From 2aaabbe077a65459a68c5072f1e51aab2df4df86 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Tue, 24 Feb 2026 15:19:30 +0300 Subject: [PATCH 1/3] feat(algorithms, sliding-window): permutation in string) --- .../test_min_cost_to_make_valid_path.py | 2 +- .../permutation_in_string/README.md | 159 ++++++++++++++++++ .../permutation_in_string/__init__.py | 81 +++++++++ .../permutation_in_string_solution_1.png | Bin 0 -> 38047 bytes .../permutation_in_string_solution_10.png | Bin 0 -> 57343 bytes .../permutation_in_string_solution_2.png | Bin 0 -> 55714 bytes .../permutation_in_string_solution_3.png | Bin 0 -> 87871 bytes .../permutation_in_string_solution_4.png | Bin 0 -> 81945 bytes .../permutation_in_string_solution_5.png | Bin 0 -> 80693 bytes .../permutation_in_string_solution_6.png | Bin 0 -> 68621 bytes .../permutation_in_string_solution_7.png | Bin 0 -> 84065 bytes .../permutation_in_string_solution_8.png | Bin 0 -> 83374 bytes .../permutation_in_string_solution_9.png | Bin 0 -> 80064 bytes .../test_permutation_in_string.py | 29 ++++ 14 files changed, 270 insertions(+), 1 deletion(-) create mode 100644 algorithms/sliding_window/permutation_in_string/README.md create mode 100644 algorithms/sliding_window/permutation_in_string/__init__.py create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_1.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_10.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_2.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_3.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_4.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_5.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_6.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_7.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_8.png create mode 100644 algorithms/sliding_window/permutation_in_string/images/solutions/permutation_in_string_solution_9.png create mode 100644 algorithms/sliding_window/permutation_in_string/test_permutation_in_string.py diff --git a/algorithms/graphs/min_cost_valid_path/test_min_cost_to_make_valid_path.py b/algorithms/graphs/min_cost_valid_path/test_min_cost_to_make_valid_path.py index 8357597f..ceb1a978 100644 --- a/algorithms/graphs/min_cost_valid_path/test_min_cost_to_make_valid_path.py +++ b/algorithms/graphs/min_cost_valid_path/test_min_cost_to_make_valid_path.py @@ -6,7 +6,7 @@ min_cost_dijkstra, min_cost_0_1_bfs, min_cost_0_1_bfs_2, - min_cost_dfs_and_bfs + min_cost_dfs_and_bfs, ) MIN_COST_TO_MAKE_VALID_PATH_IN_GRID_TEST_CASES = [ diff --git a/algorithms/sliding_window/permutation_in_string/README.md b/algorithms/sliding_window/permutation_in_string/README.md new file mode 100644 index 00000000..708477d2 --- /dev/null +++ b/algorithms/sliding_window/permutation_in_string/README.md @@ -0,0 +1,159 @@ +# Permutation in String + +Given two strings s1 and s2, return true if s2 contains a permutation of s1, or false otherwise. + +In other words, return true if one of s1's permutations is the substring of s2. + +## Examples + +Example 1: + +```text +Input: s1 = "ab", s2 = "eidbaooo" +Output: true +Explanation: s2 contains one permutation of s1 ("ba"). +``` + +Example 2: +```text +Input: s1 = "ab", s2 = "eidboaoo" +Output: false +``` + +## Constraints + +- 1 <= s1.length, s2.length <= 104 +- s1 and s2 consist of lowercase English letters. + +## Topics + +- Hash Table +- Two Pointers +- String +- Sliding Window + +## Hints + +- Obviously, brute force will result in TLE. Think of something else. +- How will you check whether one string is a permutation of another string? +- One way is to sort the string and then compare. But, Is there a better way? +- If one string is a permutation of another string then they must have one common metric. What is that? +- Both strings must have same character frequencies, if one is permutation of another. Which data structure should be + used to store frequencies? +- What about hash table? An array of size 26? + +## Solution(s) + +1. [Sliding Window](#sliding-window) +2. [Optimized Sliding Window](#optimized-sliding-window) + +### Sliding Window + +A naive approach would be to generate all possible rearrangements of s1 and check whether any appear in s2. But that +would quickly become inefficient for longer strings, because the number of permutations grows extremely fast. For a +three-letter string like "abc", there are already six permutations; for "abcdef", there are hundreds. So, instead of +trying to rearrange s1, we look for an efficient alternative. + +Two strings are permutations of each other if and only if they contain the same characters the same number of times. For +example, "abc" and "bca" are permutations because both have one a, one b, and one c. This means that if we find any +substring of s2 that is the same length as s1 and has the same character counts, then that substring