From 0cb2f0cf71cc0c8c3acf3060e156ccdb9a965517 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Tue, 13 Jan 2026 14:31:41 +0300 Subject: [PATCH 1/8] feat(algorithms, dynamic-programming): palindromic substrings --- .../palindromic_substring/README.md | 114 ++++++++++++++++++ .../palindromic_substring/__init__.py | 66 ++++++++++ .../palindromic_substring_example_1.png | Bin 0 -> 67370 bytes .../palindromic_substring_example_2.png | Bin 0 -> 48095 bytes .../palindromic_substring_solution_1.png | Bin 0 -> 116857 bytes .../palindromic_substring_solution_10.png | Bin 0 -> 88429 bytes .../palindromic_substring_solution_11.png | Bin 0 -> 100424 bytes .../palindromic_substring_solution_12.png | Bin 0 -> 115941 bytes .../palindromic_substring_solution_13.png | Bin 0 -> 114495 bytes .../palindromic_substring_solution_14.png | Bin 0 -> 91499 bytes .../palindromic_substring_solution_15.png | Bin 0 -> 108324 bytes .../palindromic_substring_solution_16.png | 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mode 100644 algorithms/dynamic_programming/palindromic_substring/images/solutions/palindromic_substring_solution_5.png create mode 100644 algorithms/dynamic_programming/palindromic_substring/images/solutions/palindromic_substring_solution_6.png create mode 100644 algorithms/dynamic_programming/palindromic_substring/images/solutions/palindromic_substring_solution_7.png create mode 100644 algorithms/dynamic_programming/palindromic_substring/images/solutions/palindromic_substring_solution_8.png create mode 100644 algorithms/dynamic_programming/palindromic_substring/images/solutions/palindromic_substring_solution_9.png rename algorithms/{two_pointers/palindrome => dynamic_programming/palindromic_substring}/longest_palindromic_substring.py (87%) create mode 100644 algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py create mode 100644 algorithms/dynamic_programming/palindromic_substring/test_palindromic_substring.py rename {pymath => algorithms/dynamic_programming}/pascals_triangle/README.md (100%) rename {pymath => algorithms/dynamic_programming}/pascals_triangle/__init__.py (96%) rename {pymath => algorithms/dynamic_programming}/pascals_triangle/test_pascals_triangle.py (100%) diff --git a/algorithms/dynamic_programming/palindromic_substring/README.md b/algorithms/dynamic_programming/palindromic_substring/README.md new file mode 100644 index 00000000..ee9154e4 --- /dev/null +++ b/algorithms/dynamic_programming/palindromic_substring/README.md @@ -0,0 +1,114 @@ +# Palindromic Substring + +## Palindromic Substring + +Given a string, s, return the number of palindromic substrings contained in it. A substring is a contiguous sequence of +characters in a string. A palindrome is a phrase, word, or sequence that reads the same forward and backward. + +### Constraints + +- 1 <= `s.length` <= 1000 +- `s` consists of lower English characters + +### Examples + +![Example 1](./images/examples/palindromic_substring_example_1.png) +![Example 2](./images/examples/palindromic_substring_example_2.png) + +### Solution + +If we look at the example above, we notice that any substring of length 3 contains a substring of length 1 at the center. +Although we had already checked all substrings of length 1, our algorithm rechecked them for substrings of longer lengths. +This rechecking consumes a lot of time, which can be avoided by storing and reusing the results of the earlier computations. +To do this, we can create a lookup table, dp, of size n×n, where n is the length of the input string. Each cell dp[i][j] +will store whether the string s[i..j] is a palindromic substring. If the cell dp[i][j] holds the result of the earlier +computation, we will utilize it in O(1) lookup time instead of making a recursive call again. + +1. First, we initialize a count variable with 0, which will count the number of palindromic substrings in s. +2. A lookup table is initialized with FALSE. +3. Base case 1: The diagonal in the lookup table is populated with TRUE because any cell in the diagonal corresponds to + a substring of length one, and any string of length one is always a palindrome. The number of one-letter palindromic + strings (i.e., the number of elements in the diagonal) is also added to the count. +4. Base case 2: We check whether all two-letter substrings are palindromes and update the count and dp accordingly. We + do this by iterating over the string, comparing