From c95ac53c1b56cb92beaec014df3c7754caa34c38 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 12:19:32 +0300 Subject: [PATCH 01/11] docs(algorithms, two-pointers): three sum documentation --- .../intervals/insert_interval/README.md | 18 +++--- algorithms/two_pointers/three_sum/README.md | 58 ++++++++++++++++++ algorithms/two_pointers/three_sum/__init__.py | 30 ++++++--- .../images/solutions/three_sum_solution_1.png | Bin 0 -> 39132 bytes .../solutions/three_sum_solution_10.png | Bin 0 -> 39651 bytes .../solutions/three_sum_solution_11.png | Bin 0 -> 38749 bytes .../solutions/three_sum_solution_12.png | Bin 0 -> 33886 bytes .../solutions/three_sum_solution_13.png | Bin 0 -> 39211 bytes .../solutions/three_sum_solution_14.png | Bin 0 -> 38405 bytes .../solutions/three_sum_solution_15.png | Bin 0 -> 35571 bytes .../solutions/three_sum_solution_16.png | Bin 0 -> 39358 bytes .../solutions/three_sum_solution_17.png | Bin 0 -> 40495 bytes .../solutions/three_sum_solution_18.png | Bin 0 -> 33294 bytes .../solutions/three_sum_solution_19.png | Bin 0 -> 30648 bytes .../images/solutions/three_sum_solution_2.png | Bin 0 -> 26538 bytes .../images/solutions/three_sum_solution_3.png | Bin 0 -> 25334 bytes .../images/solutions/three_sum_solution_4.png | Bin 0 -> 33102 bytes .../images/solutions/three_sum_solution_5.png | Bin 0 -> 36614 bytes .../images/solutions/three_sum_solution_6.png | Bin 0 -> 36663 bytes .../images/solutions/three_sum_solution_7.png | Bin 0 -> 41532 bytes .../images/solutions/three_sum_solution_8.png | Bin 0 -> 37740 bytes .../images/solutions/three_sum_solution_9.png | Bin 0 -> 38121 bytes .../two_pointers/three_sum/test_three_sum.py | 34 +++++----- 23 files changed, 104 insertions(+), 36 deletions(-) create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_1.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_10.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_11.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_12.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_13.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_14.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_15.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_16.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_17.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_18.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_19.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_2.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_3.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_4.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_5.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_6.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_7.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_8.png create mode 100644 algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_9.png diff --git a/algorithms/intervals/insert_interval/README.md b/algorithms/intervals/insert_interval/README.md index 2694b935..080dd229 100644 --- a/algorithms/intervals/insert_interval/README.md +++ b/algorithms/intervals/insert_interval/README.md @@ -25,17 +25,17 @@ Return the updated list of intervals. ## Solution -We first want to create a new list merged to store the merged intervals we will return at the end. +We first want to create a new list `merged` to store the merged intervals we will return at the end. This solution operates in 3 phases: -1. Add all the intervals ending before newInterval starts to merged. -2. Merge all overlapping intervals with newInterval and add that merged interval to merged. -3. Add all the intervals starting after newInterval to merged. +1. Add all the intervals ending before `newInterval` starts to `merged`. +2. Merge all overlapping intervals with `newInterval` and add that merged interval to `merged`. +3. Add all the intervals starting after `newInterval` to `merged`. ### Phase 1 -In this phase, we add all the intervals that end before newInterval starts to merged. This involves iterating through the -intervals list until the current interval no longer ends before newInterval starts (i.e. intervals[i][1] >= newInterval[0]). +In this phase, we add all the intervals that end before `newInterval` starts to `merged`. This involves iterating through the +`intervals` list until the current interval no longer ends before `newInterval` starts (i.e. `intervals[i][1] >= newInterval[0]`). ![Solution 1](./images/solutions/insert_interval_solution_1.png) ![Solution 2](./images/solutions/insert_interval_solution_2.png) @@ -43,9 +43,9 @@ intervals list until the current interval no longer ends before newInterval star ### Phase 2 In this phase, we merge all the intervals that overlap with newInterval together into a single interval by updating -newInterval to be the minimum start and maximum end of all the overlapping intervals. This involves iterating through -the intervals list until the current interval starts after newInterval ends (i.e. intervals[i][0] > newInterval[1]). -When that condition is met, we add newInterval to merged and move onto phase 3. +`newInterval` to be the minimum start and maximum end of all the overlapping intervals. This involves iterating through +the intervals list until the current interval starts after `newInterval` ends (i.e. `intervals[i][0] > newInterval[1]`). +When that condition is met, we add `newInterval` to merged and move onto phase 3. ![Solution 3](./images/solutions/insert_interval_solution_3.png) ![Solution 4](./images/solutions/insert_interval_solution_4.png) diff --git a/algorithms/two_pointers/three_sum/README.md b/algorithms/two_pointers/three_sum/README.md index a8a8759e..50c28079 100644 --- a/algorithms/two_pointers/three_sum/README.md +++ b/algorithms/two_pointers/three_sum/README.md @@ -32,3 +32,61 @@ Input: nums = [0,0,0] Output: [[0,0,0]] Explanation: The only possible triplet sums up to 0. ``` + +## Solution + +We can leverage the two-pointer technique to solve this problem by first sorting the array. We can then iterate through +each element in the array. The problem then reduces to finding two numbers in the rest of the array that sum to the +negative of the current element, which follows the same logic as the Two Sum (Sorted Array) problem. + +![Solution 1](./images/solutions/three_sum_solution_1.png) + +Since our first triplet sums to 0, we can add it to our result set. + +![Solution 2](./images/solutions/three_sum_solution_2.png) +![Solution 3](./images/solutions/three_sum_solution_3.png) +![Solution 4](./images/solutions/three_sum_solution_4.png) +![Solution 5](./images/solutions/three_sum_solution_5.png) +![Solution 6](./images/solutions/three_sum_solution_6.png) + +### Avoiding Duplicates + +As soon as we find a triplet that sums to 0, we can add it to our result set. We then have to move our left and right +pointers to look for the next triplet while avoiding duplicate triplets. We can do this by moving the left and right +pointers until they point to different numbers than the ones they were pointing to before. +Here we move the left pointer once until it reaches the last -1 in the array. Then, we can move both the left and right +pointers so that they both point to new numbers. + +![Solution 7](./images/solutions/three_sum_solution_7.png) +![Solution 8](./images/solutions/three_sum_solution_8.png) + +Here we can do another iteration of the Two Sum problem using the new positions of the left