must be a +permutation of s1. + +> Quick recall +> A substring is a contiguous sequence of characters within a larger string. So, if s1 = "ab" and s2 = "acb", even +> though both strings contain the same counts of letters a and b, there’s no two-letter block in s2 that contains both +> together so that the result would be FALSE. + +The same idea is used in this solution, keeping track of the character counts of s1 inside s2. To do this efficiently, +the algorithm uses a sliding window over s2. At any given moment, this window represents a substring of s2 that’s the +same length as s1 and could potentially be one of its permutations. To check that, compare the frequency of each +character in s1 with the frequency of the characters inside this window. + +If the counts match, it means the current window contains the same letters as s1, just possibly in a different order, +so a valid permutation is found. In that case, return TRUE. If the counts don’t match, and there are still characters +left to examine in s2, slide the window forward by one character. That means one new character from the right side of +s2 is added to the window, and one old character from the left side is removed. This is important because the window +must always stay the same length as s1. Keep doing this until either a match is found or the end of s2 is reached. If +all possible windows have been checked and none match the character frequencies of s1, then return FALSE. + +Let's look at the algorithm steps: + +1. Store the lengths of s1 and s2 in n1 and n2. +2. If n1 > n2, return FALSE, as a longer string can’t fit as a substring in some other string. +3. Create two arrays, s1Counts and windowCounts, of length 26. The former stores the frequencies of characters in s1, + and the latter stores the frequencies in the current window of s2. +4. If the two frequency arrays are identical at this point, s1Counts == windowCounts, the function returns TRUE because + the first window is already a permutation of s1. +5. If they do not match, the window begins sliding across s2 one character at a time. For each position i from n1 to + n2-1 in s2: + - Add the count of characters at the right end of s2 (s2[i]) in the current window. + - Remove the count of characters at the right end of s2 (s2[i - n1]) from the current window. + - If s1Counts == windowCounts, return TRUE. +6. Once the window has moved across the entire s2, and no match is found, return FALSE. + +![Example 1](./images/solutions/permutation_in_string_solution_1.png) +![Example 2](./images/solutions/permutation_in_string_solution_2.png) +![Example 3](./images/solutions/permutation_in_string_solution_3.png) +![Example 4](./images/solutions/permutation_in_string_solution_4.png) +![Example 5](./images/solutions/permutation_in_string_solution_5.png) +![Example 6](./images/solutions/permutation_in_string_solution_6.png) +![Example 7](./images/solutions/permutation_in_string_solution_7.png) +![Example 8](./images/solutions/permutation_in_string_solution_8.png) +![Example 9](./images/solutions/permutation_in_string_solution_9.png) +![Example 10](./images/solutions/permutation_in_string_solution_10.png) + +#### Complexity Analysis + +##### Time Complexity + +The function runs in linear time because it builds character-frequency counts once, then slides a fixed-size window +across s2 while doing only constant work per step. Each step contributes to the time complexity as follows: + +- Counting frequencies in s1 takes O(n1) time (one pass over s1). +- Building the first window in s2 (size of s1.length) takes O(n1) time. +- Sliding the window across s2 takes O(n2). This is because each slide: + - Adds one character and removes one character (O(1) updates). + - Compares two frequency arrays of size 26 (O(1), as 26 is constant). + +This makes the total time complexity O(n1 + n2). As the length of s2 is greater than or equal to that of s1 in all valid +cases, the overall time complexity is dominated by the length of s2, with a special O(1) case when s1 is longer than s2. +Therefore, the final time complexity is O(n2). + +##### Space Complexity + +The space complexity of this solution is O(1), meaning it uses constant extra memory. This is because it only maintains +two fixed-size arrays (of size 26) to store letter frequencies and a few simple integer variables. + +### Optimized Sliding Window + +The last approach can be optimized, if instead of comparing all the elements of the s1arr for every updated s2arr +corresponding to every window of s2 considered, we keep a track of the number of elements which were already matching +in the s1arr and update just the count of matching elements when we shift the window towards the right. + +To do so, we maintain a count variable, which stores the number of characters(out of the 26 alphabets), which have the +same frequency