MEDIUM NC#119 Dynamic Programming
72. Edit Distance
📖 Problem
Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2. You have the following three operations permitted on a word: - Insert a character - Delete a character - Replace a character
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Array DP table updates
- •State transition thinking
- •Base case initialization
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Dynamic Programming reasoning pattern
💡 Approach
- → Use dp[i][j] = min ops to convert word1[0:i] to word2[0:j+1]
- → If characters match: dp[i][j] = dp[i-1][j-1]
- → If they differ: dp[i][j] = min(dp[i-1][j-1] + 1, dp[i][j-1] + 1)
- → Base case: dp[0][0] = 0
- → Time: O(m * n), Space: O(m * n)
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Use dp[i][j] = min ops to convert word1[0:i] to word2[0:j+1]
- •If characters match: dp[i][j] = dp[i-1][j-1]
- •If they differ: dp[i][j] = min(dp[i-1][j-1] + 1, dp[i][j-1] + 1)
Common Pitfalls
- •Base case: dp[0][0] = 0
- •Time: O(m * n), Space: O(m * n)
🧪 Test Cases
Test Case 1
Not run Input:
minDistance(word1: string, word2: string); Expected:
Computed from hidden reference Test Case 2
Not run Input:
minDistance('horse', 'ros'); Expected:
Computed from hidden reference Test Case 3
Not run Input:
minDistance('intention', 'execution'); Expected:
Computed from hidden reference 📝 Code Editor
📤 Output