and right pointers. + +![Solution 9](./images/solutions/three_sum_solution_9.png) +![Solution 10](./images/solutions/three_sum_solution_10.png) +![Solution 11](./images/solutions/three_sum_solution_11.png) + +At this point our left and right pointers have crossed, so we can move our iterator to the next number in the array. + +### Avoiding Duplicates II + +In this case, since the next number in the array is the same as the previous number, we can skip it. We can do this by +moving our iterator until it points to a new number. + +![Solution 12](./images/solutions/three_sum_solution_12.png) +![Solution 13](./images/solutions/three_sum_solution_13.png) +![Solution 14](./images/solutions/three_sum_solution_14.png) + +And we're ready to start the Two Sum algorithm again, so we reset our left and right pointers, and start the algorithm. + +![Solution 15](./images/solutions/three_sum_solution_15.png) +![Solution 16](./images/solutions/three_sum_solution_16.png) +![Solution 17](./images/solutions/three_sum_solution_17.png) + +### Termination + +Our algorithm terminates when i reaches the 3rd to last element in the array (i.e., i < n - 2). This is because we need +at least 2 more elements after i for left and right to form a triplet. + +![Solution 18](./images/solutions/three_sum_solution_18.png) +![Solution 19](./images/solutions/three_sum_solution_19.png) diff --git a/algorithms/two_pointers/three_sum/__init__.py b/algorithms/two_pointers/three_sum/__init__.py index a0978d97..a0c0ca13 100644 --- a/algorithms/two_pointers/three_sum/__init__.py +++ b/algorithms/two_pointers/three_sum/__init__.py @@ -4,9 +4,14 @@ def three_sum(nums: List[int]) -> List[List[int]]: """ Complexity Analysis: + Ww assume that n is the length of the input array - Time Complexity: O(nlog(n)) + O(n^2) = O(n^2) the O(nlog(n)) is due to sorting - Space Complexity: O(1) as no extra space is taken up + Time Complexity: O(nlog(n)) + O(n^2) = O(n^2) the O(nlog(n)) is due to sorting, overall, the time complexity is O(n²). + This is due to the nested loops in the algorithm. We perform n iterations of the outer loop, and each iteration + takes O(n) time to use the two-pointer technique. + + Space Complexity: O(n²) as no extra space is taken up. We need to store all distinct triplets that sum to 0, which + can be at most O(n²) triplets. Args: nums (list): input list of integers @@ -14,24 +19,33 @@ def three_sum(nums: List[int]) -> List[List[int]]: list: list of lists of integers """ result = [] - # Time Complexity: O(nlog(n)) + # Time Complexity: O(nlog(n)) sorting in place. This may incur space complexity of O(n) due to Python's timesort + # using temporary storage to handle the in place sorting nums.sort() for idx, num in enumerate(nums): + # Increment to avoid duplicates if idx > 0 and num == nums[idx - 1]: continue left, right = idx + 1, len(nums) - 1 while left < right: - sum_ = num + nums[left] + nums[right] - if sum_ > 0: + total = num + nums[left] + nums[right] + if total > 0: right -= 1 - elif sum_ < 0: + elif total < 0: left += 1 else: + # add the triplet result.append([num, nums[left], nums[right]]) - left += 1 - while nums[left] == nums[left - 1] and left < right: + + # move the left pointer to avoid duplicates while it is still less than the right + while left < right and nums[left] == nums[left + 1]: left += 1 + while left < right and nums[right] == nums[right - 1]: + right -= 1 + left += 1 + right -= 1 + return result diff --git a/algorithms/two_pointers/three_sum/images/solutions/three_sum_solution_1.png 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b/algorithms/two_pointers/three_sum/test_three_sum.py index 529504a0..f2b41b8c 100644 --- a/algorithms/two_pointers/three_sum/test_three_sum.py +++ b/algorithms/two_pointers/three_sum/test_three_sum.py @@ -1,27 +1,23 @@ import unittest - +from typing import List +from parameterized import parameterized from algorithms.two_pointers.three_sum import three_sum +THREE_SUM_TEST_CASES = [ + ([-1, 0, 1, 2, -1, -4], [[-1, -1, 2], [-1, 0, 1]]), + ([0, 1, 1], []), + ([0, 0, 0], [[0, 0, 0]]), + ([-1, 0, 1, 2, -1, -1], [[-1, -1, 2], [-1, 0, 1]]), + ([-1, 0, 1, 2, -1, -4], [[-1, -1, 2], [-1, 0, 1]]), + ([-1, 0, 1, 2, -1, -4, 2], [[-1, -1, 2], [-1, 0, 1], [-4, 2, 2]]), + ([-1, -1, 0, 1, 1, 1, 2], [[-1, -1, 2], [-1, 0, 1]]), + ([-1, 0, 1, 2, -1, -4, -1, 2, 1], [[-1, -1, 2], [-1, 0, 1], [-4, 2, 2]]), +] -class ThreeSumTestCases(unittest.TestCase): - def test_one(self): - """Should return [[-1, -1, 2], [-1, 0, 1]] for nums = [-1, 0, 1, 2, -1, -4]""" - nums = [-1, 0, 1, 2, -1, -4] - expected = [[-1, -1, 2], [-1, 0, 1]] - actual = three_sum(nums) - self.assertEqual(expected, actual) - - def test_two(self): - """Should return [] for nums = [0, 1, 1]""" - nums = [0, 1, 1] - expected = [] - actual = three_sum(nums) - self.assertEqual(expected, actual) - def test_three(self): - """Should return [[0,0,0]] for nums = [0,0,0]""" - nums = [0, 0, 0] - expected = [[0, 0, 0]] +class ThreeSumTestCases(unittest.TestCase): + @parameterized.expand(THREE_SUM_TEST_CASES) + def test_three_sum(self, nums: List[int], expected: List[List[int]]): actual = three_sum(nums) self.assertEqual(expected, actual) From 6b00d0eda206dd90e430b1040fec28603b838e79 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 13:26:59 +0300 Subject: [PATCH 02/11] feat(algorithms, two-pointers): triangle numbers --- .../two_pointers/triangle_numbers/README.md | 83 ++++++++++++++++++ .../two_pointers/triangle_numbers/__init__.py | 51 +++++++++++ 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algorithms/two_pointers/triangle_numbers/images/solutions/triangle_numbers_solution_8.png create mode 100644 algorithms/two_pointers/triangle_numbers/images/solutions/triangle_numbers_solution_9.png create mode 100644 algorithms/two_pointers/triangle_numbers/test_triangle_numbers.py diff --git a/algorithms/two_pointers/triangle_numbers/README.md b/algorithms/two_pointers/triangle_numbers/README.md new file mode 100644 index 00000000..364e6dd2 --- /dev/null +++ b/algorithms/two_pointers/triangle_numbers/README.md @@ -0,0 +1,83 @@ +# Triangle Numbers + +Write a function to count the number of triplets in an integer array nums that could form the sides of a triangle. For +three sides to form a valid triangle, the sum of any two sides must be greater than the third side. The triplets do not +need to be unique. + +## Examples + +```text +Input: +nums = [11,4,9,6,15,18] + +Output: +10 + +Explanation: Valid combinations are... + +4, 15, 18 +6, 15, 18 +9, 15, 18 +11, 15, 18 +9, 11, 18 +6, 11, 15 +9, 11, 15 +4, 6, 9 +``` + +## Solution + +In order for a triplet to be valid lengths of a triangle, the sum of any two sides must be greater than the third side. +By sorting the array, we can leverage the two-pointer technique to count all valid triplets in O(n2) time and O(1) space. +The key to this question is realizing that if we sort three numbers from smallest to largest (say a ≤ b ≤ c), we only +need to check if a + b > c. If this condition holds, the other two conditions (a + c > b and b + c > a) are automatically +satisfied because c ≥ b and b ≥ a. For example, with 4, 8, 9, if 4 + 8 > 9 is true, then we have a valid triplet. + +![Solution 1](./images/solutions/triangle_numbers_solution_1.png) + +But not only that, triplets where the smallest number is between 4 and 8 are also valid triplets. + +![Solution 