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 characterDelete a characterReplace a character Example 1:Input: word1 = "horse", word2 = "ros"Output: 3Explanation: horse -> rorse (replace 'h' with 'r')rorse -> rose (remove 'r')rose -> ros (remove 'e')Example 2:Input: word1 = "intention", word2 = "execution"Output: 5Explanation: intention -> inention (remove 't')inention -> enention (replace 'i' with 'e')enention -> exention (replace 'n' with 'x')exention -> exection (replace 'n' with 'c')exection -> execution (insert 'u') Constraints:0 <= word1.length, word2.length <= 500word1 and word2 consist of lowercase English letters.
Question
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 characterDelete a characterReplace a character Example 1:Input: word1 = "horse", word2 = "ros"Output: 3Explanation: horse -> rorse (replace 'h' with 'r')rorse -> rose (remove 'r')rose -> ros (remove 'e')Example 2:Input: word1 = "intention", word2 = "execution"Output: 5Explanation: intention -> inention (remove 't')inention -> enention (replace 'i' with 'e')enention -> exention (replace 'n' with 'x')exention -> exection (replace 'n' with 'c')exection -> execution (insert 'u') Constraints:0 <= word1.length, word2.length <= 500word1 and word2 consist of lowercase English letters.
Solution
To find the minimum number of operations required to convert word1 to word2, we can use dynamic programming. Let's define a 2D array dp[word1.length + 1][word2.length + 1], where dp[i][j] represents the minimum number of operations required to convert word1[0...i-1] to word2[0...j-1].
We can initialize the first row and first column of dp as follows:
- dp[i][0] = i, as we need to delete i characters from word1 to convert it to an empty string.
- dp[0][j] = j, as we need to insert j characters into an empty string to convert it to word2.
Now, we can fill in the rest of the dp array using the following rules:
- If word1[i-1] is equal to word2[j-1], then dp[i][j] = dp[i-1][j-1]. No operation is required in this case.
- Otherwise, we have three options:
- Insert a character: dp[i][j] = dp[i][j-1] + 1. We insert word2[j-1] into word1.
- Delete a character: dp[i][j] = dp[i-1][j] + 1. We delete word1[i-1].
- Replace a character: dp[i][j] = dp[i-1][j-1] + 1. We replace word1[i-1] with word2[j-1].
Finally, the minimum number of operations required to convert word1 to word2 will be stored in dp[word1.length][word2.length].
For example, let's consider the given input word1 = "horse" and word2 = "ros":
- Initialize dp as a 2D array of size (6+1) x (3+1).
- Fill in the first row and first column of dp.
- Fill in the rest of the dp array using the rules mentioned above.
- The minimum number of operations required to convert "horse" to "ros" is dp[6][3] = 3.
Similarly, we can apply the same approach to the second example word1 = "intention" and word2 = "execution" to find the minimum number of operations required, which is dp[9][9] = 5.
Similar Questions
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