s[i] and s[i+1], and storing the result at dp[i][i+1]. After that, we + also increment the count if the value of dp[i][i+1] is TRUE, which tells us that the two-letter substring was a + palindrome. +5. After these base cases, we check all substrings of lengths greater than two. However, we only compare the first and + the last characters. The rest of the string is checked using the lookup table. For example, for a given string “zing”, + we want to check whether “zin” is a palindrome. We’ll only compare ‘z’ and ‘n’ and check the value of dp[1][1], which + will tell whether the remaining string “i”, represented by s[1..1], is a palindrome. We’ll take the logical AND of + these two results and store it at dp[0][2] because “zin” is represented by the substring s[0..2]. This way, we’ll + avoid redundant computations and check all possible substrings using the lookup table. + +![Solution 1](./images/solutions/palindromic_substring_solution_1.png) +![Solution 2](./images/solutions/palindromic_substring_solution_2.png) +![Solution 3](./images/solutions/palindromic_substring_solution_3.png) +![Solution 4](./images/solutions/palindromic_substring_solution_4.png) +![Solution 5](./images/solutions/palindromic_substring_solution_5.png) +![Solution 6](./images/solutions/palindromic_substring_solution_6.png) +![Solution 7](./images/solutions/palindromic_substring_solution_7.png) +![Solution 8](./images/solutions/palindromic_substring_solution_8.png) +![Solution 9](./images/solutions/palindromic_substring_solution_9.png) +![Solution 10](./images/solutions/palindromic_substring_solution_10.png) +![Solution 11](./images/solutions/palindromic_substring_solution_11.png) +![Solution 12](./images/solutions/palindromic_substring_solution_12.png) +![Solution 13](./images/solutions/palindromic_substring_solution_13.png) +![Solution 14](./images/solutions/palindromic_substring_solution_14.png) +![Solution 15](./images/solutions/palindromic_substring_solution_15.png) +![Solution 16](./images/solutions/palindromic_substring_solution_16.png) +![Solution 17](./images/solutions/palindromic_substring_solution_17.png) + +#### Solution Summary + +To recap, the solution to this problem can be divided into the following five main parts: + +1. We count all one-letter substrings since any one-letter string is always a palindrome. These results are also stored + in a lookup table to be used later. +2. Next, the algorithm checks all two-letter substrings and updates the count and the lookup table accordingly. +3. After these base cases, the algorithm checks all possible substrings of lengths greater than three. However, it only + compares the first and last characters, and the rest of the substring is checked using the lookup table. +4. Whenever a palindromic substring is found, the count and the lookup table are updated accordingly. +5. After checking all possible substrings, the algorithm terminates and returns the count of the palindromic substrings. + +#### Complexity Analysis + +##### Time Complexity + +The time complexity of this algorithm is O(n^2), where n is the length of the input string. This is the time required to +populate the lookup table. + +##### Space Complexity + +The space complexity of this algorithm is O(n^2), where n is the length of the input string. This is the space occupied +by the lookup table. + +--- + +## Longest Palindromic Substring + +Problem Description + +Given a string A of size N, find and return the longest palindromic substring in A. + +Substring of string A is A[i...j] where 0 <= i <= j < len(A) + +Palindrome string: + +A string which reads the same backwards. More formally, A is palindrome if reverse(A) = A. + +Incase of conflict, return the substring which occurs first ( with the least starting index). + +Input Format +First and only argument is a string A. + +Output Format +Return a string denoting the longest palindromic substring of string A. + +Example Input +A = "aaaabaaa" + +Example Output +"aaabaaa" + +Example Explanation +We can see that longest palindromic substring is of length 7 and the string is "aaabaaa". diff --git a/algorithms/dynamic_programming/palindromic_substring/__init__.py b/algorithms/dynamic_programming/palindromic_substring/__init__.py new file mode 100644 index 00000000..58a3802a --- /dev/null +++ b/algorithms/dynamic_programming/palindromic_substring/__init__.py @@ -0,0 +1,66 @@ +def count_palindromic_substrings(s: str) -> int: + """ + Counts the number of palindromic substrings that can be found in the given string + Args: + s(str): string to check for palindromic substrings + Returns: + int: number of palindromic substrings + """ + n = len(s) + dp = [[False] * n for _ in range(n)] + + count = 0 + # Set all the strings of length 1 to true, these are all palindromes + for i in range(n): + count += 1 + dp[i][i] = True + + # iterate over pairs i, i+1, checking if they are equal, if they are, then they are palindromes + for i in range(n - 1): + if s[i] == s[i + 1]: + count += 1 + dp[i][i + 1] = True + + for diff in range(2, n): + for i in range(n - diff): + j = i + diff + if s[i] == s[j] and dp[i + 1][j - 1]: + count += 1 + dp[i][j] = True + + return count + + +def count_palindromic_substrings_2(s: str) -> int: + """ + Counts the number of palindromic substrings that can be found in the given string + Args: + s(str): string to check for palindromic substrings + Returns: + int: number of palindromic substrings + """ + n = len(s) + dp = [[False] * n for _ in range(n)] + + count = 0 + # Set all the strings of length 1 to true, these are all palindromes + for i in range(n): + count += 1 + 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9fddd371..2dd1e41a 100644 --- a/algorithms/two_pointers/palindrome/longest_palindromic_substring.py +++ b/algorithms/dynamic_programming/palindromic_substring/longest_palindromic_substring.py @@ -1,8 +1,9 @@ -from . import is_palindrome +from algorithms.two_pointers.palindrome import is_palindrome def longest_palindromic_substring(phrase: str) -> str: - """Finds the longest palindromic substring from a given string and returns it. If the string has + """ + Finds the longest palindromic substring from a given string and returns it. If the string has more than 1 palindromic substring, the first is returned, that is, the first with the lowest index. Args: diff --git a/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py b/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py new file mode 100644 index 00000000..b270d4d7 --- /dev/null +++ b/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py @@ -0,0 +1,26 @@ +import unittest +from parameterized import parameterized +from algorithms.dynamic_programming.palindromic_substring.longest_palindromic_substring import ( + longest_palindromic_substring, +) + +LONGEST_PALINDROMIC_SUBSTRING_TEST_CASES = [ + ("mnm", "mnm"), + ("zzz", "zzz"), + ("cat", "c"), + ("lever", "eve"), + ("xyxxyz", "yxxy"), + ("wwwwwwwwww", "wwwwwwwwww"), + ("tattarrattat", "tattarrattat"), +] + + +class LongestPalindromicSubstringTestCase(unittest.TestCase): + @parameterized.expand(LONGEST_PALINDROMIC_SUBSTRING_TEST_CASES) + def test_longest_palindromic_substrings(self, s: str, expected: str): + actual = longest_palindromic_substring(s) + self.assertEqual(expected, actual) + + +if __name__ == "__main__": + unittest.main() diff --git a/algorithms/dynamic_programming/palindromic_substring/test_palindromic_substring.py b/algorithms/dynamic_programming/palindromic_substring/test_palindromic_substring.py new file mode 100644 index 00000000..ad79e807 --- /dev/null +++ b/algorithms/dynamic_programming/palindromic_substring/test_palindromic_substring.py @@ -0,0 +1,34 @@ +import unittest +from parameterized import parameterized +from algorithms.dynamic_programming.palindromic_substring import ( + count_palindromic_substrings, + count_palindromic_substrings_2, +) + +COUNT_PALINDROMIC_SUBSTRINGS_TEST_CASES = [ + ("abc", 3), + ("aaa", 6), + ("mnm", 4), + ("zzz", 6), + ("cat", 3), + ("lever", 6), + ("xyxxyz", 9), + ("wwwwwwwwww", 55), + ("tattarrattat", 24), +] + + +class CountPalindromicSubstringsTestCase(unittest.TestCase): + @parameterized.expand(COUNT_PALINDROMIC_SUBSTRINGS_TEST_CASES) + def test_count_palindromic_substrings(self, s: str, expected: int): + actual = count_palindromic_substrings(s) + self.assertEqual(expected, actual) + + @parameterized.expand(COUNT_PALINDROMIC_SUBSTRINGS_TEST_CASES) + def test_count_palindromic_substrings_2(self, s: str, expected: int): + actual = count_palindromic_substrings_2(s) + self.assertEqual(expected, actual) + + +if __name__ == "__main__": + unittest.main() diff --git a/pymath/pascals_triangle/README.md b/algorithms/dynamic_programming/pascals_triangle/README.md similarity index 100% rename from pymath/pascals_triangle/README.md rename to