Merge pull request #139 from BrianLusina/feat/strings-shortest-common-supersequence

feat(algorithms, strings): shortest common supersequence

Author: BrianLusina

DIRECTORY.md

@@ -73,6 +73,8 @@
       * [Test Min Distance](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/min_distance/test_min_distance.py)
     * Min Path Sum
       * [Test Min Path Sum](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/min_path_sum/test_min_path_sum.py)
+    * Shortest Common Supersequence
+      * [Test Shortest Common Supersequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/shortest_common_supersequence/test_shortest_common_supersequence.py)
     * Unique Paths
       * [Test Unique Paths](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/unique_paths/test_unique_paths.py)
     * Word Break
@@ -182,8 +184,12 @@
     * Repeated Dna Sequences
       * [Test Repeated Dna Sequences](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sliding_window/repeated_dna_sequences/test_repeated_dna_sequences.py)
   * Sorting
+    * Heapsort
+      * [Test Heap Sort](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sorting/heapsort/test_heap_sort.py)
     * Insertionsort
       * [Test Insertion Sort](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sorting/insertionsort/test_insertion_sort.py)
+    * Mergesort
+      * [Test Merge Sort](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sorting/mergesort/test_merge_sort.py)
     * Quicksort
       * [Test Quicksort](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/sorting/quicksort/test_quicksort.py)
     * Selection

algorithms/dynamic_programming/shortest_common_supersequence/README.md

@@ -0,0 +1,26 @@
+# Shortest Common Supersequence
+
+You are given two strings, str1 and str2. Your task is to find the shortest common supersequence (SCS). The shortest 
+possible string that contains both str1 and str2 as subsequences.
+
+If multiple strings satisfy this condition, you may return any one of them.
+
+> Note: A string s is considered a subsequence of another string t if s can be obtained by deleting zero or more 
+> characters from t without changing the order of the remaining characters.
+
+## Constraints
+
+- 1 <= `str1.length`, `str2.length` <= 10^3
+- str1 and str2 consist of lowercase English letters.
+
+## Examples
+
+![Example 1](images/examples/shortest_common_supersequence_example_1.png)
+![Example 2](images/examples/shortest_common_supersequence_example_2.png)
+![Example 3](images/examples/shortest_common_supersequence_example_3.png)
+![Example 4](images/examples/shortest_common_supersequence_example_4.png)
+
+## Related Topics
+
+- String
+- Dynamic Programming

algorithms/dynamic_programming/shortest_common_supersequence/__init__.py

@@ -0,0 +1,64 @@
+def shortest_common_supersequence(str1: str, str2: str) -> str:
+    str1_length = len(str1)
+    str2_length = len(str2)
+
+    # Create a 2D array dp of size (str1_length + 1) x (str2_length + 1), where dp[i][j] represents the length of the
+    # shortest common supersequence (SCS) for the first i characters of str1 and the first j characters of str2.
+    dp = [[0 for _ in range(str2_length + 1)] for _ in range(str1_length + 1)]
+
+    # Initialize the base cases, the first row.
+    # When str2 is empty, the supersequence is str1 itself (length = row index).
+    # This is because if str2 is empty, the only option is to append all characters of str1.
+    for row in range(str1_length + 1):
+        dp[row][0] = row
+
+    # When str1 is empty, the supersequence is str2 itself (length = col index)
+    # because if str1 is empty, the only option is to append all characters of str2.
+    for col in range(str2_length + 1):
+        dp[0][col] = col
+
+    # Fill the DP table using bottom-up DP programming
+    # If characters at str1[row - 1] and str2[col - 1] match, inherit dp[row - 1][col - 1] and add 1 (since the common
+    # character is counted once).
+    # Otherwise, take the minimum of dp[row - 1][col] and dp[row][col - 1], then add 1 (since we need to include either
+    # str1[row - 1] or str2[col - 1]).
+    for row in range(1, str1_length + 1):
+        for col in range(1, str2_length + 1):
+            if str1[row - 1] == str2[col - 1]:
+                # If characters match, inherit the length from the diagonal +1
+                dp[row][col] = dp[row - 1][col - 1] + 1
+            else:
+                # If characters do not match, take the minimum length option +1
+                dp[row][col] = min(dp[row - 1][col], dp[row][col - 1]) + 1
+
+    # Reconstruct the supersequence
+    super_sequence = []
+    row, col = str1_length, str2_length
+
+    while row > 0 and col > 0:
+        if str1[row - 1] == str2[col - 1]:
+            # If characters match, take it from diagonal
+            super_sequence.append(str1[row - 1])
+            row -= 1
+            col -= 1
+        elif dp[row - 1][col] < dp[row][col - 1]:
+            # If str1’s character is part of the supersequence, move up
+            super_sequence.append(str1[row - 1])
+            row -= 1
+        else:
+            # If str2’s character is part of the supersequence, move left
+            super_sequence.append(str2[col - 1])
+            col -= 1
+
+    # Append any remaining characters
+    # If there are leftover characters in str1
+    while row > 0:
+        super_sequence.append(str1[row - 1])
+        row -= 1
+    # If there are leftover characters in str2
+    while col > 0:
+        super_sequence.append(str2[col - 1])
+        col -= 1
+
+    # Reverse the built sequence to get the correct order
+    return "".join(super_sequence[::-1])

algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_1.png

@@ -0,0 +1,29 @@
+import unittest
+from parameterized import parameterized
+from algorithms.dynamic_programming.shortest_common_supersequence import (
+    shortest_common_supersequence,
+)
+
+TEST_CASES = [
+    ("apple", "plejuice", "applejuice"),
+    ("educative", "educative", "educative"),
+    ("ababa", "babab", "ababab"),
+    ("race", "ecar", "racecar"),
+    ("ab", "ac", "abc"),
+    # ("abcxyz", "axbycz", "abcxxyyz"),
+    ("abc", "ab", "abc"),
+    ("aab", "azb", "aabz"),
+    ("abac", "cab", "aabcc"),
+    ("aaaaaaaa", "aaaaaaaa", "aaaaaaaa"),
+]
+
+
+class ShortestCommonSuperSequenceTestCase(unittest.TestCase):
+    @parameterized.expand(TEST_CASES)
+    def test_shortest_common_supersequence(self, str1: str, str2: str, expected: str):
+        actual = shortest_common_supersequence(str1, str2)
+        self.assertEqual(sorted(expected), sorted(actual))
+
+
+if __name__ == "__main__":
+    unittest.main()

algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_2.png

@@ -1,12 +1,15 @@
-def left_child_index(parent_index):
+from typing import List, Any
+
+
+def left_child_index(parent_index: int) -> int:
     return parent_index * 2 + 1
 
 
-def right_child_index(parent_index):
+def right_child_index(parent_index: int) -> int:
     return parent_index * 2 + 2
 
 
-def bubble_down(heap, heap_length, index):
+def bubble_down(heap: List, heap_length: int, index: int):
     """
     Restore a max heap where the value at index may be out of place
     """
@@ -37,7 +40,7 @@ def bubble_down(heap, heap_length, index):
             break
 
 
-def remove_max(heap, heap_length):
+def remove_max(heap: List, heap_length: int):
     """
     Remove and return the largest item from a heap
     Updates the heap in-place, maintaining validity
@@ -54,13 +57,37 @@ def remove_max(heap, heap_length):
     return max_value
 
 
-def heapify(the_list):
+def heapify(the_list: List[Any]):
     # bubble down from the leaf nodes up to the top
     for index in range(len(the_list) - 1, -1, -1):
         bubble_down(the_list, len(the_list), index)
 
 
-def heapsort(the_list: list):
+def heapify_2(the_list: List[Any], n: int, i: int):
+    # Assume the current index i is the largest
+    largest = i
+    # index of left child
+    left = 2 * i + 1
+    # index of right child
+    right = 2 * i + 2
+
+    # Check if the left child exists and is greater than the current largest
+    if left < n and the_list[left] > the_list[largest]:
+        largest = left
+
+    # Check if the right child exists and is greater than the current largest
+    if right < n and the_list[right] > the_list[largest]:
+        largest = right
+
+    # If the largest is not the root, swap and continue heapifying the affected subtree
+    if largest != i:
+        # swap
+        the_list[i], the_list[largest] = the_list[largest], the_list[i]
+        # recursively heapify the sub-tree
+        heapify_2(the_list, n, largest)
+
+
+def heapsort(the_list: List[Any]):
     heapify(the_list)
 
     heap_size = len(the_list)
@@ -73,3 +100,21 @@ def heapsort(the_list: list):
         # store the removed value at the end of the list,
         # after the entries used by the heap
         the_list[heap_size] = largest_size
+
+
+def heapsort_2(the_list: List[Any]) -> List[Any]:
+    n = len(the_list)
+    # Step 1: Build a max heap from the input array
+    # (Start from the last non-leaf node and heapify each one)
+    for i in range(n // 2 - 1, -1, -1):
+        heapify_2(the_list, n, i)
+    # Step 2: Extract elements one by one from the heap
+    # Move the current root (largest element) to the end,
+    # then reduce the heap size and re-heapify the root
+    for i in range(n - 1, 0, -1):
+        # move current max to the end
+        the_list[0], the_list[i] = the_list[i], the_list[0]
+        # heapify reduced heap
+        heapify_2(the_list, i, 0)
+    # Return the sorted array (ascending order)
+    return the_list

algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_3.png

@@ -0,0 +1,28 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.sorting.heapsort import heapsort, heapsort_2
+
+TEST_CASES = [
+    ([5, 2, 3, 1], [1, 2, 3, 5]),
+    ([9, -3, 5, 0, -10, 8], [-10, -3, 0, 5, 8, 9]),
+    ([2, 2, 1, 3, 1], [1, 1, 2, 2, 3]),
+    ([4, -1, -1, 2, -2, 0], [-2, -1, -1, 0, 2, 4]),
+    ([0, 0, 0, 0], [0, 0, 0, 0]),
+]
+
+
+class HeapSortTestCase(unittest.TestCase):
+    @parameterized.expand(TEST_CASES)
+    def test_heap_sort(self, nums: List[int], expected: List[int]):
+        heapsort(nums)
+        self.assertEqual(expected, nums)
+
+    @parameterized.expand(TEST_CASES)
+    def test_heap_sort_2(self, nums: List[int], expected: List[int]):
+        actual = heapsort_2(nums)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()