2](./images/solutions/triangle_numbers_solution_2.png) + +This means that if we sort the input array, and then iterate from the end of the array to the beginning, we can use the +two-pointer technique to efficiently count all valid triplets. + +![Solution 3](./images/solutions/triangle_numbers_solution_3.png) + +The pointers i, left, and right represent the current triplet we are considering. If nums[left] + nums[right] > nums[i] +then we know there are a total of right - left valid triplets, since all triplets between left and right are also valid +triplets. We can then decrement right to check for the valid triplets that can be made by decreasing the middle value. + +![Solution 4](./images/solutions/triangle_numbers_solution_4.png) +![Solution 5](./images/solutions/triangle_numbers_solution_5.png) +![Solution 6](./images/solutions/triangle_numbers_solution_6.png) +![Solution 7](./images/solutions/triangle_numbers_solution_7.png) + +When nums[left] + nums[right] < nums[i], we know that all triplets between left and right are also invalid, so we +increment left to look for a larger smallest value. + +![Solution 8](./images/solutions/triangle_numbers_solution_8.png) + +Each time left and right cross, we decrement i and reset left and right to their positions at opposite ends of the array. +This happens until i is less than 2, at which point we have counted all valid triplets. + +![Solution 9](./images/solutions/triangle_numbers_solution_9.png) +![Solution 10](./images/solutions/triangle_numbers_solution_10.png) +![Solution 11](./images/solutions/triangle_numbers_solution_11.png) +![Solution 12](./images/solutions/triangle_numbers_solution_12.png) +![Solution 13](./images/solutions/triangle_numbers_solution_13.png) +![Solution 14](./images/solutions/triangle_numbers_solution_14.png) +![Solution 15](./images/solutions/triangle_numbers_solution_15.png) +![Solution 16](./images/solutions/triangle_numbers_solution_16.png) +![Solution 17](./images/solutions/triangle_numbers_solution_17.png) +![Solution 18](./images/solutions/triangle_numbers_solution_18.png) +![Solution 19](./images/solutions/triangle_numbers_solution_19.png) +![Solution 20](./images/solutions/triangle_numbers_solution_20.png) +![Solution 21](./images/solutions/triangle_numbers_solution_21.png) +![Solution 22](./images/solutions/triangle_numbers_solution_22.png) +![Solution 23](./images/solutions/triangle_numbers_solution_23.png) +![Solution 24](./images/solutions/triangle_numbers_solution_24.png) +![Solution 25](./images/solutions/triangle_numbers_solution_25.png) +![Solution 26](./images/solutions/triangle_numbers_solution_26.png) +![Solution 27](./images/solutions/triangle_numbers_solution_27.png) +![Solution 28](./images/solutions/triangle_numbers_solution_28.png) diff --git a/algorithms/two_pointers/triangle_numbers/__init__.py b/algorithms/two_pointers/triangle_numbers/__init__.py new file mode 100644 index 00000000..2d40373c --- /dev/null +++ b/algorithms/two_pointers/triangle_numbers/__init__.py @@ -0,0 +1,51 @@ +from typing import List + + +def triangle_number(heights: List[int]) -> int: + """ + Finds the count of valid triangles that can be formed from the given input of numbers. A valid triangle is a triangle + which has any two sides whose sum is greater than the third side. This assumes that it is okay to manipulate the + input list. Therefore callers of this function should be aware that the input list is manipulated in place. + + Args: + heights (list): list of integers that represent sides of a triangle + Returns: + int: number of valid triangles that can be formed + """ + # If there are no heights, or we have an empty list, return 0 early as no valid triangles can be formed here. + if not heights: + return 0 + + # Sorts the heights in place. This incurs a time complexity cost of O(n log(n)) and space cost of O(n) as this sorting + # requires temporary storage using Python's timsort + heights.sort() + + # Keeps track of number of valid triangles that can be formed + count = 0 + + # Iterate through the list starting from the back, idx will be at the last position, this will be the third pointer + for idx in range(len(heights) - 1, 1, -1): + # Initialize the two pointers to keep track of the other two indices that will point to the two other numbers that + # can form a valid triangle. + left = 0 + right = idx - 1 + + # This is a micro-optimization to get the largest side and use it in the loop below + largest_side = heights[idx] + + while left < right: + # A valid triplet is found by satisfying the condition a + b > c. If this condition holds, then the other + # two conditions hold as well, a + c > b and b + c > a. + is_valid_triplet = heights[left] + heights[right] > largest_side + if is_valid_triplet: + # The numbers between the right and left pointers form valid triplets with the number at the idx position + # we find all the possible triplets(triangles) that can be formed by finding the difference. + count += right - left + # we decrement right to check if there are valid triplets that can be formed by decreasing the middle valid + right -= 1 + else: + # Increase the left to find the next maximum minimum number that can form a valid triplet + left += 1 + + # return the count of the triangles that can be formed + return count diff --git a/algorithms/two_pointers/triangle_numbers/images/solutions/triangle_numbers_solution_1.png b/algorithms/two_pointers/triangle_numbers/images/solutions/triangle_numbers_solution_1.png new file mode 100644 index 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zINz5rjSFl%c#a*s6@1;uuEA>rg$=Y8Ncl7f)%8FfyHUArj5kumd?Qy4--lF?*{^D(0>xRs1`UFg;jv0W(C z-1rp9m+EPT!S*30-q*i}z-sx^45A#b&@wH&0&Jv_Vx}px-H_F$&vP__oG(!ud|J|ph!d1->qB?~03G*pg)!c$5yg_|yt!I;#OlTUro z?g7P*_%L2UufN}hCG!y0a%1)~A;JBmOvOOtDlyiZd`Gv(r>6UpOMhRzk||_cPT4_z zFaqwr1?>8N2TINB8v8Dwcxus_F`zAlB1f(P=+!9z_Pm~vasi+N>H>3*mw5*DY8V*$ z>unQ*sWL6o7htP~%kLrQs}r;|z_kp`;Wyc6=nsGk4$^Nk(lWiU06r&g=LXQ9eRU0- z9rf(<6<{~Z1=tdKC@aPt33fS6u#m{iknVRoNX6P}nad+U@9zO1>{~OS(Dat|)L;G0 zMtr~o@Dg%TCjd_fRRFel?cl)wn~r!T6-c>V(`YyD-zab1 z3qal1(^6wpe}lYsoWSC|SF7EB1I2OYfW9Ho$wB7aZw&X35dRmN2tTHC*SmU?F($ Date: Thu, 8 Jan 2026 10:27:20 +0000 Subject: [PATCH 03/11] updating DIRECTORY.md --- DIRECTORY.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 3aabf9af..6dd350af 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -224,6 +224,8 @@ * [Test Sort Colors](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/sort_colors/test_sort_colors.py) * Three Sum * [Test Three Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/three_sum/test_three_sum.py) + * Triangle Numbers + * [Test Triangle Numbers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/triangle_numbers/test_triangle_numbers.py) * Unique Bsts * [Unique Bsts](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/unique_bsts/unique_bsts.py) * Word Count From 8ccae814a433cf1a7e5f43bfb8830e2c98a62a3e Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 14:07:08 +0300 Subject: [PATCH 04/11] refactor(algorithms, two-pointers, move-zeroes): move algorithm to correct package --- .../two_pointers}/array_3_pointers/README.md | 0 .../array_3_pointers/__init__.py | 0 .../array_3_pointers/test_array_3_pointers.py | 0 algorithms/two_pointers/move_zeroes/README.md | 44 +++++++++++++++ .../two_pointers}/move_zeroes/__init__.py | 11 ++-- .../solutions/move_zeroes_solution_1.png | 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puzzles/arrays/move_zeroes/README.md