algorithms/dynamic_programming/pascals_triangle/README.md diff --git a/pymath/pascals_triangle/__init__.py b/algorithms/dynamic_programming/pascals_triangle/__init__.py similarity index 96% rename from pymath/pascals_triangle/__init__.py rename to algorithms/dynamic_programming/pascals_triangle/__init__.py index 3a8a70c8..f4769494 100644 --- a/pymath/pascals_triangle/__init__.py +++ b/algorithms/dynamic_programming/pascals_triangle/__init__.py @@ -29,7 +29,7 @@ def pascal_nth_row(nth: int) -> List[int]: We instead use the formula: NCr = (NCr - 1 * (N - r + 1)) / r where 1 ≤ r ≤ N as the nth row consists of the following sequence: - NC0, NC1, ......, NCN - 1, NCN + NC0, NC1, ..., NCN - 1, NCN """ ncr_1 = 1 row: List[int] = [ncr_1] diff --git a/pymath/pascals_triangle/test_pascals_triangle.py b/algorithms/dynamic_programming/pascals_triangle/test_pascals_triangle.py similarity index 100% rename from pymath/pascals_triangle/test_pascals_triangle.py rename to algorithms/dynamic_programming/pascals_triangle/test_pascals_triangle.py diff --git a/algorithms/two_pointers/palindrome/README.md b/algorithms/two_pointers/palindrome/README.md index c3d76fac..ee04f954 100755 --- a/algorithms/two_pointers/palindrome/README.md +++ b/algorithms/two_pointers/palindrome/README.md @@ -97,36 +97,6 @@ This string is already a palindrome, so we print . Removing any one of the chara --- -## Longest Palindromic Substring - -Problem Description - -Given a string A of size N, find and return the longest palindromic substring in A. - -Substring of string A is A[i...j] where 0 <= i <= j < len(A) - -Palindrome string: - -A string which reads the same backwards. More formally, A is palindrome if reverse(A) = A. - -Incase of conflict, return the substring which occurs first ( with the least starting index). - -Input Format -First and only argument is a string A. - -Output Format -Return a string denoting the longest palindromic substring of string A. - -Example Input -A = "aaaabaaa" - -Example Output -"aaabaaa" - -Example Explanation -We can see that longest palindromic substring is of length 7 and the string is "aaabaaa". - - ## Palindrome Number Given an integer, x, return TRUE if it is a palindrome; otherwise, FALSE. From 780f9dc08cc72d7f3892f30041dc57525963ca74 Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Tue, 13 Jan 2026 11:32:04 +0000 Subject: [PATCH 2/8] updating DIRECTORY.md --- DIRECTORY.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 9c577921..8757088a 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -69,6 +69,12 @@ * [Test Min Distance](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/min_distance/test_min_distance.py) * Min Path Sum * [Test Min Path Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/min_path_sum/test_min_path_sum.py) + * Palindromic Substring + * [Longest Palindromic Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/palindromic_substring/longest_palindromic_substring.py) + * [Test Longest Palindromic Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py) + * [Test Palindromic Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/palindromic_substring/test_palindromic_substring.py) + * Pascals Triangle + * [Test Pascals Triangle](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/pascals_triangle/test_pascals_triangle.py) * Shortest Common Supersequence * [Test Shortest Common Supersequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/shortest_common_supersequence/test_shortest_common_supersequence.py) * Unique Paths @@ -231,7 +237,6 @@ * Largest Palindrome Product * [Test Largest Palindrome Product](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/palindrome/largest_palindrome_product/test_largest_palindrome_product.py) * [Longest Palindrome](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/palindrome/longest_palindrome.py) - * [Longest Palindromic Substring](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/palindrome/longest_palindromic_substring.py) * [Palindrome Index](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/palindrome/palindrome_index.py) * [Palindrome Pairs](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/palindrome/palindrome_pairs.py) * Permutation Palindrome @@ -804,8 +809,6 @@ * [Test Mini Max Sum](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/mini_max_sum/test_mini_max_sum.py) * Multiply 5 * [Test Multiply 5](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/multiply_5/test_multiply_5.py) - * Pascals