Скачать или смотреть Edit Distance – Master Dynamic Programming for String Transformations! 🔥

📌 Edit Distance is a classic Dynamic Programming problem often asked in top coding interviews! Learn how to solve it optimally using Bottom-Up DP (O(N × M)) instead of brute force recursion.

🔹 Problem Statement:
✅ Given two strings word1 and word2, find the minimum number of operations (Insert, Delete, Replace) to convert word1 into word2.
✅ Example:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation:
horse → rorse (Replace 'h' with 'r')
rorse → rose (Delete 'r')
rose → ros (Delete 'e')
🔹 Approach:
🚀 Brute Force (O(3^(N+M))): Try all operations recursively ❌
⚡ Optimal Dynamic Programming Approach (O(N × M)) ✅

Step 1: Use a 2D DP table where dp[i][j] stores the min operations to convert word1[0:i] to word2[0:j].
Step 2: Recurrence Relation:
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If word1[i] == word2[j]: dp[i][j] = dp[i-1][j-1]
Else: dp[i][j] = 1 + min(
dp[i-1][j], # Delete
dp[i][j-1], # Insert
dp[i-1][j-1] # Replace
)
Step 3: Fill the DP table iteratively for an optimal solution.
💡 Stay till the end for step-by-step explanation, dry run, & live coding demo!

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