delete mode 100644 puzzles/arrays/move_zeroes/test_move_zeroes.py diff --git a/puzzles/arrays/array_3_pointers/README.md b/algorithms/two_pointers/array_3_pointers/README.md similarity index 100% rename from puzzles/arrays/array_3_pointers/README.md rename to algorithms/two_pointers/array_3_pointers/README.md diff --git a/puzzles/arrays/array_3_pointers/__init__.py b/algorithms/two_pointers/array_3_pointers/__init__.py similarity index 100% rename from puzzles/arrays/array_3_pointers/__init__.py rename to algorithms/two_pointers/array_3_pointers/__init__.py diff --git a/puzzles/arrays/array_3_pointers/test_array_3_pointers.py b/algorithms/two_pointers/array_3_pointers/test_array_3_pointers.py similarity index 100% rename from puzzles/arrays/array_3_pointers/test_array_3_pointers.py rename to algorithms/two_pointers/array_3_pointers/test_array_3_pointers.py diff --git a/algorithms/two_pointers/move_zeroes/README.md b/algorithms/two_pointers/move_zeroes/README.md new file mode 100644 index 00000000..c96f9be7 --- /dev/null +++ b/algorithms/two_pointers/move_zeroes/README.md @@ -0,0 +1,44 @@ +# Move Zeroes + +Given an integer array nums, move all 0's to the end of it while maintaining the relative order of the non-zero +elements. + +Note that you must do this in-place without making a copy of the array. + +```plain + +Example 1: + +Input: nums = [0,1,0,3,12] +Output: [1,3,12,0,0] +Example 2: + +Input: nums = [0] +Output: [0] +``` + +## Related Topics + +- Array +- Two Pointers + +## Solution + +We can solve this problem by keeping a pointer i that iterates through the array and another pointer nextNonZero that +points to the position where the next non-zero element should be placed. We can then swap the elements at i and nextNonZero +if the element at i is non-zero. This way, we can maintain the relative order of the non-zero elements while moving all +the zeroes to the end of the array. + +![Solution 1](./images/solutions/move_zeroes_solution_1.png) +![Solution 2](./images/solutions/move_zeroes_solution_2.png) +![Solution 3](./images/solutions/move_zeroes_solution_3.png) +![Solution 4](./images/solutions/move_zeroes_solution_4.png) +![Solution 5](./images/solutions/move_zeroes_solution_5.png) +![Solution 6](./images/solutions/move_zeroes_solution_6.png) +![Solution 7](./images/solutions/move_zeroes_solution_7.png) +![Solution 8](./images/solutions/move_zeroes_solution_8.png) +![Solution 9](./images/solutions/move_zeroes_solution_9.png) +![Solution 10](./images/solutions/move_zeroes_solution_10.png) +![Solution 11](./images/solutions/move_zeroes_solution_1.png) +![Solution 12](./images/solutions/move_zeroes_solution_12.png) +![Solution 13](./images/solutions/move_zeroes_solution_13.png) diff --git a/puzzles/arrays/move_zeroes/__init__.py b/algorithms/two_pointers/move_zeroes/__init__.py similarity index 90% rename from puzzles/arrays/move_zeroes/__init__.py rename to algorithms/two_pointers/move_zeroes/__init__.py index ca761d99..04c1a2a6 100644 --- a/puzzles/arrays/move_zeroes/__init__.py +++ b/algorithms/two_pointers/move_zeroes/__init__.py @@ -19,11 +19,12 @@ def move_zeroes(nums: List[int]) -> None: if len(nums) == 1: return - left_pointer = 0 - for current in range(len(nums)): - if nums[current] != 0: - nums[left_pointer], nums[current] = nums[current], nums[left_pointer] - left_pointer += 1 + next_non_zero = 0 + for idx in range(len(nums)): + if nums[idx] != 0: + if idx != next_non_zero: + nums[next_non_zero], nums[idx] = nums[idx], nums[next_non_zero] + next_non_zero += 1 def move_zeroes_one(nums: List[int]) -> None: diff --git a/algorithms/two_pointers/move_zeroes/images/solutions/move_zeroes_solution_1.png b/algorithms/two_pointers/move_zeroes/images/solutions/move_zeroes_solution_1.png new file mode 100644 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--git a/DIRECTORY.md b/DIRECTORY.md index 6dd350af..0a0054b5 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -19,10 +19,6 @@ * [Test Sorted Squared Array](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/arrays/sorted_squared_array/test_sorted_squared_array.py) * Subsequence * [Test Is Valid Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/arrays/subsequence/test_is_valid_subsequence.py) - * Two Sum - * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/arrays/two_sum/test_two_sum.py) - * Two Sum Less K - * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/arrays/two_sum_less_k/test_two_sum.py) * Backtracking * Combination * [Test Combination 2](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/backtracking/combination/test_combination_2.py) @@ -210,10 +206,14 @@ * Taxi Numbers * [Taxi Numbers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/taxi_numbers/taxi_numbers.py) * Two Pointers + * Array 3 Pointers + * [Test Array 3 Pointers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/array_3_pointers/test_array_3_pointers.py) * Find Sum Of Three * [Test Find Sum Of Three](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/find_sum_of_three/test_find_sum_of_three.py) * Merge Sorted Arrays * [Test Merge Sorted Arrays](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/merge_sorted_arrays/test_merge_sorted_arrays.py) + * Move Zeroes + * [Test Move Zeroes](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/move_zeroes/test_move_zeroes.py) * Next Permutation * [Test Next Permutation](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/next_permutation/test_next_permutation.py) * Pair With Sum In Array @@ -226,6 +226,10 @@ * [Test Three Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/three_sum/test_three_sum.py) * Triangle Numbers * [Test Triangle Numbers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/triangle_numbers/test_triangle_numbers.py) + * Two Sum + * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/two_sum/test_two_sum.py) + * Two Sum Less K + * [Test Two Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/two_sum_less_k/test_two_sum.py) * Unique Bsts * [Unique Bsts](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/unique_bsts/unique_bsts.py) * Word Count @@ -579,8 +583,6 @@ * Allergies * [Test Allergies](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/allergies/test_allergies.py) * Arrays - * Array 3 Pointers - * [Test Array 3 Pointers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/array_3_pointers/test_array_3_pointers.py) * Can Place Flowers * [Test Can Place Flowers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/can_place_flowers/test_can_place_flowers.py) * Candy @@ -607,8 +609,6 @@ * [Test Max Average Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/maximum_average_subarray/test_max_average_subarray.py) * Maxlen Contiguous Binary Subarray * [Test Maxlen Contiguous Binary Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/maxlen_contiguous_binary_subarray/test_maxlen_contiguous_binary_subarray.py) - * Move Zeroes - * [Test Move Zeroes](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/move_zeroes/test_move_zeroes.py) * Product Of Array Except Self * [Test Product Except Self](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/product_of_array_except_self/test_product_except_self.py) * Rain Water Trapped From b1d3bafda01490f1a587035ea03ba769b322b969 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 14:08:32 +0300 Subject: [PATCH 06/11] chore(docstring): fix typo Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/two_pointers/three_sum/__init__.