November 8, 2023
Understanding the problem
To find the longest common prefix, we compare the characters of each string at the same index until a mismatch is found. This operation is performed iteratively or recursively, stopping when the shortest string's length is reached or a differing character is encountered.
Implementing a solution
How the solution works
- Initialize the prefix to the first string in the array.
- Iterate over the array of strings.
- Use the
indexOffunction to check if the current string contains the prefix at the start.
- If not, reduce the prefix by one character from the end and repeat the process.
- If the prefix is empty or the prefix is found at the start of each string, return the prefix.
The horizontal scanning technique involves taking the first string as the initial prefix and then comparing it with the next string, shortening the prefix from the end with each mismatch. This process is continued for all strings in the array.
The time complexity of this solution is (O(S)), where (S) is the sum of all characters in all strings. The worst-case scenario occurs when all strings are identical.
The space complexity is (O(1)), as the space used by the algorithm is constant and does not grow with the size of the input array.
Let's validate our function with a few test cases:
Tips for optimization
- Early stopping if a string is empty or if the prefix is reduced to zero length at any point.
- Using a divide and conquer technique can improve performance on large datasets.
- Implementing a trie data structure might yield better performance for a large number of strings with a complex set of common prefixes.
Vertical scanning explained
- Check if the array is empty; if so, return an empty string.
- Loop through each character of the first string.
- Compare the current character with the corresponding character of all other strings.
- If a mismatch is found or the end of a string is reached, return the common prefix up to the previous character.
- If the loop completes without a mismatch, the entire first string is the longest common prefix.
Test cases for vertical scanning
You can verify the correctness of the vertical scanning function with these test cases:
When to use vertical scanning
Vertical scanning is particularly effective when:
- The array has a very long string and the prefix is short because it stops checking once the shortest string's length is reached.
- The number of strings is significantly greater than the length of the shortest string.
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