The fastest solution applies state transition dynamic programming to track minimal operations for each substring. By considering replace, swap, and reverse actions while ensuring no character is reused per operation, you build a DP table of optimal transformations. This approach guarantees finding the fewest operations while respecting the constraints on substring manipulation and operation counts.
Problem Statement
Given two strings, word1 and word2, of equal length, transform word1 into word2 by splitting it into contiguous substrings and applying operations to each substring. Operations allowed are replace, swap, or reverse on each substring, with each character usable only once per operation type.
Determine the minimum number of operations required to fully convert word1 into word2. Each substring can be independently manipulated, but no index may participate in more than one operation of the same type. Output the minimal steps necessary to complete the transformation.
Examples
Example 1
Input: word1 = "abcdf", word2 = "dacbe"
Output: 4
Divide word1 into "ab" , "c" , and "df" . The operations are:
Example 2
Input: word1 = "abceded", word2 = "baecfef"
Output: 4
Divide word1 into "ab" , "ce" , and "ded" . The operations are:
Example 3
Input: word1 = "abcdef", word2 = "fedabc"
Output: 2
Divide word1 into "abcdef" . The operations are:
Constraints
- 1 <= word1.length == word2.length <= 100
- word1 and word2 consist only of lowercase English letters.
Solution Approach
Dynamic Programming Table
Define dp[i] as the minimal operations to transform the first i characters. Iterate over all possible substrings ending at i and compute dp[i] as the minimum of dp[j] plus one operation for substring word1[j:i].
Consider All Substring Operations
For each substring, evaluate replace, swap, and reverse while ensuring no character is reused for the same operation type. Update the DP table only if the operation yields fewer total steps.
Greedy State Transitions
When multiple operations result in the same substring match, prefer operations that maximize future matches to reduce total steps. This greedy tie-breaking combined with DP ensures an optimal solution.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time and space complexity depend on substring enumeration and DP table size. Naively checking all substrings yields O(n^3) time, but careful pruning and state caching reduce redundant operations.
What Interviewers Usually Probe
- Check if you are correctly handling overlapping operations on characters.
- Verify DP state transitions properly account for minimal operations for all substrings.
- Look for potential greedy choices that can reduce total operation count.
Common Pitfalls or Variants
Common pitfalls
- Reusing characters in multiple operations of the same type within a substring.
- Incorrectly updating DP states when substring operations overlap.
- Failing to consider reverse or swap operations that reduce overall steps.
Follow-up variants
- Allow unlimited operations per character but still minimize total steps.
- Restrict operations to only replace and reverse, disallow swaps.
- Change problem to count maximal substring matches instead of minimal steps.
How GhostInterview Helps
- Automatically tracks minimal DP states and calculates optimal substring operations.
- Highlights failed or overlapping operations to prevent common mistakes.
- Provides step-by-step breakdowns showing why each operation contributes to the minimal step count.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the optimal approach for Minimum Steps to Convert String with Operations?
Use state transition dynamic programming with careful handling of replace, swap, and reverse operations on substrings.
Can characters be used in multiple operations on the same substring?
No, each character may only participate once per operation type within each substring.
What should I watch out for in DP updates?
Avoid double-counting operations and ensure overlapping substrings are correctly accounted for in minimal steps.
Is there a greedy shortcut for this problem?
Greedy choices help break ties when multiple operations produce equal substrings, but DP ensures overall minimal steps.
Does this problem fit the state transition DP pattern?
Yes, each substring transformation represents a DP state, and transitions model the minimal operations to reach the next state.
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Stay in the same pattern family
Determine the maximum number of non-overlapping substrings in a word, each at least four characters and matching start-end letters.
Open problem page#3458 Select K Disjoint Special SubstringsDetermine if k non-overlapping special substrings exist in a string using dynamic programming and careful substring tracking.
Open problem page#3302 Find the Lexicographically Smallest Valid SequenceDetermine the lexicographically smallest valid index sequence by using state transition dynamic programming over word1 and word2.
Open problem page