Triangle - * [Test Pascals Triangle](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/pascals_triangle/test_pascals_triangle.py) * Perfect Square * [Test Perfect Squares](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/perfect_square/test_perfect_squares.py) * Rectangle Area From fc749ac3a510da9cc65e6031d3b81aa2d04509e1 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Wed, 14 Jan 2026 09:35:25 +0300 Subject: [PATCH 3/8] feat(algorithms, heap): minimum machines to schedule tasks --- algorithms/heap/__init__.py | 0 algorithms/heap/schedule_tasks/README.md | 78 ++++++++++++++++++ algorithms/heap/schedule_tasks/__init__.py | 23 ++++++ ...le_tasks_on_minimum_machines_example_1.png | Bin 0 -> 83551 bytes ...le_tasks_on_minimum_machines_example_2.png | Bin 0 -> 52385 bytes ...le_tasks_on_minimum_machines_example_3.png | Bin 0 -> 61237 bytes ...le_tasks_on_minimum_machines_example_4.png | Bin 0 -> 98809 bytes ...e_tasks_on_minimum_machines_solution_1.png | Bin 0 -> 59748 bytes ..._tasks_on_minimum_machines_solution_10.png | Bin 0 -> 68354 bytes 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algorithms/heap/schedule_tasks/images/solutions/schedule_tasks_on_minimum_machines_solution_7.png create mode 100644 algorithms/heap/schedule_tasks/images/solutions/schedule_tasks_on_minimum_machines_solution_8.png create mode 100644 algorithms/heap/schedule_tasks/images/solutions/schedule_tasks_on_minimum_machines_solution_9.png create mode 100644 algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py diff --git a/algorithms/heap/__init__.py b/algorithms/heap/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/algorithms/heap/schedule_tasks/README.md b/algorithms/heap/schedule_tasks/README.md new file mode 100644 index 00000000..08d56a47 --- /dev/null +++ b/algorithms/heap/schedule_tasks/README.md @@ -0,0 +1,78 @@ +# Schedule Tasks on Minimum Machines + +We are given an input array, tasks, where tasks[i]=[starti ,endi] represents the start and end times of n tasks. Our +goal is to schedule these tasks on machines given the following criteria: + +- A machine can execute only one task at a time. +- A machine can begin executing a new task immediately after completing the previous one. +- An unlimited number of machines are available. + +Find the minimum number of machines required to complete these n tasks. + +## Constraints + +- n == `tasks.length` +- 1 <= `tasks.length` <= 10^3 +- 0 <= `tasksi.start` < `tasksi.end` <= 10^4 + +## Examples + +![Example 1](images/examples/schedule_tasks_on_minimum_machines_example_1.png) +![Example 2](images/examples/schedule_tasks_on_minimum_machines_example_2.png) +![Example 3](images/examples/schedule_tasks_on_minimum_machines_example_3.png) +![Example 4](images/examples/schedule_tasks_on_minimum_machines_example_4.png) + +## Solution + +The core intuition for solving this problem is to allocate tasks to the minimum number of machines by reusing machines +whenever possible. The algorithm efficiently manages machine availability by sorting tasks by their start times and using +a min heap to track end times. If the earliest available machine (top of the heap) finishes before or as a task starts, +it is reused and removed from the heap. Otherwise, a new machine is allocated, and the current task’s end time is pushed +into the heap. The heap size at the end represents the minimum number of machines required. + +Using the intuition above, we implement the algorithm as follows: + +1. Sort the tasks array by the start time of each task to process them in chronological order. +2. Initialize a min heap (machines) to keep track of the end times of tasks currently using machines. +3. Iterate over each task in the sorted tasks array. + - Extract the start and end times of the current task. + - Check if the machine with the earliest finish time is free, i.e., top of machines is less than or equal to the + current task’s start time. If it is, remove it from the heap, as the machine can be reused. + - Push the end time of the current task into the heap, indicating that a machine is now in use until that time. +4. After processing all tasks, return the size of the heap, which represents the minimum number of machines required. + +![Solution 1](images/solutions/schedule_tasks_on_minimum_machines_solution_1.png) +![Solution 2](images/solutions/schedule_tasks_on_minimum_machines_solution_2.png) +![Solution 