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/two_pointers/three_sum/__init__.py b/algorithms/two_pointers/three_sum/__init__.py index a0c0ca13..012cc0fc 100644 --- a/algorithms/two_pointers/three_sum/__init__.py +++ b/algorithms/two_pointers/three_sum/__init__.py @@ -4,7 +4,7 @@ def three_sum(nums: List[int]) -> List[List[int]]: """ Complexity Analysis: - Ww assume that n is the length of the input array + We assume that n is the length of the input array Time Complexity: O(nlog(n)) + O(n^2) = O(n^2) the O(nlog(n)) is due to sorting, overall, the time complexity is O(n²). This is due to the nested loops in the algorithm. We perform n iterations of the outer loop, and each iteration From 6aada08a170f877a3ee1f69e122cb71f184cb440 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 14:40:39 +0300 Subject: [PATCH 07/11] refactor(algorithms, two-pointers, sort-colors): add documentation and code cleanup --- algorithms/two_pointers/sort_colors/README.md | 57 ++++++++ .../two_pointers/sort_colors/__init__.py | 42 ++---- .../solutions/sort_colors_solution_1.png | Bin 0 -> 30127 bytes .../solutions/sort_colors_solution_10.png | Bin 0 -> 38933 bytes .../solutions/sort_colors_solution_11.png | Bin 0 -> 39919 bytes .../solutions/sort_colors_solution_12.png | Bin 0 -> 36301 bytes .../solutions/sort_colors_solution_2.png | Bin 0 -> 37839 bytes .../solutions/sort_colors_solution_3.png | Bin 0 -> 35508 bytes .../solutions/sort_colors_solution_4.png | Bin 0 -> 38775 bytes .../solutions/sort_colors_solution_5.png | Bin 0 -> 37450 bytes .../solutions/sort_colors_solution_6.png | Bin 0 -> 37957 bytes .../solutions/sort_colors_solution_7.png | Bin 0 -> 40615 bytes .../solutions/sort_colors_solution_8.png | Bin 0 -> 39304 bytes .../solutions/sort_colors_solution_9.png | Bin 0 -> 39451 bytes .../sort_colors/test_sort_colors.py | 132 +++--------------- 15 files changed, 85 insertions(+), 146 deletions(-) create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_1.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_10.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_11.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_12.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_2.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_3.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_4.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_5.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_6.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_7.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_8.png create mode 100644 algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_9.png diff --git a/algorithms/two_pointers/sort_colors/README.md b/algorithms/two_pointers/sort_colors/README.md index e46cae49..bf8b5183 100644 --- a/algorithms/two_pointers/sort_colors/README.md +++ b/algorithms/two_pointers/sort_colors/README.md @@ -16,3 +16,60 @@ Input: colors = [2,0,2,1,1,0] Output: [0,0,1,1,2,2] ``` +## Solution + +- [Sorting 0s](#sorting-os) +- [Sorting 1s](#sorting-1s) +- [Sorting 2s](#sorting-2s) +- [Termination](#termination) + +We can understand this algorithm by looking at the invariants which hold true after each iteration: + +1. All elements to the left of the left are 0s. +2. All elements between left and i - 1 are 1s. +3. All elements between i and right are unsorted. +4. All elements to the right of right are 2s. + +![Solution 1](./images/solutions/sort_colors_solution_1.png) +![Solution 2](./images/solutions/sort_colors_solution_2.png) + +Let's now see how we maintain these invariants as we iterate through the array. + +### Sorting Os + +When nums[i] is equal to 0, invariant 2 tells us there are two possible values for left: 0 or 1. +Let's consider the case when left == 1 first. We swap i with left. This allows us to increment the left pointer to +maintain invariant 1. Since we know that the new item at i is a 1, we can also increment i to maintain variant 2. + +![Solution 3](./images/solutions/sort_colors_solution_3.png) +![Solution 4](./images/solutions/sort_colors_solution_4.png) + +Now let's consider what happens when left == 0, which happens when we haven't encountered any 1s yet and i == left. We +swap i with left (which is itself) and increment left to maintain invariant 1. Since we still haven't encountered any 1s, +we can increment i to maintain invariant 2. In other words, the "ones" region remains empty. + +![Solution 5](./images/solutions/sort_colors_solution_5.png) +![Solution 6](./images/solutions/sort_colors_solution_6.png) + +### Sorting 1s + +When nums[i] == 1, we can simply increment i to maintain invariant 2. + +![Solution 7](./images/solutions/sort_colors_solution_7.png) +![Solution 8](./images/solutions/sort_colors_solution_8.png) + +### Sorting 2s + +When nums[i] == 2, we swap nums[i] with nums[right]. This allows us to decrement right to maintain invariant 4. But +since the new item at i came from the unsorted region, the new item at i is still unsorted, so we have to go through +another iteration to correctly sort it. + +![Solution 9](./images/solutions/sort_colors_solution_9.png) +![Solution 10](./images/solutions/sort_colors_solution_10.png) + +### Termination + +When i surpasses right the unsorted region is empty and the entire array is sorted. + +![Solution 11](./images/solutions/sort_colors_solution_11.png) +![Solution 12](./images/solutions/sort_colors_solution_12.png) diff --git a/algorithms/two_pointers/sort_colors/__init__.py b/algorithms/two_pointers/sort_colors/__init__.py index ddc101ac..dbcb8c7a 100644 --- a/algorithms/two_pointers/sort_colors/__init__.py +++ b/algorithms/two_pointers/sort_colors/__init__.py @@ -22,51 +22,25 @@ def sort_colors(colors: List[int]) -> List[int]: Returns: list: sorted list of 0s, 1s, and 2s """ + # Initialize the three pointers, low to track 0s, mid to track 1s and high to track 2s low, mid, high = 0, 0, len(colors) - 1 + # Perform our loop. + # We compare mid and high pointers because the elements at low will be swapped with elements at mid if necessary. + # And mid will be moving up until the end of the list, while high will be moving down until it is equal to high. while mid <= high: if colors[mid] == 0: + # Swap the mid and the low elements and move the low pointer up and the mid pointer up to find the next + # elements that are potentially 0 and 1 colors[low], colors[mid] = colors[mid], colors[low] low += 1 mid += 1 elif colors[mid] == 1: + # Move the 'mid' pointer up, because the element is already at the correct position, no need to swap it mid += 1 else: + # Move the high pointer down. We don't move the mid pointer, because it could be a 0 or a 1 colors[mid], colors[high] = colors[high], colors[mid] high -= 1 return colors - - -def sort_colors_v2(colors: List[int]) -> List[int]: - """ - Sorts a list of 0s, 1s, and 2s in place using two pointers - - This algorithm uses two pointers: low and high. The low pointer is used to track the position where the next 0 - should be placed, and the high pointer is used to track the position where the next 2 should be placed. - - The algorithm works by iterating through the list with the low pointer. If it encounters a 0, it simply increments - low. If it encounters a 2, it decrements high. If it encounters a 1, it swaps it with the element at the high index - and decrements high. This swapping process ensures that all the 1s are placed between the 0s and the 2s. - - This algorithm has a time complexity of O(n) and a space complexity of O(1), making it efficient for sorting lists - of 0s, 1s, and 2s using only two pointers. - - Args: - colors (list): list of 0s, 1s, and 2s - Returns: - list: sorted list of 0s, 1s, and 2s - """ - red, blue = 0, len(colors) - 1 - i = 0 - while i <= blue: - if colors[i] == 0: - colors[red], colors[i] = colors[i], colors[red] - red += 1 - i += 1 - elif colors[i] == 2: - colors[blue], colors[i] = colors[i], colors[blue] - blue -= 1 - else: - i += 1 - return colors diff --git a/algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_1.png b/algorithms/two_pointers/sort_colors/images/solutions/sort_colors_solution_1.png new file mode 100644 index 0000000000000000000000000000000000000000..12b6e505f0deafcf87b4cb6b8e46b7bf18765a67 GIT binary patch literal 30127 zcmeFZXH-*L*FPE%ks@6{P#|=qccfS8MX3S;mH<+t^xlioQF;{-kS?J~R}l!k2}lR& zEwqFh$ldWdp7Xr#{eQV1?zrQQaTp`X&faUyHRo^5HQQR`^?hA65+Zsc5C}w~p{}A2 z0^z|xARIvgeBe(0qld8|5K)z#vhsZmWo7Vv7pRS$qcsSm{yI7Jn&I0?