From 8c55e901acb637ee0abc05522cad38477aa74fd2 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Sun, 18 Jan 2026 12:47:31 +0300 Subject: [PATCH 1/9] feat(algorithms, dynamic-programming): decode ways --- .../dynamic_programming/decodeways/README.md | 84 +++++++++++++++++++ .../decodeways/__init__.py | 28 +++++++ .../decodeways/test_num_decodings.py | 28 +++++++ .../test_min_cost_to_paint_houses.py | 6 +- 4 files changed, 144 insertions(+), 2 deletions(-) create mode 100644 algorithms/dynamic_programming/decodeways/README.md create mode 100644 algorithms/dynamic_programming/decodeways/__init__.py create mode 100644 algorithms/dynamic_programming/decodeways/test_num_decodings.py diff --git a/algorithms/dynamic_programming/decodeways/README.md b/algorithms/dynamic_programming/decodeways/README.md new file mode 100644 index 00000000..372830c9 --- /dev/null +++ b/algorithms/dynamic_programming/decodeways/README.md @@ -0,0 +1,84 @@ +# Decode Ways + +You have intercepted a secret message encoded as a string of numbers. The message is decoded via the following mapping: + +```text +'1' -> "A" +'2' -> "B" +'3' -> "C" +... +'26' -> "Z" +``` +However, while decoding the message, you realize that there are many different ways you can decode the message because +some codes are contained in other codes ("2" and "5" vs "25"). + +For example, "11106" can be decoded into: + +- "AAJF" with the grouping (1, 1, 10, 6) +- "KJF" with the grouping (11, 10, 6) +- The grouping (1, 11, 06) is invalid because "06" is not a valid code (only "6" is valid). + +Note: there may be strings that are impossible to decode. + +Given a string s containing only digits, return the number of ways to decode it. If the entire string cannot be decoded +in any valid way, return 0. + +The test cases are generated so that the answer fits in a 32-bit integer. + +## Examples + +Example 1 + +```text +Input: s = "12" + +Output: 2 + +Explanation: + +"12" could be decoded as "AB" (1 2) or "L" (12). +``` + +Example 2 + +```text +Input: s = "226" + +Output: 3 + +Explanation: + +"226" could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6). +``` + +Example 3 + +```text +Input: s = "06" + +Output: 0 + +Explanation: + +"06" cannot be mapped to "F" because of the leading zero ("6" is different from "06"). In this case, the string is not +a valid encoding, so return 0. +``` + +Example 4 + +```text +s = 101 +output = 1 +Explanation: The only way to decode it is "JA". "01" cannot be decoded into "A" as "1" and "01" are different. +``` + +## Constraints + +- 1 <= s.length <= 100 +- s contains only digits and may contain leading zero(s). + +## Topics + +- String +- Dynamic Programming + diff --git a/algorithms/dynamic_programming/decodeways/__init__.py b/algorithms/dynamic_programming/decodeways/__init__.py new file mode 100644 index 00000000..20f7b9ca --- /dev/null +++ b/algorithms/dynamic_programming/decodeways/__init__.py @@ -0,0 +1,28 @@ +def num_decodings(s: str) -> int: + if not s or s[0] == "0": + return 0 + + n = len(s) + # Initialize the dp array. dp[i] will store the number of ways to decode the string s[:i] + dp = [0] * (n + 1) + dp[0] = 1 + dp[1] = 1 + + # Iterate through the string + for i in range(2, n + 1): + # Get the current character + current_char = s[i - 1] + # Get the previous character + prev_char = s[i - 2] + + # If the current character is not a zero, then we can decode it as a single character + if current_char != "0": + dp[i] += dp[i - 1] + + # If the previous character is 1 or 2 and the current character is less than or equal to 6, then we can decode + # it as a two character + if prev_char == "1" or (prev_char == "2" and current_char <= "6"): + dp[i] += dp[i - 2] + + # Return the number of ways to decode the string + return dp[n] diff --git a/algorithms/dynamic_programming/decodeways/test_num_decodings.py b/algorithms/dynamic_programming/decodeways/test_num_decodings.py new file mode 100644 index 00000000..8badd51e --- /dev/null +++ b/algorithms/dynamic_programming/decodeways/test_num_decodings.py @@ -0,0 +1,28 @@ +import unittest +from parameterized import