Merge pull request #193 from BrianLusina/feat/algorithms-backtracking-additive-number

feat(algorithms, backtracking): is additive number

Author: BrianLusina

DIRECTORY.md

@@ -22,6 +22,8 @@
     * Subsequence
       * [Test Is Valid Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/arrays/subsequence/test_is_valid_subsequence.py)
   * Backtracking
+    * Additive Number
+      * [Test Additive Number](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/backtracking/additive_number/test_additive_number.py)
     * Combination
       * [Test Combination](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/backtracking/combination/test_combination.py)
       * [Test Combination 2](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/backtracking/combination/test_combination_2.py)
@@ -59,6 +61,9 @@
         * [Shortest Reach](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/bfs/graphs/shortest_reach/shortest_reach.py)
       * Smallest Set Of Vertices
         * [Smallest Set Of Vertices](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/bfs/graphs/smallest_set_of_vertices/smallest_set_of_vertices.py)
+  * Counting
+    * Rank Teams By Votes
+      * [Test Rank Teams By Votes](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/counting/rank_teams_by_votes/test_rank_teams_by_votes.py)
   * Dollar Bills
     * [Make Change](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dollar_bills/make_change.py)
   * Dynamic Programming
@@ -114,6 +119,8 @@
       * [Test Pascals Triangle](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/pascals_triangle/test_pascals_triangle.py)
     * Shortest Common Supersequence
       * [Test Shortest Common Supersequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/shortest_common_supersequence/test_shortest_common_supersequence.py)
+    * Total Appeal Of A String
+      * [Test Appeal Of A String](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/total_appeal_of_a_string/test_appeal_of_a_string.py)
     * Unique Paths
       * [Test Unique Paths](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/unique_paths/test_unique_paths.py)
     * Word Break
@@ -153,6 +160,7 @@
     * Network Delay Time
       * [Test Network Delay Time](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/network_delay_time/test_network_delay_time.py)
     * Number Of Islands
+      * [Test Number Of Distinct Islands](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/number_of_islands/test_number_of_distinct_islands.py)
       * [Test Number Of Islands](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/number_of_islands/test_number_of_islands.py)
       * [Union Find](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/number_of_islands/union_find.py)
     * Number Of Provinces
@@ -165,6 +173,8 @@
       * [Test Reorder Routes](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/reorder_routes/test_reorder_routes.py)
     * Rotting Oranges
       * [Test Rotting Oranges](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/rotting_oranges/test_rotting_oranges.py)
+    * Shortest Path Length
+      * [Test Shortest Path Length](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/shortest_path_length/test_shortest_path_length.py)
     * Single Cycle Check
       * [Test Single Cycle Check](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/graphs/single_cycle_check/test_single_cycle_check.py)
     * Sort Items By Group
@@ -249,6 +259,8 @@
     * Employee Free Time
       * [Interval](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/employee_free_time/interval.py)
       * [Test Employee Free Time](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/employee_free_time/test_employee_free_time.py)
+    * Find Right Interval
+      * [Test Find Right Interval](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/find_right_interval/test_find_right_interval.py)
     * Full Bloom Flowers
       * [Test Full Bloom Flowers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/full_bloom_flowers/test_full_bloom_flowers.py)
     * Insert Interval
@@ -266,6 +278,8 @@
       * [Test Non Overlapping Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/non_overlapping_intervals/test_non_overlapping_intervals.py)
     * Remove Intervals
       * [Test Remove Covered Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/remove_intervals/test_remove_covered_intervals.py)
+    * Remove Min Intervals
+      * [Test Remove Min Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/remove_min_intervals/test_remove_min_intervals.py)
     * Task Scheduler
       * [Test Task Scheduler](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/task_scheduler/test_task_scheduler.py)
   * Josephus Circle
@@ -755,6 +769,13 @@
     * [Circuit Breaker](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/circuit_breaker/circuit_breaker.py)
   * Continuous Median
     * [Test Continuous Median Handler](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/continuous_median/test_continuous_median_handler.py)
+  * Creational
+    * Factory
+      * Notification
+        * [Email Notification](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/creational/factory/notification/email_notification.py)
+        * [Notification](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/creational/factory/notification/notification.py)
+        * [Notification Factory](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/creational/factory/notification/notification_factory.py)
+        * [Sms Notification](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/creational/factory/notification/sms_notification.py)
   * Event Stream
     * [Audit Logger](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/event_stream/audit_logger.py)
     * [Batch Event Processor](https://github.com/BrianLusina/PythonSnips/blob/master/design_patterns/event_stream/batch_event_processor.py)