3](images/solutions/schedule_tasks_on_minimum_machines_solution_3.png) +![Solution 4](images/solutions/schedule_tasks_on_minimum_machines_solution_4.png) +![Solution 5](images/solutions/schedule_tasks_on_minimum_machines_solution_5.png) +![Solution 6](images/solutions/schedule_tasks_on_minimum_machines_solution_6.png) +![Solution 7](images/solutions/schedule_tasks_on_minimum_machines_solution_7.png) +![Solution 8](images/solutions/schedule_tasks_on_minimum_machines_solution_8.png) +![Solution 9](images/solutions/schedule_tasks_on_minimum_machines_solution_9.png) +![Solution 10](images/solutions/schedule_tasks_on_minimum_machines_solution_10.png) +![Solution 11](images/solutions/schedule_tasks_on_minimum_machines_solution_11.png) +![Solution 12](images/solutions/schedule_tasks_on_minimum_machines_solution_12.png) +![Solution 13](images/solutions/schedule_tasks_on_minimum_machines_solution_13.png) +![Solution 14](images/solutions/schedule_tasks_on_minimum_machines_solution_14.png) +![Solution 15](images/solutions/schedule_tasks_on_minimum_machines_solution_15.png) +![Solution 16](images/solutions/schedule_tasks_on_minimum_machines_solution_16.png) +![Solution 17](images/solutions/schedule_tasks_on_minimum_machines_solution_17.png) +![Solution 18](images/solutions/schedule_tasks_on_minimum_machines_solution_18.png) +![Solution 19](images/solutions/schedule_tasks_on_minimum_machines_solution_19.png) + +### Time Complexity + +The time complexity of the above algorithm is O(nlogn), where n is the number of tasks represented by the length of the +tasks array. This is because: + +- Sorting the array takes O(nlogn). +- The total cost for heap operations is O(nlogn) because we process n tasks, and each operation on the min-heap has a + time complexity of O(logn). + +Therefore, the overall time complexity is O(nlogn). + +### Space Complexity + +The algorithm’s space complexity is O(n) because the min heap can grow up to a maximum size of n if every task requires +a separate machine. diff --git a/algorithms/heap/schedule_tasks/__init__.py b/algorithms/heap/schedule_tasks/__init__.py new file mode 100644 index 00000000..d84a1c15 --- /dev/null +++ b/algorithms/heap/schedule_tasks/__init__.py @@ -0,0 +1,23 @@ +from typing import List +from heapq import heappush, heappop, heapify + + +def minimum_machines(tasks: List[List[int]]) -> int: + # sort tasks by their start time in place, Time cost is O(n log(n)) with space cost being O(n) due to timsort + tasks.sort(key=lambda x: x[0]) + + # initialize a min heap to keep track of the end times + machines: List[int] = [] + heapify(machines) + + for current_task in tasks: + task_start, task_end = current_task + # check if a machine with the earliest finish time is free + if machines and machines[0] <= task_start: + # reuse machine + heappop(machines) + + # assign a machine to the current task + heappush(machines, task_end) + # Return the size of the heap representing the minimum number of machines required + return len(machines) diff --git a/algorithms/heap/schedule_tasks/images/examples/schedule_tasks_on_minimum_machines_example_1.png b/algorithms/heap/schedule_tasks/images/examples/schedule_tasks_on_minimum_machines_example_1.png new file mode 100644 index 0000000000000000000000000000000000000000..fb416115892d3c272b6d5730475033a994bb36ee GIT binary patch literal 83551 zcmeEucT`i`_AVez5D*cOj-Y@bMXIy_(nOjR=}qY+poAU>(tA;mB2|hYRl1=g3P=kb z=^`aS2tA>M@;2w*UpXGfc>lk5Ge(k~T~?WEt-0p><~I}hL{o)=jDZXf5066ik)jSB z9^nce9zhH#F>pppq5d8o9$BS>g2EG31qHSzZmzZt&Ng^>k0Rfukmw~&UVF85UKk#7 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z3;9@f5tRNpKs&S*#riy94-YFlIXNM^lByKXZy3xP16xZoSC=OQ0dOp7B;p*om?DH) z&iIB@EX0iL-d=b8h>;AZ>%q;Z&;9ykVA{DWziTr5Fp;u1J8U|uav`EfA@GAdfVAI8 zWgxs|X>Dz1X=%w4*$vsCK&u?SQIn6y6m4M~lOVfoTU&2`FdT30cIc_vW4nK?iPBbk z>|pu26D1Mlv~J%QKd0C=Um4mnWq}KyG8D!QWtCre-rVyJsHIo2^T7Xk*F8lTu?7;X zirF(x(yN}HjRUq(9#~l<>h;|Z_r13CCcbyC_vXGJ}rRJW<*B=;#Na)AVj69B8Ji?zay5E>J|U1y&d?7X&uF z2@%+Uipu}aPSWAs@MqN8Rnz~^LF~we$l$`y{TNL}|I51va^c;li&2p3tr|1(@Bi(# ai!#B18$ayU&m&{t&(_MpvdY}+ Date: Wed, 14 Jan 2026 06:35:46 +0000 Subject: [PATCH 4/8] updating DIRECTORY.md --- DIRECTORY.