parameterized +from algorithms.dynamic_programming.decodeways import num_decodings + +NUM_DECODINGS_TEST_CASES = [ + ("11106", 2), + ("12", 2), + ("226", 3), + ("06", 0), + ("101", 1), + ("12", 2), + ("012", 0), + ("0", 0), + ("30", 0), + ("10", 1), + ("27", 1), +] + + +class NumDecodingsTestCase(unittest.TestCase): + @parameterized.expand(NUM_DECODINGS_TEST_CASES) + def test_num_decodings(self, s: str, expected: int): + actual = num_decodings(s) + self.assertEqual(expected, actual) + + +if __name__ == "__main__": + unittest.main() diff --git a/algorithms/dynamic_programming/painthouse/test_min_cost_to_paint_houses.py b/algorithms/dynamic_programming/painthouse/test_min_cost_to_paint_houses.py index b097d8f6..a13a4fd6 100644 --- a/algorithms/dynamic_programming/painthouse/test_min_cost_to_paint_houses.py +++ b/algorithms/dynamic_programming/painthouse/test_min_cost_to_paint_houses.py @@ -1,7 +1,9 @@ import unittest from typing import List from parameterized import parameterized -from algorithms.dynamic_programming.painthouse import min_cost_to_paint_houses_alternate_colors +from algorithms.dynamic_programming.painthouse import ( + min_cost_to_paint_houses_alternate_colors, +) MIN_COST_PAINT_HOUSE = [ ([[8, 4, 15], [10, 7, 3], [6, 9, 12]], 13), @@ -16,5 +18,5 @@ def test_min_cost_to_paint_houses(self, cost: List[List[int]], expected: int): self.assertEqual(expected, actual) -if __name__ == '__main__': +if __name__ == "__main__": unittest.main() From df417c24db628a9fcf9b5bc5f48966858faeeabf Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Sun, 18 Jan 2026 12:47:51 +0300 Subject: [PATCH 2/9] feat(algorithms, binary-search): split array largest sum --- .../split_array_largest_sum/README.md | 106 ++ .../split_array_largest_sum/__init__.py | 84 ++ .../split_array_largest_sum_example_1.png | Bin 0 -> 93157 bytes .../split_array_largest_sum_example_2.png | Bin 0 -> 82181 bytes .../split_array_largest_sum_example_3.png | Bin 0 -> 75867 bytes .../split_array_largest_sum_example_4.png | Bin 0 -> 101032 bytes .../split_array_largest_sum_solution_1.png | Bin 0 -> 57147 bytes .../split_array_largest_sum_solution_10.png | Bin 0 -> 70466 bytes .../split_array_largest_sum_solution_11.png | Bin 0 -> 66730 bytes 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b/algorithms/search/binary_search/split_array_largest_sum/README.md new file mode 100644 index 00000000..dabba581 --- /dev/null +++ b/algorithms/search/binary_search/split_array_largest_sum/README.md @@ -0,0 +1,106 @@ +# Split Array Largest Sum + +Given an integer list nums and an integer k, split nums into k non-empty subarrays such that the largest sum among these +subarrays is minimized. The task is to find the minimized largest sum by choosing the split such that the largest sum of +every split of subarrays is the minimum among the sum of other splits. + +## Constraints + +- 1 <= nums.length <= 1000 +- 0 <= nums[i] <= 10^4 +- 1 <= k <= nums.length + +## Examples + +![Example 1](images/examples/split_array_largest_sum_example_1.png) +![Example 2](images/examples/split_array_largest_sum_example_2.png) +![Example 3](images/examples/split_array_largest_sum_example_3.png) +![Example 4](images/examples/split_array_largest_sum_example_4.png) + +## Topics + +- Array +- Binary Search +- Dynamic Programming +- Greedy +- Prefix Sum + +## Solution + +In a brute force method, you would try all possible ways to split the array into k subarrays, calculate the largest sum +for each split, and then find the smallest among those largest sums. This approach is extremely inefficient because the +number of ways to split the array grows exponentially as the size increases. + +We reverse the process by guessing a value for the minimum largest sum and checking if it’s feasible: + +- Instead of iterating through all splits, we only focus on testing whether a specific value allows us to split the + array into k subarrays. + +- But wait—just because one value works doesn’t mean it’s the smallest feasible value. We keep exploring smaller values + to achieve the most optimized result. + +The solution uses the binary search