Dsa Dp Edit Distance

In this tutorial, you'll learn about How to Fix Edit Distance Errors. We cover key concepts, practical examples, and best practices.

Fix edit distance errors when cost matrix indexing off-by-one or operation order wrong.

Quick Fix

Wrong

def ed(a,b):
    n,m=len(a),len(b)
    dp=[[0]*m for _ in range(n)]
    for i in range(n):
        for j in range(m):
            if a[i]==b[j]: dp[i][j]=dp[i-1][j-1]
            else: dp[i][j]=1+min(dp[i-1][j],dp[i][j-1],dp[i-1][j-1])

Index -1 wraps around in Python. First row/col must handle empty string base cases.

Right

def ed(a,b):
    n,m=len(a),len(b)
    dp=[[0]*(m+1) for _ in range(n+1)]
    for i in range(n+1): dp[i][0]=i
    for j in range(m+1): dp[0][j]=j
    for i in range(1,n+1):
        for j in range(1,m+1):
            if a[i-1]==b[j-1]: dp[i][j]=dp[i-1][j-1]
            else: dp[i][j]=1+min(dp[i-1][j],dp[i][j-1],dp[i-1][j-1])
    return dp[n][m]

ed('horse','ros')=3. O(n*m).

Prevention

Initialize base row/col for empty string prefixes. dp[i][0]=i deletions, dp[0][j]=j insertions.

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FAQ