Intuition

The task is to determine if one of the permutations of the string s1 is present as a substring in s2. To achieve this, we use a sliding window approach that compares character frequencies between the current window of s2 and s1.

 

Approach: Counting + Sliding Window

We maintain a frequency array (freq[26]) that tracks the difference in character counts between the current window in s2 and the string s1. A key idea is that if all character frequencies match (i.e., their differences are zero), the current window of s2 contains a permutation of s1.

Explanation:

1. Initial Setup:
2. We first check if the length of s1 is greater than s2. If s1 is longer, it's impossible for a permutation of s1 to be in s2, so we return false.
3. We initialize freq[26] to store the frequency difference between s1 and the first window (substring) of s2 of length n (length of s1).

4. diffCount keeps track of how many characters have non-zero frequency differences between s1 and the current window in s2.

5. Processing the First Window:

6. For the first n characters of s2, we decrement the frequency for the characters of s1 and increment it for the corresponding characters of s2.

7. We update diffCount based on the frequency values. If a frequency changes from zero to non-zero or vice versa, diffCount is adjusted accordingly.

8. Sliding the Window:

9. For each subsequent character in s2 (starting from index n), we update the window by removing the effect of the character that is sliding out (at index i - n) and adding the effect of the new character (at index i).

10. After adjusting the frequencies, we check if diffCount is zero, which indicates that the current window matches a permutation of s1.

11. Termination:

12. If at any point diffCount becomes zero, we return true.
13. If we finish sliding through s2 without finding a valid window, we return false.

Complexity

• Time complexity: $O(m)$, where m is the length of s2. We perform constant-time updates on the frequency array for each character in s2.
• Space complexity: $O(d)$, where d is the number of distinct characters (in this case, d = 26 for lowercase English letters).

Code

int freq[26];

class Solution {
public:
    bool checkInclusion(string& s1, string& s2) {
        int n = s1.size(), m = s2.size();
        if (n > m) return false;

        memset(freq, 0, sizeof(freq));
        int diffCount = 0;

        for (size_t i = 0; i < n; i++) {
            diffCount += (freq[s1[i] - 'a'] == 0) - (--freq[s1[i] - 'a'] == 0);
            diffCount += (freq[s2[i] - 'a'] == 0) - (++freq[s2[i] - 'a'] == 0);
        }

        if (diffCount == 0) return true;

        for (size_t i = n; i < m; i++) {
            diffCount += (freq[s2[i - n] - 'a'] == 0) - (--freq[s2[i - n] - 'a'] == 0);
            diffCount += (freq[s2[i] - 'a'] == 0) - (++freq[s2[i] - 'a'] == 0);

            if (diffCount == 0) return true;
        }

        return false;
    }
};