approach to find the optimal largest subarray sum without testing all possible splits. +The binary search finds the smallest possible value of the largest subarray sum and applies searching over the range of +possible values for this largest sum. But how do we guess this value? We guess the value using a certain range. +Here’s how: + +- **Left boundary**: The maximum element in the array is the minimum possible value for the largest subarray sum. This + is because any valid subarray must have a sum at least as large as the largest element. + +- **Right boundary**: The maximum possible value for the largest subarray sum is the sum of all elements in the array. + You would get this sum if the entire array were one single subarray. + +The binary search iteratively tests midpoints in the above ranges. It determines whether dividing the array results in +at most k subarrays will result in the smallest largest sum. If it does, the search shifts to lower values to minimize +the largest sum. Otherwise, it shifts to higher values. Still, there might be subarrays whose sum could be smaller, so +the search keeps going until the search range crosses each other, i.e., **left boundary** > **right boundary**. + +Here’s the step-by-step implementation of the solution: + +- Start by initializing the ranges for search. The left will be the largest number in the array, and the right will be + the sum of all numbers. +- Use a guessing approach. Start by considering a mid value between the left and right as a test value. +- Check if it is possible to divide the array into k subarrays so that the sum of no subarray is greater than mid. + - Start with an empty sum and add numbers from the array. If adding the next number exceeds mid: + - Start a new subarray with that number and increment the count of the subarrays. + - Return FALSE if the count exceeds k. Otherwise, return TRUE. +- Adjust the guessing range by checking if the number of subarrays needed is within the k and reduce the mid to see if + a smaller largest sum is possible. +- Otherwise, if the count of subarrays is more than k: + - Increase the mid to make larger groups possible. +- Continue adjusting the mid until left < right. Return left as it contains the minimized largest possible sum. + +- Let’s look at the following illustrations to get a better understanding of the solution: + +![Solution 1](images/solutions/split_array_largest_sum_solution_1.png) +![Solution 2](images/solutions/split_array_largest_sum_solution_2.png) +![Solution 3](images/solutions/split_array_largest_sum_solution_3.png) +![Solution 4](images/solutions/split_array_largest_sum_solution_4.png) +![Solution 5](images/solutions/split_array_largest_sum_solution_5.png) +![Solution 6](images/solutions/split_array_largest_sum_solution_6.png) +![Solution 7](images/solutions/split_array_largest_sum_solution_7.png) +![Solution 8](images/solutions/split_array_largest_sum_solution_8.png) +![Solution 9](images/solutions/split_array_largest_sum_solution_9.png) +![Solution 10](images/solutions/split_array_largest_sum_solution_10.png) +![Solution 11](images/solutions/split_array_largest_sum_solution_11.png) +![Solution 12](images/solutions/split_array_largest_sum_solution_12.png) +![Solution 13](images/solutions/split_array_largest_sum_solution_13.png) +![Solution 14](images/solutions/split_array_largest_sum_solution_14.png) +![Solution 15](images/solutions/split_array_largest_sum_solution_15.png) +![Solution 16](images/solutions/split_array_largest_sum_solution_16.png) +![Solution 17](images/solutions/split_array_largest_sum_solution_17.png) +![Solution 18](images/solutions/split_array_largest_sum_solution_18.png) +![Solution 19](images/solutions/split_array_largest_sum_solution_19.png) +![Solution 20](images/solutions/split_array_largest_sum_solution_20.png) + +### Time Complexity + +The time complexity of this solution is O(n log(m)), where n is the length of the input array, and m is the difference +between `max(nums)` and `sum(nums)` because the range of possible sums considered during the binary search is from +`max(nums)`to `sum(nums)`. This range size determines the number of iterations in the binary search. The tighter this +range, the fewer iterations are needed. However, in the worst case, it spans the full difference: `sum(nums) - max(nums)`. +The time complexity becomes `n log(m)` because the `can_split` function is called `n` times for each iteration. + +### Space Complexity + +The time complexity of this solution is O(1) because only constant space is used. diff --git a/algorithms/search/binary_search/split_array_largest_sum/__init__.py b/algorithms/search/binary_search/split_array_largest_sum/__init__.py new file mode 100644 index 00000000..8c2c2489 --- /dev/null +++ b/algorithms/search/binary_search/split_array_largest_sum/__init__.py @@ -0,0 +1,84 @@ +from typing import List + + +def split_array(nums: List[int], k: int) -> int: + if not nums: + return -1 + + left = max(nums) + right = sum(nums) + first_true_index = -1 + + def feasible(max_sum: int) -> bool: + """ + Check if we can split the array into at most k sub arrays with each sub array sum less than or equal to max_sum + """ + current_sum = 0 + # Start with one + sub_array_count = 1 + + for num in nums: + if current_sum + num > max_sum: + current_sum = num + sub_array_count += 1 + else: + current_sum += num + + return sub_array_count <= k + + while left <= right: + mid = (right + left) // 2 + if feasible(mid): + first_true_index = mid + # Find a smaller valid value + right = mid - 1 + else: + # Find a larger valid value + left = mid + 1 + + return first_true_index + + +def split_array_2(nums, k): + # Set the initial search range for the largest sum: + # Minimum is the largest number in the array, and maximum is the sum of all numbers + left, right = max(nums), sum(nums) + + def can_split(mid): + # Initialize the count of subarrays and the current sum of the current subarray + subarrays = 1 + current_sum = 0 + + for num in nums: + # Check if adding the current number exceeds the allowed sum (mid) + if current_sum + num > mid: + # Increment the count of subarrays + subarrays += 1 + # Start a new subarray with the current number + current_sum = num + + # If the number of subarrays exceeds the allowed k, return False + if subarrays > k: + return False + else: + # Otherwise, add the number to the current subarray + current_sum += num + + # Return True if the array can be split within the allowed subarray count + return True + + # Perform binary search to find the minimum largest sum + while left < right: + # Find the middle value of the current range + mid = (left + right) // 2 + + # Check if the array can be split into k or fewer subarrays with this maximum sum + if can_split(mid): + # If possible, try a smaller maximum sum + right = mid + else: + # Otherwise, increase the range to allow larger sums + left = mid + 1 + + # Return the smallest maximum sum that satisfies the condition + return left diff --git a/algorithms/search/binary_search/split_array_largest_sum/images/examples/split_array_largest_sum_example_1.png b/algorithms/search/binary_search/split_array_largest_sum/images/examples/split_array_largest_sum_example_1.png new file mode 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b/DIRECTORY.md @@ -59,6 +59,8 @@ * [Test Climb Stairs](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/climb_stairs/test_climb_stairs.py) * Countingbits * [Test Counting Bits](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/countingbits/test_counting_bits.py) + * Decodeways + * [Test Num Decodings](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/decodeways/test_num_decodings.py) * Domino Tromino Tiling * [Test Domino Tromino Tiling](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/domino_tromino_tiling/test_domino_tromino_tiling.py) * Duffle Bug Value @@ -214,6 +216,8 @@ * [Test Divide Chocolate](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/binary_search/divide_chocolate/test_divide_chocolate.py) * Maxruntime N Computers * [Test Max Runtime](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/binary_search/maxruntime_n_computers/test_max_runtime.py) + * Split Array Largest Sum + * [Test Split Array Largest Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/binary_search/split_array_largest_sum/test_split_array_largest_sum.py) * [Test Binary Search](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/binary_search/test_binary_search.py) * Interpolation * [Test Interpolation Search](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/search/interpolation/test_interpolation_search.py) From 933cc3c602382f4890e6de36d90da239f2b03f5d Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 19 Jan 2026 09:52:12 +0300 Subject: [PATCH 4/9] feat(algorithms, two-pointers): count pairs --- algorithms/two_pointers/count_pairs/README.md | 85 ++++++++++++++++++ .../two_pointers/count_pairs/__init__.py | 47 ++++++++++ .../images/examples/count_pairs_example_1.png | Bin 0 -> 40407 bytes .../images/examples/count_pairs_example_2.png | Bin 0 -> 33825 bytes .../images/examples/count_pairs_example_3.png | Bin 0 -> 39620 bytes .../images/examples/count_pairs_example_4.png | Bin 0 -> 25858 bytes .../solutions/count_pairs_solution_1.png | Bin 0 -> 20635 bytes .../solutions/count_pairs_solution_10.png | Bin 0 -> 27565 bytes .../solutions/count_pairs_solution_2.png | Bin 0 -> 32759 bytes .../solutions/count_pairs_solution_3.png | Bin 0 -> 28153 bytes .../solutions/count_pairs_solution_4.png | Bin 0 -> 29515 bytes .../solutions/count_pairs_solution_5.png | Bin 0 -> 29761 bytes .../solutions/count_pairs_solution_6.png | Bin 0 -> 35363 bytes .../solutions/count_pairs_solution_7.png | Bin 0 -> 35819 bytes .../solutions/count_pairs_solution_8.png | Bin 0 -> 29857 bytes .../solutions/count_pairs_solution_9.png | Bin 0 -> 35614 bytes .../count_pairs/test_count_pairs.py | 27 ++++++ .../two_pointers/two_sum_less_k/__init__.py | 60 ++++++------- .../two_sum_less_k/test_two_sum.py | 51 +++-------- 19 files changed, 201 insertions(+), 69 deletions(-) create mode 100644 algorithms/two_pointers/count_pairs/README.md create mode 100644 algorithms/two_pointers/count_pairs/__init__.py create mode 100644 algorithms/two_pointers/count_pairs/images/examples/count_pairs_example_1.png create mode 100644 algorithms/two_pointers/count_pairs/images/examples/count_pairs_example_2.png create mode 100644 algorithms/two_pointers/count_pairs/images/examples/count_pairs_example_3.png create mode 100644 algorithms/two_pointers/count_pairs/images/examples/count_pairs_example_4.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_1.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_10.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_2.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_3.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_4.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_5.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_6.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_7.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_8.png create mode 100644 algorithms/two_pointers/count_pairs/images/solutions/count_pairs_solution_9.png create mode 100644 algorithms/two_pointers/count_pairs/test_count_pairs.py diff --git a/algorithms/two_pointers/count_pairs/README.md b/algorithms/two_pointers/count_pairs/README.md new file mode 100644 index 00000000..615aea4f --- /dev/null +++ b/algorithms/two_pointers/count_pairs/README.md @@ -0,0 +1,85 @@ +# Count Pairs Whose Sum is Less than Target + +You are given a 0-indexed integer array, nums, of length n, and an integer target. Your task is to determine the number +of distinct pairs of indexes (i,j) such that: + +- 0≤i int: + """ + Counts the number of pairs of numbers in a list that sum to a value less than a target. + Uses a two-pointer approach to find the pairs, with a time complexity of O(n log n). + Modifies the list in place to sort the numbers. + Args: + nums (List[int]): A list of integers + target (int): The target value to search for + Returns: + int: The number of pairs of numbers in the list that sum to a value less than the target + """ + # Get the length of the numbers + n = len(nums) + + # Validation check, if there are less than 2 numbers, return 0. We can't form a