algorithms/backtracking/additive_number/README.md

@@ -0,0 +1,87 @@
+# Additive Number
+
+An additive number is a string whose digits can form an additive sequence.
+
+A valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent
+number in the sequence must be the sum of the preceding two.
+
+Given a string containing only digits, return true if it is an additive number or false otherwise.
+
+> Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.
+
+## Examples
+
+Example 1:
+```text
+Input: "112358"
+Output: true
+Explanation: 
+The digits can form an additive sequence: 1, 1, 2, 3, 5, 8. 
+1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
+```
+
+Example 2:
+```text
+Input: "199100199"
+Output: true
+Explanation: 
+The additive sequence is: 1, 99, 100, 199. 
+1 + 99 = 100, 99 + 100 = 199
+```
+
+## Constraints
+
+- 1 <= num.length <= 35
+- num consists only of digits.
+
+## Topics
+
+- String
+- Backtracking
+
+## Solution
+
+The key intuition behind this problem is that once we fix the first two numbers in the sequence, the entire rest of the
+sequence is completely determined, each subsequent number must equal the sum of the two preceding ones. Therefore, we
+use backtracking to try all possible ways to choose the first and second numbers by varying their lengths, and for each
+choice, we greedily verify whether the remaining digits of the string can be partitioned to satisfy the additive property.
+The backtrack function processes the string from left to right, extracting candidate numbers of increasing length. For
+the first two numbers (count < 2), we freely explore all possible lengths. Once we have at least two numbers, we compute
+the `expectedSum` and prune: if `currentNum` exceeds `expectedSum`, we break (longer substrings will only be larger); if
+`currentNum` is less, we continue to try a longer substring. If `currentNum` matches, we recurse deeper. The recursion
+succeeds when we consume the entire string with at least 3 numbers in the sequence.
+
+Now, let's look at the solution steps below:
+
+1. Initialize n as the length of the input string num.
+2. Define a recursive helper function `backtrack(start, prev1, prev2, count)` where `start` is the current index in `num`,
+   `prev1` is the second-to-last number, `prev2` is the last number, and count tracks how many numbers have been placed
+   so far.
+3. **Base case**: If `start` equals `n` (the entire string has been consumed), return true if count ≥ 3, otherwise return
+   false.
+4. Iterate over all possible end positions `end` from `start + 1` to `n` (inclusive) to form candidate substrings
+   `num[start:end]`.
+   - If the substring has length greater than 1 and starts with '0', break out of the loop — this handles the leading-zero
+     constraint, since any longer substring starting from the same position will also have a leading zero.
+   - Convert the `substring` to an integer `currentNum`.
+   - If `count ≥ 2` (meaning we already have at least two numbers), compute `expectedSum` as `prev1 + prev2`.
+     - If `currentNum` > `expectedSum`, break as no need to try longer substrings since they will only yield larger values.
+     - If `currentNum` < `expectedSum`, continue and try a longer substring that might match the expected sum.
+     - If `currentNum` = `expectedSum`, proceed to recurse.
+   - Recursively call `backtrack(end, prev2, currentNum, count + 1)`. If it returns true, propagate true upward immediately.
+5. If no valid partition is found after exhausting all candidates, return false.
+6. Invoke backtrack(0, 0, 0, 0) and return its result.
+
+### Time Complexity
+
+The time complexity is commonly described as O(n^3): O(n^2) choices for the first two numbers, and O(n) to validate the
++rest for each choice. If you also account for substring-to-integer parsing cost, the practical bound can be higher.
+
+> Note that Python natively handles arbitrarily large integers, which addresses the follow-up question about overflow
+> for very large inputs, no special handling is needed.
+
+### Space Complexity
+
+The space complexity of the solution is O(n) because the recursion depth is at most O(n) (in the case where each number
+is a single digit), and each recursive call uses a constant amount of additional space aside from the call stack.
+Substring creation also uses up to O(n) space.