%Aj3LQDhhm z0fQ2Wg%r+*upuRi51}8!*c8BFHwn0(D$|%ezDGfUL%d!R6jG}HJ?<)T^y6J(7Vgc) zhoABe0v5<;{MTAM=a#h*$Aj{oh#AS_91(dC#3}9}Zx}TWoZMRL+eM3A)ysX+8DbE# zJT4eVi&R3Z?>aFt{wwYHz*Mq&ax0YzbDi&J$Hy3>Brh~CKj{9=ZyL?K&iLQd$S=N7 zYr$|7cGR{bqN_WoW}-hu;c1XBa#CdpcjR*1wREzv)0HQOWdo!8-A8 zCJjyD=CZ=qD$>>CfP?`Oj@3>1n#E0UqIa9@UthoxOI-s9`=x+ zGSaMc^eM}#c3;^;Q)ijh_}v)2q&};x9X@j{-s^8q55q5oeT{X)9G%5o?%J+KblazO z5?;@=`GT9S@aiMpkb>aB@)ZT~K#imCst?nD6;LW_+Kb1&o)MRe<@;r3KC5A?b5-%JpasnkqwpUk(L9`!2uCpC>fXT}6!{6O>1Z65x z|HSbK_Fn+q#hd!_@&*1Qkcoo8XF^11fFPb_2*n;wj3RkhD4hK2NDvbI42}y6y_s-r znfR*m;{Dr61O*B#>O?Dw4)30Ryj~JwpXakKvCid&--w4&^vuI~e$$88Klp(lp>eSL zV=6D2zM%9MhK}d_$DPDcnQ(+PnOrM@SYVksDzn zQ485@lw4$M9HT<~yS8WWn@%xTJE_|{zdzL%j1~${BkE(+CSH|U<**?*#EI_EuW~CB z5eMCh)M@8$PkCJbB(tih%KxY0HWz8+=oiz4nU{HYN%?P?yqb=hj+YK^in#U7|6A`O zYR|(<-cQCdY_Q8@;np7K{>0wk-ZQ*=Awpl1$u$=!QYbYEn+O@gO2e4H-F)y`owJdO z^|jsivG1BssrF^|arU#bva*7+qGujS2G4LeXf}kp(5~Pw%e_s~SY@NR6U@e5&bh;$ z%`wZ~!uqzG10vueBbnKp^GHulD?sIvO)s%N#kTiw*`&v$x4y^fZD6^=eL>^L+`RYU zMj!9rEqh_Kn9QO$tddv&fAA>pVY!##e%-H+l=r%g?-<@uE>M|mW@bWi>`eiN(1!~qRMy6wmVrK5I?Q1s) z#{#&c?3Jty!hh&*GH>#2(uy&N71CQdWt+X76042hG~2Y?^h2?rY*3k-R-(`8Tj@9G zZ;4HbGTOfv>la(I=O3S`@U}cmPKip%q%kQ~-%1#lb$U4cNcxd)`Vs$*^UebX3x+_3 zssZEdYN<-M;zr9xyT+A9PWMO@mk*;4Zi`EcfserR5>XBv_0kX7`LXK`Ti4dLP!1?x zWY_g|{0I1_`2F}~B(Ec`w?o=p+I8D0SY`9c^JVf?^L;zw7g*m-urnvL97jkTqPc*sP==#utwK#Qntsj}Vig z2ztpM`H+7t|_9oY6 zxldhNS=u#N9$hNkzO`b$atE+`{B1H7A^{6R(cjW6(6+})wy`#*f*-~syr&3DidmfG5fFYL~q1rQ#Z*RX=d4E zfh%MgX_*+>I0M{rcANVTBPefE5m7n!7Y$koV@7cMuYSAANyE*%%qx@iN+U+YQ61ew zxbowr>f4_hVj8TEXgrCJ*$1Od25zl39rm6KzL|a7`zE*ObCIJaoi0kdT-~4jF<}WF zbOd+AF4-I?T8fBS<^Ecud+0lp6}9yqPJ>$AVeuBoM>)tH(gU{Q}Wt*}B=_73%a?v*-3 z9vZKa@Y?cMTHutcn+-RNys-Y-lV@~UdQ{F)p=)*F+o}^_dU-A;v9Y?7>R-F@^mAiM` zxo2B(niOjm$5jVo&wG-3Tzc^(!X54TijrxQ+vb~J92O8oMlqPbGXG$H#uLgjT~F^c z`w8V>WIxt#zq`3gzmwrE##FywXEBYaZLy0Si2KE0$^{haFPm~l^XXbv)FIIZo( zFGoPCN!EJ8w_k4_8A9sLXmi_H>Z#v{!tfFOA4IkMP7HQhPFv7;hh1rUubS%i^8A%F zR8>nCD&8dbzU%{^H(s!X<&)wWgZ!e7BCBi-Ns*ropAIi4e^yHj^vh1T%B`b2hy!Q` zJcOEbE!^6?&~LU1@>A(jrz`GS*zI_1JD<+(AEz)D<&2jOm`wXx_(-4G9A`JLdhhhP z=WfwDe}X=0kX*BwFaK!n>C8EUXlrjeL|5z~GJPeFI}w#WLEiU~_xGQ4uUYY@B``Wvv7p_ffU6B_NzE*v{LP&kI%eK*C zu4dqPv$((ivOr~9quNuoh&lDSm^MD|qJ8IG-^k*ID6=b2(`W8$MFDF+}tK}t7tb@3N=EJ5&>p!*4}S$Cl&^*J}5 zZ~8ud^Cj?C@ujbR!axBb9mf>QxE+X;#s1gTAejT1Vaj_xI6vns3rGF;AcJzu50|&B ziw5y#XK%P)K`R%YoiZIT?4*R0xz$3 zxPMyX!QNf@bB!YiJOe2jC~If{p9ardtgW40pF`ai&hVkzLmh3YXHX~pClKgUYkn`M7g#zV880c|(#hKG3E0cY(b-kXOP1w#3n}0l zds~17{JV*pgDlHKo%>*AsEajNoL`V%kVTFN3%m=jKbM?a5aJgU_?tG+RR()k>b{+qwWFzu zofCi=Fov9nps396_W!ph|BU!wJsDoT1T2yF9)0ik z-JNf0k(Qp76={)$HeNgQ=X&g8dAyZ#s(t);Rie@=6_w6%1CLw*g!8}O4!B+*zu&QS zGT?~ooi^(wfF0O$NBy4~;^Ps(ep3IRo_|F&sAyE}>FIGXO9}sH=x@a2kZ_6otGI~(Pb~YxH-TYZ-3tQq(0GVP{Tadw zcqYSU2!3o51n#X6a8Lu7aU>vzOy0N7{tpx2AO$a+kg`3S8U^qhkfJf096c+*Tour$ zbdN;L}F<{|gR!Fc`PIhO(!h*$S@hSoATjnrs zusSZDY2wLqEN0(X0P4ijx9*ePWyc2Z10p03BtetGFJ(u-j)a51{v#2tZ&Gqw&{&pbVo0 z!-=4(#CR-(G z`~xMqB_LBX9Uu8CHUOH}@tuG`3cNt0s!!Dq{vhy$RUu)8IS&`733%Y)Zz>J+eyj`# z9KpTyTQ{*Y{I4?ot4#kY)4!JKU(59WcQ?lc1Rt!kEwaIf*>wKtwq%*+;@dfEy4K#| zhQ@|oo5jEVIb7#mWu+eST7=vo=d*5M-%m~{$2-Dz-fs42-r?zmEi4eF|MB~HMP~#}*sUD0CCmWFGHW9$q@- zCy^oF*H$_I@&DycxgG#Mo6>*Ldn%k_UGP~25^@VI`(1glCW-tZFE;Fo zQ2+xw2M(`{*jJG68NQY(QvL0SfiPu7EDt}pnQ+;4&lBHsaJu&!Hp&c+!9Bf=&i*

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a/algorithms/two_pointers/sort_colors/test_sort_colors.py b/algorithms/two_pointers/sort_colors/test_sort_colors.py index ff008baa..bb101646 100644 --- a/algorithms/two_pointers/sort_colors/test_sort_colors.py +++ b/algorithms/two_pointers/sort_colors/test_sort_colors.py @@ -1,119 +1,27 @@ import unittest -from . import sort_colors, sort_colors_v2 - - -class SortColorsV2TestCase(unittest.TestCase): - def test_1(self): - """should sort colors = [1,0,2,1,2,2] to [0,1,1,2,2,2]""" - colors = [1, 0, 2, 1, 2, 2] - expected = [0, 1, 1, 2, 2, 2] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_2(self): - """should sort colors = [0,1,1,2,0,2,0,2,1,2] to [0,0,0,1,1,1,2,2,2,2]""" - colors = [0, 1, 1, 2, 0, 2, 0, 2, 1, 2] - expected = [0, 0, 0, 1, 1, 1, 2, 2, 2, 2] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_3(self): - """should sort colors = [0] to [0]""" - colors = [0] - expected = [0] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_4(self): - """should sort colors = [0,1,0] to [0,0,1]""" - colors = [0, 1, 0] - expected = [0, 0, 1] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_5(self): - """should sort colors = [1] to [1]""" - colors = [1] - expected = [1] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_6(self): - """should sort colors = [2,2] to [2,2]""" - colors = [2, 2] - expected = [2, 2] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_7(self): - """should sort colors = [1,1,0,2] to [0,1,1,2]""" - colors = [1, 1, 0, 2] - expected = [0, 1, 1, 2] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) - - def test_8(self): - """should sort colors = [2,1,1,0,0] to [0,0,1,1,2]""" - colors = [2, 1, 1, 0, 0] - expected = [0, 0, 1, 1, 2] - actual = sort_colors_v2(colors) - self.assertEqual(expected, actual) +from typing import List +from parameterized import parameterized +from algorithms.two_pointers.sort_colors import sort_colors + +SORT_COLORS_TEST_CASES = [ + ([1, 0, 2, 1, 2, 2], [0, 1, 1, 2, 2, 2]), + ([0, 1, 1, 2, 0, 2, 0, 2, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2, 2]), + ([0], [0]), + ([0, 1, 0], [0, 0, 1]), + ([1], [1]), + ([2, 2], [2, 2]), + ([1, 2, 0], [0, 1, 2]), + ([2, 2, 1], [1, 2, 2]), + ([2, 1, 2, 0, 1, 2, 2, 0], [0, 0, 1, 1, 2, 2, 2, 2]), + ([1, 1, 0, 2], [0, 1, 1, 2]), + ([2, 1, 1, 0, 0], [0, 0, 1, 1, 2]), + ([2, 0, 2, 1, 1, 0], [0, 0, 1, 1, 2, 2]), +] class SortColorsTestCase(unittest.TestCase): - def test_1(self): - """should sort colors = [1,0,2,1,2,2] to [0,1,1,2,2,2]""" - colors = [1, 0, 2, 1, 2, 2] - expected = [0, 1, 1, 2, 2, 2] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_2(self): - """should sort colors = [0,1,1,2,0,2,0,2,1,2] to [0,0,0,1,1,1,2,2,2,2]""" - colors = [0, 1, 1, 2, 0, 2, 0, 2, 1, 2] - expected = [0, 0, 0, 1, 1, 1, 2, 2, 2, 2] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_3(self): - """should sort colors = [0] to [0]""" - colors = [0] - expected = [0] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_4(self): - """should sort colors = [0,1,0] to [0,0,1]""" - colors = [0, 1, 0] - expected = [0, 0, 1] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_5(self): - """should sort colors = [1] to [1]""" - colors = [1] - expected = [1] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_6(self): - """should sort colors = [2,2] to [2,2]""" - colors = [2, 2] - expected = [2, 2] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_7(self): - """should sort colors = [1,1,0,2] to [0,1,1,2]""" - colors = [1, 1, 0, 2] - expected = [0, 1, 1, 2] - actual = sort_colors(colors) - self.assertEqual(expected, actual) - - def test_8(self): - """should sort colors = [2,1,1,0,0] to [0,0,1,1,2]""" - colors = [2, 1, 1, 0, 0] - expected = [0, 0, 1, 1, 2] + @parameterized.expand(SORT_COLORS_TEST_CASES) + def test_sort_colors(self, colors: List[int], expected: List[int]): actual = sort_colors(colors) self.assertEqual(expected, actual) From cf07d9408662a623a7426e8f9fcf6c8a68239525 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 15:16:54 +0300 Subject: [PATCH 08/11] refactor(algorithms, two-pointers): trapped rain water --- .../two_pointers/rain_water_trapped/README.md | 107 ++++++++++++++++++ .../rain_water_trapped/__init__.py | 27 +++++ .../trapped_rain_water_solution_1.png | Bin 0 -> 29674 bytes .../trapped_rain_water_solution_10.png | Bin 0 -> 46647 bytes .../trapped_rain_water_solution_11.png | Bin 0 -> 44488 bytes .../trapped_rain_water_solution_2.png | Bin 0 -> 30073 bytes .../trapped_rain_water_solution_3.png | Bin 0 -> 26786 bytes .../trapped_rain_water_solution_4.png | Bin 0 -> 44558 bytes .../trapped_rain_water_solution_5.png | Bin 0 -> 44539 bytes .../trapped_rain_water_solution_6.png | Bin 0 -> 44970 bytes .../trapped_rain_water_solution_7.png | Bin 0 -> 44281 bytes .../trapped_rain_water_solution_8.png | Bin 0 -> 46751 bytes .../trapped_rain_water_solution_9.png | Bin 0 -> 45455 bytes .../test_trapped_rain_water.py | 22 ++++ puzzles/arrays/rain_water_trapped/README.md | 44 ------- puzzles/arrays/rain_water_trapped/__init__.py | 21 ---- .../test_trapped_rain_water.py | 29 ----- 17 files changed, 156 insertions(+), 94 deletions(-) create mode 100644 algorithms/two_pointers/rain_water_trapped/README.md create mode 100644 algorithms/two_pointers/rain_water_trapped/__init__.py create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_1.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_10.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_11.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_2.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_3.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_4.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_5.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_6.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_7.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_8.png create mode 100644 algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_9.png create mode 100644 algorithms/two_pointers/rain_water_trapped/test_trapped_rain_water.py delete mode 100644 puzzles/arrays/rain_water_trapped/README.md delete mode 100644 puzzles/arrays/rain_water_trapped/__init__.py delete mode 100644 puzzles/arrays/rain_water_trapped/test_trapped_rain_water.py diff --git a/algorithms/two_pointers/rain_water_trapped/README.md b/algorithms/two_pointers/rain_water_trapped/README.md new file mode 100644 index 00000000..953e7706 --- /dev/null +++ b/algorithms/two_pointers/rain_water_trapped/README.md @@ -0,0 +1,107 @@ +# Trapping Rain-Water + +Given an integer array A of non-negative integers representing an elevation map where the width of each bar is 1, +compute how much water it is able to trap after raining. + +Input Format +The only argument given is integer array A. + +Output Format +Return the total water it is able to trap after raining. + +```plain +Example Input +Input 1: + +A = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1] +Input 2: + +A = [1, 2] + +Example Output +Output 1: + +6 +Output 2: + +0 + +Example Explanation +Explanation 1: + +In this case, 6 units of rain water (blue section) are being trapped. +Explanation 2: + +No water is trapped. +``` + +## Related Topics + +- Array +- Two Pointers +- Dynamic Programming +- Stack +- Monotonic Stack + +## Solution + +We can use the two-pointer technique to solve this problem in O(n) time and O(1) space. +In order for any index in the array to be able to trap rain water, there must be higher bars on both the left and right +side of the index. For example, index 2 in the following array has height 1. It can trap water because there are higher +bars to the left and right of it. + +![Solution 1](./images/solutions/trapped_rain_water_solution_1.png) + +To calculate the exact amount of water that can be trapped at index 2, we first take the minimum height of the highest +bars to the left and right of it, which in this case is 4. We then subtract the height of the bar at index 2, which is 1, + +![Solution 2](./images/solutions/trapped_rain_water_solution_2.png) + +So if we knew the height of the highest bars to the left and right of every index, we could iterate through the array +and calculate the amount of water that can be trapped at each index. +But we don't need to know the exact height of both the highest bars to the left and right of every index. For example, +let's say we know the highest bar to the right of index 7 with height 0 has a height of 2. + +![Solution 3](./images/solutions/trapped_rain_water_solution_3.png) + +If we also knew that there exists a higher bar than 2 anywhere to the left of index 7, then we also know that the minimum +height of the highest bars to the left and right of index 7 is 2. This means that we have enough information to calculate +the amount of water that can be trapped at index 7, which is 2 - 0 = 2. +This is the insight behind how the two-pointer technique can be used to solve this problem. We initialize two pointers +left and right at opposite ends of the array. We also keep two variables leftMax and rightMax to keep track of the highest +bars each pointer has seen. + +![Solution 4](./images/solutions/trapped_rain_water_solution_4.png) + +We now use the values of leftMax and rightMax to visit every single index in the array exactly once. We start by +comparing leftMax and rightMax. In this case, rightMax is smaller than leftMax, so we know that: + +1. The maximum height of the highest bar to the right of right - 1 is rightMax +2. There exists a higher bar than rightMax somewhere to the left of right + +These two facts mean that we have enough information to calculate the amount of water that can be trapped at index +right - 1. So first we move the right pointer back by 1: + +![Solution 5](./images/solutions/trapped_rain_water_solution_5.png) + +There are two possible cases to consider when calculating the amount of water that can be trapped at the current index +of right: +1. The height of the bar at index right is smaller than rightMax +2. The height of the bar at index right is greater than or equal to rightMax + +In our case, the height of the bar at index right is smaller than rightMax, so we know that the amount of water that +can be trapped at index 1 is rightMax - height[right], and we can move to the next iteration, which follows the same logic: + +![Solution 6](./images/solutions/trapped_rain_water_solution_6.png) +![Solution 7](./images/solutions/trapped_rain_water_solution_7.png) +![Solution 