n – lcs)
# Driver Code
if __name__ == “__main__”:
X = “abc”
Y = “acd”
# This code is contributed by ita_c
Time Complexity : O(m * n)
Auxiliary Space : O(m * n)
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