algorithms/backtracking/additive_number/__init__.py

@@ -0,0 +1,73 @@
+def is_additive_number_dfs(num: str) -> bool:
+    if not num:
+        return False
+
+    n = len(num)
+
+    def dfs(a: int, b: int, number: str) -> bool:
+        if not number:
+            return True
+
+        if a + b > 0 and number[0] == "0":
+            return False
+
+        for i in range(1, len(number) + 1):
+            if a + b == int(number[:i]):
+                if dfs(b, a + b, number[i:]):
+                    return True
+        return False
+
+    for x in range(1, n - 1):
+        for y in range(x + 1, n):
+            if x > 1 and num[0] == "0":
+                break
+            if y - x > 1 and num[x] == "0":
+                continue
+            if dfs(int(num[:x]), int(num[x:y]), num[y:]):
+                return True
+
+    return False
+
+
+def is_additive_number_backtrack(num: str) -> bool:
+    n = len(num)
+
+    def backtrack(start: int, prev1: int, prev2: int, count: int) -> bool:
+        # Base case: we've consumed the entire string
+        if start == n:
+            # Valid only if we have at least 3 numbers in the sequence
+            return count >= 3
+
+        # Try every possible next number by varying its length
+        for end in range(start + 1, n + 1):
+            # Extract the substring representing the current number
+            substring = num[start:end]
+
+            # Skip numbers with leading zeros (e.g., "03"), but "0" itself is allowed
+            if len(substring) > 1 and substring[0] == "0":
+                break  # No point trying longer substrings; they'll also have leading zero
+
+            current_num = int(substring)
+
+            # If we already have at least 2 numbers, validate the additive property
+            if count >= 2:
+                expected_sum = prev1 + prev2
+
+                # If current number is too large, no need to try longer substrings
+                if current_num > expected_sum:
+                    break
+
+                # If current number doesn't match the expected sum, try next length
+                if current_num < expected_sum:
+                    continue
+
+                # current_num == expected_sum, so recurse with updated sequence
+
+            # Recurse: prev2 becomes prev1, current_num becomes the new prev2
+            if backtrack(end, prev2, current_num, count + 1):
+                return True
+
+        return False
+
+    # Start backtracking from index 0 with no previous numbers and count = 0
+    return backtrack(0, 0, 0, 0)

algorithms/backtracking/additive_number/test_additive_number.py

@@ -0,0 +1,34 @@
+import unittest
+from algorithms.backtracking.additive_number import (
+    is_additive_number_dfs,
+    is_additive_number_backtrack,
+)
+from parameterized import parameterized
+
+IS_ADDITIVE_NUMBER_TEST_CASES = [
+    ("112358", True),
+    ("199100199", True),
+    ("11235813", True),
+    ("12345", False),
+    ("000", True),
+    ("1", False),
+    ("0", False),
+    ("101", True),
+    ("1023", False),
+]
+
+
+class AdditiveNumberTestCase(unittest.TestCase):
+    @parameterized.expand(IS_ADDITIVE_NUMBER_TEST_CASES)
+    def test_is_additive_number_dfs(self, num: str, expected: bool):
+        actual = is_additive_number_dfs(num)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(IS_ADDITIVE_NUMBER_TEST_CASES)
+    def test_is_additive_number_backtrack(self, num: str, expected: bool):
+        actual = is_additive_number_backtrack(num)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()