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This approach uses the sliding window technique to efficiently find the maximum number of vowels in any substring of length k.
We first calculate the number of vowels in the initial window of length k. Then, for each subsequent character, we slide the window by one character to the right: we remove the character that goes out of the window and add the one that comes into the window, updating our vowel count accordingly.
This ensures that we examine each character in the string only once, leading to an O(n) time complexity.
Time Complexity: O(n), where n is the length of the string. We iterate through the string with a constant number of operations for each character.
Space Complexity: O(1), as we use a fixed amount of extra space.
1public class MaxVowels {
2 private boolean isVowel(char ch) {
3 return "aeiou".indexOf(ch) != -1;
4
In Java, vowels are checked using a simple string lookup within a helper function. The loop initializes the vowel count with the first k characters. As we slide the window across the string, currentCount is adjusted by adding the vowel status of the entering character and subtracting the vowel status of the exiting character. maxCount keeps track of the highest encountered vowel count within a window.
Another way to tackle this problem is to use a combination of prefix sums and binary search to precompute regions of vowels.
First, we establish a prefix sum array that accumulates the number of vowels encountered at each character index in the string. Then, we use a binary search within this prefix sum to efficiently find the maximum number of vowels in any moving window of length k.
This approach is more complex and is generally less optimal than the sliding window approach but provides an alternative methodology.
Time Complexity: O(n), for prefix sum construction and analysis.
Space Complexity: O(n), for the prefix sum array.
The C solution creates a prefix sum array to accumulate the number of vowels found up to each point in the string. Using this prefix sum, the maximum number of vowels in any contiguous substring of length k can be determined by calculating the difference between pairs of prefix sums separated by k indices.