8](./images/solutions/trapped_rain_water_solution_8.png) +![Solution 9](./images/solutions/trapped_rain_water_solution_9.png) + +Now, we run into case 2, where height[right] is greater than or equal to rightMax. This means we can't trap any water at +this index, so instead we update rightMax to the height of the bar at index right to prepare for the next iteration. + +![Solution 10](./images/solutions/trapped_rain_water_solution_10.png) +![Solution 11](./images/solutions/trapped_rain_water_solution_11.png) + +The same logic applies when leftMax is less than rightMax, and this continues until every index has been visited exactly +once, for a total time complexity of O(n) and a space complexity of O(1). diff --git a/algorithms/two_pointers/rain_water_trapped/__init__.py b/algorithms/two_pointers/rain_water_trapped/__init__.py new file mode 100644 index 00000000..aa4f4381 --- /dev/null +++ b/algorithms/two_pointers/rain_water_trapped/__init__.py @@ -0,0 +1,27 @@ +from typing import List + + +def trapped_rain_water(heights: List[int]) -> int: + if not heights: + return 0 + # Initialize the pointers left and right at both ends of the array + left, right = 0, len(heights) - 1 + # initialize left_max and right_max that will keep track of the highest bars each pointer has seen + left_max, right_max = heights[left], heights[right] + # Keeps track of the total trapped rain wayter + result = 0 + + while left < right: + if left_max < right_max: + left += 1 + if heights[left] >= left_max: + left_max = heights[left] + else: + result += left_max - heights[left] + else: + right -= 1 + if heights[right] >= right_max: + right_max = heights[right] + else: + result += right_max - heights[right] + return result diff --git a/algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_1.png b/algorithms/two_pointers/rain_water_trapped/images/solutions/trapped_rain_water_solution_1.png new file mode 100644 index 0000000000000000000000000000000000000000..485086e99f6e2b9a01f0a7c096df1efd265910e3 GIT binary patch literal 29674 zcmeFZbySpH|2N8v0}ddvFEy*WTa#`S#x5ePN`AnmiuPLmUhY3_L{zSuG5V zJ75e9P#qKtXgP7!c!`05Q(-G3qoF7xL!;s9WMyk_iGiUInUZ$*andAV(C$rfcnArU 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zLV5RH1M&Xsa~x(Y#yIJ}_^+rJ-kYo$Qn^jXPV;63m`~g@kv(!zd$ZMJjbkwFcyxf@ z%kTt?z?XN7hvX^kalC64h)t-@%60&Z3LQWM(;hD1Aq_z;amRI>}Ho54WqbO z!v}eos9vDdy|y6uxGbXOgsbotS?xKRyKbG9(b^#f0|>+SaN$!rQtu9^S#D8VSElQQ zuh(Ge7P#`&TZQf-AQ#0 int: - if not heights or len(heights) == 1: - return 0 - left, right = 0, len(heights) - 1 - result = 0 - mx, mi = 0, 0 - - while left <= right: - mi = min(heights[left], heights[right]) - mx = max(mx, mi) - - result += mx - mi - - if heights[left] < heights[right]: - left += 1 - else: - right -= 1 - return result diff --git a/puzzles/arrays/rain_water_trapped/test_trapped_rain_water.py b/puzzles/arrays/rain_water_trapped/test_trapped_rain_water.py deleted file mode 100644 index 6a45ed43..00000000 --- a/puzzles/arrays/rain_water_trapped/test_trapped_rain_water.py +++ /dev/null @@ -1,29 +0,0 @@ -import unittest -from . import trapped_rain_water - - -class TrappedRainWaterTestCase(unittest.TestCase): - def test_1(self): - """Should return 6 for input of [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]""" - a = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1] - expected = 6 - actual = trapped_rain_water(a) - self.assertEqual(expected, actual) - - def test_2(self): - """Should return 0 for input of [1, 2]""" - a = [1, 2] - expected = 0 - actual = trapped_rain_water(a) - self.assertEqual(expected, actual) - - def test_3(self): - """Should return 9 for input of [4,2,0,3,2,5]""" - a = [4, 2, 0, 3, 2, 5] - expected = 9 - actual = trapped_rain_water(a) - self.assertEqual(expected, actual) - - -if __name__ == "__main__": - unittest.main() From 3efcce49f815ba42f30fc372f59e093252465e75 Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Thu, 8 Jan 2026 12:17:21 +0000 Subject: [PATCH 09/11] updating DIRECTORY.md --- DIRECTORY.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 0a0054b5..fa59b1d8 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -218,6 +218,8 @@ * [Test Next Permutation](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/next_permutation/test_next_permutation.py) * Pair With Sum In Array * [Test Pair With Sum In Array](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/pair_with_sum_in_array/test_pair_with_sum_in_array.py) + * Rain Water Trapped + * [Test Trapped Rain Water](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/rain_water_trapped/test_trapped_rain_water.py) * Reverse Array * [Test Reverse Array](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/reverse_array/test_reverse_array.py) * Sort Colors @@ -611,8 +613,6 @@ * [Test Maxlen Contiguous Binary Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/maxlen_contiguous_binary_subarray/test_maxlen_contiguous_binary_subarray.py) * Product Of Array Except Self * [Test Product Except Self](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/product_of_array_except_self/test_product_except_self.py) - * Rain Water Trapped - * [Test Trapped Rain Water](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/rain_water_trapped/test_trapped_rain_water.py) * Rotation * Cyclic Rotation * [Test Cyclic Rotation](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/rotation/cyclic_rotation/test_cyclic_rotation.py) From e899c0b6b59ef7bdbfa05154daa0353a01e56aa4 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 15:18:48 +0300 Subject: [PATCH 10/11] test(algorithms, two-pointers, move_zeroes): update image reference Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/two_pointers/move_zeroes/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/two_pointers/move_zeroes/README.md b/algorithms/two_pointers/move_zeroes/README.md index c96f9be7..07057a59 100644 --- a/algorithms/two_pointers/move_zeroes/README.md +++ b/algorithms/two_pointers/move_zeroes/README.md @@ -39,6 +39,6 @@ the zeroes to the end of the array. ![Solution 8](./images/solutions/move_zeroes_solution_8.png) ![Solution 9](./images/solutions/move_zeroes_solution_9.png) ![Solution 10](./images/solutions/move_zeroes_solution_10.png) -![Solution 11](./images/solutions/move_zeroes_solution_1.png) +![Solution 11](./images/solutions/move_zeroes_solution_11.png) ![Solution 12](./images/solutions/move_zeroes_solution_12.png) ![Solution 13](./images/solutions/move_zeroes_solution_13.png) From 6df7b66467726021a144397a914d3bd1ae2a8965 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Thu, 8 Jan 2026 15:19:04 +0300 Subject: [PATCH 11/11] test(algorithms, two-pointers, move_zeroes): update type hint in test Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/two_pointers/move_zeroes/test_move_zeroes.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/two_pointers/move_zeroes/test_move_zeroes.py b/algorithms/two_pointers/move_zeroes/test_move_zeroes.py index 8cb5857f..c77af71d 100644 --- a/algorithms/two_pointers/move_zeroes/test_move_zeroes.py +++ b/algorithms/two_pointers/move_zeroes/test_move_zeroes.py @@ -17,7 +17,7 @@ class MoveZeroesTestCase(unittest.TestCase): @parameterized.expand(MOVE_ZEROES_TEST_CASES) - def test_move_zeroes(self, nums: List[int], expected: [List]): + def test_move_zeroes(self, nums: List[int], expected: List[int]): move_zeroes(nums) self.assertEqual(expected, nums)

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