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 8757088a..60ece2b8 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -137,6 +137,9 @@ * [Test Find Min Arrows](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/min_arrows/test_find_min_arrows.py) * Spread Stones * [Test Minimum Moves To Spread Stones](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/spread_stones/test_minimum_moves_to_spread_stones.py) + * Heap + * Schedule Tasks + * [Test Schedule Tasks On Minimum Machines](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py) * Huffman * [Decoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/decoding.py) * [Encoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/encoding.py) From 6e149e5d5787a3a66c150b27f8bc6e4a88d62b2a Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Wed, 14 Jan 2026 13:21:56 +0300 Subject: [PATCH 5/8] Update algorithms/dynamic_programming/palindromic_substring/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/dynamic_programming/palindromic_substring/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/dynamic_programming/palindromic_substring/README.md b/algorithms/dynamic_programming/palindromic_substring/README.md index ee9154e4..1ac8b51a 100644 --- a/algorithms/dynamic_programming/palindromic_substring/README.md +++ b/algorithms/dynamic_programming/palindromic_substring/README.md @@ -65,7 +65,7 @@ To recap, the solution to this problem can be divided into the following five ma 1. We count all one-letter substrings since any one-letter string is always a palindrome. These results are also stored in a lookup table to be used later. 2. Next, the algorithm checks all two-letter substrings and updates the count and the lookup table accordingly. -3. After these base cases, the algorithm checks all possible substrings of lengths greater than three. However, it only +3. After these base cases, the algorithm checks all possible substrings of lengths greater than two. However, it only compares the first and last characters, and the rest of the substring is checked using the lookup table. 4. Whenever a palindromic substring is found, the count and the lookup table are updated accordingly. 5. After checking all possible substrings, the algorithm terminates and returns the count of the palindromic substrings. From 97a8c1666d79715ef82b7ebfea99c37fe69d4b8e Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Wed, 14 Jan 2026 13:22:10 +0300 Subject: [PATCH 6/8] Update algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- .../test_longest_palindromic_substring.py | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py b/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py index b270d4d7..989ca9fc 100644 --- a/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py +++ b/algorithms/dynamic_programming/palindromic_substring/test_longest_palindromic_substring.py @@ -5,6 +5,10 @@ ) LONGEST_PALINDROMIC_SUBSTRING_TEST_CASES = [ + ("", ""), + ("a", "a"), + ("aab", "aa"), + ("baa", "aa"), ("mnm", "mnm"), ("zzz", "zzz"), ("cat", "c"), From 4d46a381b5905810ac75576eaeed7fab62c60dce Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Wed, 14 Jan 2026 13:22:35 +0300 Subject: [PATCH 7/8] Update algorithms/heap/schedule_tasks/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/heap/schedule_tasks/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/heap/schedule_tasks/README.md b/algorithms/heap/schedule_tasks/README.md index 08d56a47..24daf5e4 100644 --- a/algorithms/heap/schedule_tasks/README.md +++ b/algorithms/heap/schedule_tasks/README.md @@ -13,7 +13,7 @@ Find the minimum number of machines required to complete these n tasks. - n == `tasks.length` - 1 <= `tasks.length` <= 10^3 -- 0 <= `tasksi.start` < `tasksi.end` <= 10^4 +- 0 <= `tasks[i].start` < `tasks[i].end` <= 10^4 ## Examples From 65dc2500230665954478e4c3550f9776ac238812 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Wed, 14 Jan 2026 13:23:58 +0300 Subject: [PATCH 8/8] test: fix failing test --- .../schedule_tasks/test_schedule_tasks_on_minimum_machines.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py b/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py index 7d46e6fb..07bdc218 100644 --- a/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py +++ b/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py @@ -14,7 +14,7 @@ ([[1, 3], [3, 5], [5, 9], [9, 12], [12, 13], [13, 16], [16, 17]], 1), ([[1, 3], [2, 6], [5, 9], [4, 7], [8, 10], [8, 10], [12, 15]], 3), ([[5, 6], [5, 6], [5, 6], [5, 6], [6, 7]], 4), - ([[5, 6], [6, 7], [1, 7], [10, 14], [8, 13]], 4), + ([[5, 6], [6, 7], [1, 7], [10, 14], [8, 13]], 2), ]

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