grid47 Exploring patterns and algorithms
Oct 30, 2024
5 min read
Solution to LeetCode 72: Edit Distance Problem
Given two strings str1 and str2, your task is to determine the minimum number of operations required to transform str1 into str2. The allowed operations are: Insert a character, Delete a character, and Replace a character.
Problem
Approach
Steps
Complexity
Input: You are given two strings str1 and str2.
Example: str1 = 'kitten', str2 = 'sitting'
Constraints:
• 0 <= str1.length, str2.length <= 500
• str1 and str2 consist of lowercase English letters.
Output: Return the minimum number of operations needed to transform str1 into str2.
Example: 3
Constraints:
• The output should be a single integer.
Goal: Calculate the minimum number of operations needed.
Steps:
• Use dynamic programming to store the results of subproblems.
• For each pair of indices (i, j), consider the operations: insert, delete, or replace.
• Build the solution iteratively using the recurrence relation.
Goal: Constraints on the problem.
Steps:
• 0 <= str1.length, str2.length <= 500
• The strings consist of lowercase English letters.
Assumptions:
• The input strings are non-empty.
• Both strings contain only lowercase alphabets.
• Input: str1 = 'kitten', str2 = 'sitting'
• Explanation: We need 3 operations to convert 'kitten' into 'sitting': 1) Replace 'k' with 's', 2) Replace 'e' with 'i', 3) Insert 'g'.
• Input: str1 = 'flaw', str2 = 'lawn'
• Explanation: We need 2 operations to convert 'flaw' into 'lawn': 1) Remove 'f', 2) Insert 'n'.
Approach: The problem can be solved using dynamic programming, where we calculate the minimum number of operations to transform substrings of str1 into substrings of str2.
Observations:
• The problem can be broken down into smaller subproblems.
• We can use dynamic programming to solve this efficiently.
• Use a 2D array to store intermediate results.
Steps:
• Define a 2D dp array where dp[i][j] stores the minimum number of operations to convert the first i characters of str1 to the first j characters of str2.
• Initialize the dp array for base cases where one of the strings is empty.
• Fill the dp array using the recurrence relation for each pair of indices (i, j).
Empty Inputs:
• If either str1 or str2 is empty, the minimum operations are the length of the other string.
Large Inputs:
• Handle the case when both strings are of maximum length (500).
Special Values:
• Consider cases where str1 and str2 are already equal, in which case the answer is 0.
Constraints:
• Ensure the solution is optimized for the problem's constraints.