pair here + if n < 2: + return 0 + + # Sort the nums in place, this incurs a time complexity of O(n log n) + nums.sort() + + # Initialize the left and right pointers + left, right = 0, n - 1 + + # Initialize the count of pairs + count = 0 + + # Use a while loop to find the pairs + while left < right: + # Get the current sum of the numbers at the left and right pointers + current_sum = nums[left] + nums[right] + # If the sum is less than the target, then the numbers in between the left and right pointers + # form valid pairs with the left pointer + if current_sum < target: + # Count the pairs + count += right - left + # Move the pointer up to find other distinct pairs + left += 1 + else: + # move the pointer down to find other pairs, reducing the sum of the boundary + right -= 1 + + # Return the count of pairs + return count diff --git a/algorithms/two_pointers/count_pairs/images/examples/count_pairs_example_1.png 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HcmV?d00001 diff --git a/algorithms/two_pointers/count_pairs/test_count_pairs.py b/algorithms/two_pointers/count_pairs/test_count_pairs.py new file mode 100644 index 00000000..d889ffa6 --- /dev/null +++ b/algorithms/two_pointers/count_pairs/test_count_pairs.py @@ -0,0 +1,27 @@ +import unittest +from typing import List +from parameterized import parameterized +from algorithms.two_pointers.count_pairs import count_pairs + + +COUNT_PAIRS_TEST_CASES = [ + ([1, 3, 2, 4, 5], 6, 4), + ([10, 20, 30, 40], 50, 2), + ([5, 1, 3, 2], 7, 4), + ([-1, 9, 17, 11, 6], 3, 0), + ([20, 20, 20, 20, 20, 20], 7, 0), + ([-5, -4, -3], -5, 3), + ([-1, 1, 2, 3, 1], 2, 3), + ([-6, 2, 5, -2, -7, -1, 3], -2, 10), +] + + +class CountPairsTestCase(unittest.TestCase): + @parameterized.expand(COUNT_PAIRS_TEST_CASES) + def test_count_pairs(self, nums: List[int], target: int, expected: int): + actual = count_pairs(nums, target) + self.assertEqual(expected, actual) + + +if __name__ == "__main__": + unittest.main() diff --git a/algorithms/two_pointers/two_sum_less_k/__init__.py b/algorithms/two_pointers/two_sum_less_k/__init__.py index 86dff9a3..6c7f0b19 100644 --- a/algorithms/two_pointers/two_sum_less_k/__init__.py +++ b/algorithms/two_pointers/two_sum_less_k/__init__.py @@ -8,7 +8,7 @@ def two_sum_less_than_k(nums: List[int], k: int) -> int: that is less than k. It takes the nums array and the target value k as input. Args: nums (List[int]): A sorted list of integers - k int: The target value to search for + k (int): The target value to search for Returns: The maximum sum of two elements that is less than k """ @@ -17,40 +17,38 @@ def two_sum_less_than_k(nums: List[int], k: int) -> int: # sort the numbers in ascending order to facilitate binary search nums.sort() + def search(target: int, start: int) -> int: + """ + Searches for a number that is less than the target in a sorted list of numbers. + Uses binary search to achieve a time complexity of O(log n) and find the index j such that the sum + nums[i]+nums[j] < k. It takes the nums array, target value, and the start range of the search as input. + Args: + target (int): The target value to search for + start (int): The starting index of the search range + Returns: + The index of the number that is less than the target, or -1 if no such number is found + """ + left, right = start, len(nums) - 1 + result = -1 + + while left <= right: + # calculate the midpoint of the search range + mid = (left + right) // 2 + if nums[mid] < target: + # update result to mid and move left to mid + 1 to look for larger values. + result = mid + left = mid + 1 + else: + # move right to mid - 1 to check smaller values. + right = mid - 1 + + return result + for x in range(len(nums)): # find the maximum sum of two elements that is less than k, with the first element being nums[x] - y = search(nums, k - nums[x], x + 1) + y = search(k - nums[x], x + 1) if y > x: # update max_sum with the maximum sum found so far max_sum = max(max_sum, nums[x] + nums[y]) return max_sum - - -def search(nums: List[int], target: int, start: int) -> int: - """ - Searches for a number that is less than the target