How do you compute the minimum number of insert, delete, or replace operations needed to convert one string into another (e.g., "horse" → "ros")?

def minDistance(word1: str, word2: str) -> int:
    m, n = len(word1), len(word2)
    prev, curr = list(range(n+1)), [0]*(n+1)
    
    for i in range(1, m+1):
        curr[0] = i
        for j in range(1, n+1):
            cost = 0 if word1[i-1] == word2[j-1] else 1
            curr[j] = min(prev[j-1] + cost, prev[j] + 1, curr[j-1] + 1)
        prev, curr = curr, prev
    
    return prev[n]

print(minDistance("horse", "ros"))  # 3
      

h o r s e
↓replace ↓delete ↓delete
r o s