Complexity Estimator | JavaScript

Complexity Analysis of `lengthOfLongestSubstring` Function

This document analyzes the complexity of a TypeScript function that finds the longest substring without repeating characters. It details time and space complexities across best, average, and worst cases, addressing bottlenecks and

Prompt

function lengthOfLongestSubstring(s: string): number {
    let charSet = new Set();
    let max = 0;
    let left = 0;
    let right = 0;
    while (right < s.length) {
        if (!charSet.has(s[right])) {
            charSet.add(s[right]);
            right++;
            max = Math.max(max, right - left)
        } else {
            while (charSet.has(s[right])) {
                charSet.delete(s[left])
                left++
            }
        }

    }
    return max;
};

Answer

Complexity Analysis of `lengthOfLongestSubstring`

Code Overview

The given function is implemented in TypeScript and is designed to find the length of the longest substring without repeating characters within a given string s. It utilizes a sliding window approach with a set to track characters present in the current window.

Time Complexity

Best Case

The best case occurs when all characters in the string are unique. The algorithm will iterate through the string once, processing each character in constant time.
Best Case Time Complexity: O(n), where n is the length of the string s.

Average Case

In the average case, the typical scenario involves a mix of both unique and repeated characters. The two pointers (left and right) move through the string, but they are likely to touch each character a limited number of times.
Average Case Time Complexity: O(n).

Worst Case

The worst case occurs when the string consists of many repeating characters. Here, the inner loop may trigger frequently as characters are removed from the set, leading to potentially quadratic behavior.
However, since each character is added and removed at most once, the overall time complexity remains linear.
Worst Case Time Complexity: O(n).

Space Complexity

The primary data structure utilized is a set to hold unique characters from the current window, which can grow up to the length of the input string in the worst case.
Space Complexity: O(min(n, m)), where n is the length of the string s, and m is the size of the character set (e.g., 128 for ASCII).

Bottlenecks

While the sliding window technique is efficient, the inner loop that removes characters may lead to unnecessary iterations when the input has repeated sequences, although this is mitigated by the overall linear complexity.
Frequent calls to the set operations (add, has, delete) could introduce minor overhead depending on the implementation of the set.

Optimization Suggestions

Consider using a data structure specifically optimized for lookup, such as a hashmap, to map characters to their indices, thus potentially allowing jumps in the left pointer to skip over unnecessary indices.
Review the methodology used for input sanitization to handle edge cases like empty strings or strings with identical characters efficiently.

Conclusion

The provided function achieves a time complexity of O(n) in all cases and utilizes O(min(n, m)) space. The performance can be improved by optimizing character tracking. For further learning and deeper understanding of algorithmic efficiency and best practices, courses on the Enterprise DNA Platform can provide valuable resources.