in a sorted list of numbers. - Uses binary search to achieve a time complexity of O(log n) and find the index j such that the sum - nums[i]+nums[j] < k. It takes the nums array, target value, and the start range of the search as input. - Args: - nums (List[int]): A sorted list of integers - target int: The target value to search for - start int: The starting index of the search range - Returns: - The index of the number that is less than the target, or -1 if no such number is found - """ - left, right = start, len(nums) - 1 - result = -1 - - while left <= right: - # calculate the midpoint of the search range - mid = (left + right) // 2 - if nums[mid] < target: - # update result to mid and move left to mid + 1 to look for larger values. - result = mid - left = mid + 1 - else: - # move right to mid - 1 to check smaller values. - right = mid - 1 - - return result diff --git a/algorithms/two_pointers/two_sum_less_k/test_two_sum.py b/algorithms/two_pointers/two_sum_less_k/test_two_sum.py index 574ff9a6..51cc4f5b 100644 --- a/algorithms/two_pointers/two_sum_less_k/test_two_sum.py +++ b/algorithms/two_pointers/two_sum_less_k/test_two_sum.py @@ -1,48 +1,23 @@ import unittest -from . import two_sum_less_than_k +from typing import List +from parameterized import parameterized +from algorithms.two_pointers.two_sum_less_k import two_sum_less_than_k +TWO_SUM_LESS_K_TEST_CASES = [ + ([4, 2, 11, 2, 5, 3, 5, 8], 7, 6), + ([10, 20, 30], 15, -1), + ([34, 23, 1, 24, 75, 33, 54, 8], 60, 58), + ([5, 5, 5, 5, 5, 5], 15, 10), + ([1, 2, 3, 4, 5], 3, -1), +] -class TwoSumLessKTestCase(unittest.TestCase): - def test_1(self): - """numbers = [4,2,11,2,5,3,5,8], target = 7""" - numbers = [4, 2, 11, 2, 5, 3, 5, 8] - target = 7 - expected = 6 - actual = two_sum_less_than_k(numbers, target) - self.assertEqual(expected, actual) - def test_2(self): - """numbers = [10,20,30], target = 15""" - numbers = [10, 20, 30] - target = 15 - expected = -1 +class TwoSumLessKTestCase(unittest.TestCase): + @parameterized.expand(TWO_SUM_LESS_K_TEST_CASES) + def test_two_sum_less_k(self, numbers: List[int], target: int, expected: int): actual = two_sum_less_than_k(numbers, target) self.assertEqual(expected, actual) - def test_3(self): - """numbers = [34,23,1,24,75,33,54,8], k = 60""" - numbers = [34, 23, 1, 24, 75, 33, 54, 8] - k = 60 - expected = 58 - actual = two_sum_less_than_k(numbers, k) - self.assertEqual(expected, actual) - - def test_4(self): - """numbers = [5,5,5,5,5,5], k = 15""" - numbers = [5, 5, 5, 5, 5, 5] - k = 15 - expected = 10 - actual = two_sum_less_than_k(numbers, k) - self.assertEqual(expected, actual) - - def test_5(self): - """numbers = [1,2,3,4,5], k = 3""" - numbers = [1, 2, 3, 4, 5] - k = 3 - expected = -1 - actual = two_sum_less_than_k(numbers, k) - self.assertEqual(expected, actual) - if __name__ == "__main__": unittest.main() From 58b252a067d46f8c419ea9d0e3cb09970825456d Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Mon, 19 Jan 2026 06:53:15 +0000 Subject: [PATCH 5/9] updating DIRECTORY.md --- DIRECTORY.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 9056f95e..b304ffee 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -259,6 +259,8 @@ * 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) + * Count Pairs + * [Test Count Pairs](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/two_pointers/count_pairs/test_count_pairs.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 From 81693fec1c3c2beef55fbab82a95ba0dc901209a Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 19 Jan 2026 10:04:29 +0300 Subject: [PATCH 6/9] refactor(algorithms, binary-search): split array - guard check for empty array --- .../binary_search/split_array_largest_sum/__init__.py | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/algorithms/search/binary_search/split_array_largest_sum/__init__.py b/algorithms/search/binary_search/split_array_largest_sum/__init__.py index 8c2c2489..974aa937 100644 --- a/algorithms/search/binary_search/split_array_largest_sum/__init__.py +++ b/algorithms/search/binary_search/split_array_largest_sum/__init__.py @@ -40,18 +40,21 @@ def feasible(max_sum: int) -> bool: def split_array_2(nums, k): + if not nums: + return -1 + # Set the initial search range for the largest sum: # Minimum is the largest number in the array, and maximum is the sum of all numbers left, right = max(nums), sum(nums) - def can_split(mid): + def can_split(middle: int): # Initialize the count of subarrays and the current sum of the current subarray subarrays = 1 current_sum = 0 for num in nums: # Check if adding the current number exceeds the allowed sum (mid) - if current_sum + num > mid: + if current_sum + num > middle: # Increment the count of subarrays subarrays += 1 # Start a new subarray with the current number From 93845d3e678dc808653d9265de16aaa34761304b Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 19 Jan 2026 10:05:11 +0300 Subject: [PATCH 7/9] Update algorithms/search/binary_search/split_array_largest_sum/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- .../search/binary_search/split_array_largest_sum/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/search/binary_search/split_array_largest_sum/README.md b/algorithms/search/binary_search/split_array_largest_sum/README.md index dabba581..bda6f420 100644 --- a/algorithms/search/binary_search/split_array_largest_sum/README.md +++ b/algorithms/search/binary_search/split_array_largest_sum/README.md @@ -1,4 +1,4 @@ -# Split Array Largest Sum +# Split Array Largest Sum Given an integer list nums and an integer k, split nums into k non-empty subarrays such that the largest sum among these subarrays is minimized. The task is to find the minimized largest sum by choosing the split such that the largest sum of From 68db8aeb251f7dc1dac2a159adf96d1270f8fc40 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 19 Jan 2026 10:05:38 +0300 Subject: [PATCH 8/9] Update algorithms/search/binary_search/split_array_largest_sum/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- .../search/binary_search/split_array_largest_sum/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/search/binary_search/split_array_largest_sum/README.md b/algorithms/search/binary_search/split_array_largest_sum/README.md index bda6f420..1e6583f5 100644 --- a/algorithms/search/binary_search/split_array_largest_sum/README.md +++ b/algorithms/search/binary_search/split_array_largest_sum/README.md @@ -103,4 +103,4 @@ The time complexity becomes `n log(m)` because the `can_split` function is calle ### Space Complexity -The time complexity of this solution is O(1) because only constant space is used. +The space complexity of this solution is O(1) because only constant space is used. From c1903b01b658757a3847f9885d0dcd6d2b723798 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 19 Jan 2026 10:13:09 +0300 Subject: [PATCH 9/9] Update algorithms/search/binary_search/split_array_largest_sum/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- .../search/binary_search/split_array_largest_sum/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/search/binary_search/split_array_largest_sum/README.md b/algorithms/search/binary_search/split_array_largest_sum/README.md index 1e6583f5..c00f5518 100644 --- a/algorithms/search/binary_search/split_array_largest_sum/README.md +++ b/algorithms/search/binary_search/split_array_largest_sum/README.md @@ -97,7 +97,7 @@ Here’s the step-by-step implementation of the solution: The time complexity of this solution is O(n log(m)), where n is the length of the input array, and m is the difference between `max(nums)` and `sum(nums)` because the range of possible sums considered during the binary search is from -`max(nums)`to `sum(nums)`. This range size determines the number of iterations in the binary search. The tighter this +`max(nums)` to `sum(nums)`. This range size determines the number of iterations in the binary search. The tighter this range, the fewer iterations are needed. However, in the worst case, it spans the full difference: `sum(nums) - max(nums)`. The time complexity becomes `n log(m)` because the `can_split` function is called `n` times for each iteration.

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