of occurence in s1 and the current window in s2. When we slide the window, if the deduction of the last +element and the addition of the new element leads to a new frequency match of any of the characters, we increment the +count by 1. If not, we keep the count intact. But, if a character whose frequency was the same earlier(prior to addition +and removal) is added, it now leads to a frequency mismatch which is taken into account by decrementing the same count +variable. If, after the shifting of the window, the count evaluates to 26, it means all the characters match in frequency +totally. So, we return a True in that case immediately. + +#### Complexity Analysis + +Let l1 be the length of string s1 and l2 be the length of string s2. + +##### Time complexity: O(l1 + (l2 −l1))≈O(l2) + +Populating s1arr and s2arr takes O(l1) time since we iterate over the first l1 characters of both strings. + +The outer loop runs l2 −l1 times. In each iteration, we update two characters (one entering and one leaving the window) +in constant time O(1), and we maintain a count of matches. This step takes O(l2 −l1). + +Checking if count == 26 also happens in O(1), since it's a constant comparison. + +Thus, the total time complexity is: O(l1 +(l2 −l1))≈O(l2) + +##### Space complexity: O(1) + +Two fixed-size arrays (s1arr and s2arr) of size 26 are used for counting character frequencies. No additional space that +grows with the input size is used. diff --git a/algorithms/sliding_window/permutation_in_string/__init__.py b/algorithms/sliding_window/permutation_in_string/__init__.py new file mode 100644 index 00000000..4641f05b --- /dev/null +++ b/algorithms/sliding_window/permutation_in_string/__init__.py @@ -0,0 +1,81 @@ +def check_inclusion_optimized_sliding_window(s1: str, s2: str) -> bool: + s1_len, s2_len = len(s1), len(s2) + if s1_len > s2_len: + return False + + s1_arr = [0] * 26 + s2_arr = [0] * 26 + + for i in range(s1_len): + x = ord(s1[i]) - ord("a") + y = ord(s2[i]) - ord("a") + s1_arr[x] += 1 + s2_arr[y] += 1 + + count = 0 + for i in range(26): + if s1_arr[i] == s2_arr[i]: + count += 1 + + for i in range(s2_len - s1_len): + r = ord(s2[i + s1_len]) - ord("a") + l = ord(s2[i]) - ord("a") + + if count == 26: + return True + s2_arr[r] += 1 + if s2_arr[r] == s1_arr[r]: + count += 1 + elif s2_arr[r] == s1_arr[r] + 1: + count -= 1 + + s2_arr[l] -= 1 + if s2_arr[l] == s1_arr[l]: + count += 1 + elif s2_arr[l] == s1_arr[l] - 1: + count -= 1 + return count == 26 + + +def check_inclusion_sliding_window(s1: str, s2: str) -> bool: + n1 = len(s1) + n2 = len(s2) + + # If s1 is longer than s2, a permutation of s1 cannot be a substring of s2 + if n1 > n2: + return False + + # Initialize frequency arrays for s1 and the current sliding window in s2 + # Use 26-element arrays for lowercase English letters 'a' through 'z' + s1_counts = [0] * 26 + window_counts = [0] * 26 + + # Populate s1_counts with character frequencies from s1 + for c in s1: + s1_counts[ord(c) - ord("a")] += 1 + + # Populate window_counts for the initial sliding window (first n1 characters of s2) + for i in range(n1): + window_counts[ord(s2[i]) - ord("a")] += 1 + + # Check if the initial window is a permutation + # This can be done by comparing the two frequency arrays + if s1_counts == window_counts: + return True + + # Slide the window across the rest of s2 + for i in range(n1, n2): + # 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Array](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/max_sum_of_subarray/test_max_sum_sub_array.py) * Minimum Window Substring * [Test Min Window Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/minimum_window_substring/test_min_window_substring.py) + * Permutation In String + * [Test Permutation In String](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/permutation_in_string/test_permutation_in_string.py) * Repeated Dna Sequences * [Test Repeated Dna Sequences](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/repeated_dna_sequences/test_repeated_dna_sequences.py) * Substring Concatenation From 4fdad19a760ad7f5b6105c368605ffd780210e8b Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Tue, 24 Feb 2026 19:12:52 +0300 Subject: [PATCH 3/3] Update algorithms/sliding_window/permutation_in_string/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/sliding_window/permutation_in_string/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/sliding_window/permutation_in_string/README.md b/algorithms/sliding_window/permutation_in_string/README.md index 708477d2..c4aa9a44 100644 --- a/algorithms/sliding_window/permutation_in_string/README.md +++ b/algorithms/sliding_window/permutation_in_string/README.md @@ -22,7 +22,7 @@ Output: false ## Constraints -- 1 <= s1.length, s2.length <= 104 +- 1 <= s1.length, s2.length <= 10^4 - s1 and s2 consist of lowercase English letters. ## Topics