Problem:
Given a string s, find the length of the longest substring without repeating characters.

Example:

Input:  "abcabcbb"
Output: 3
Explanation: "abc"

🔥 Best Approach (HashMap Jump Optimization)

Instead of removing one by one,
jump left directly to the correct position.

⚙️ Algorithm

Use hashmap<char, last_index>

For each character:
    if already seen inside current window:
         move left = last_index + 1

    update answer
    update last seen index

💻 C++ Optimal Solution

class Solution {
public:
    int lengthOfLongestSubstring(string s) {
        unordered_map<char, int> lastSeen;

        int left = 0;
        int ans = 0;

        for (int right = 0; right < s.size(); right++) {

            char ch = s[right];

            // duplicate inside current window
            if (lastSeen.count(ch)) {
                left = max(left, lastSeen[ch] + 1);
            }

            lastSeen[ch] = right;

            ans = max(ans, right - left + 1);
        }

        return ans;
    }
};

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🔍 Dry Run

Input:

"abcabcbb"

right	char	left	window	ans
0	a	0	a	1
1	b	0	ab	2
2	c	0	abc	3
3	a	1	bca	3
4	b	2	cab	3
5	c	3	abc	3
6	b	5	cb	3
7	b	7	b	3

---

⏱️ Complexity

Optimal

• Time: O(n)
• Space: O(charset)

Because:

• Each character processed once
• left never moves backward