chore:Consolidating LCS and LIS Algorithm Implementations into a Single File

dynamic_programming/subsequence_algorithms.py

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+"""
+Author  : Mehdi ALAOUI
+
+This is a pure Python implementation of Dynamic Programming solutions to:
+1. Longest Increasing Subsequence (LIS)
+2. Longest Common Subsequence (LCS)
+
+1. LIS Problem: Given an array, find the longest increasing sub-array and return it.
+Example: [10, 22, 9, 33, 21, 50, 41, 60, 80] -> [10, 22, 33, 41, 60, 80]
+
+2. LCS Problem: Given two sequences, find the length and content of the longest
+common subsequence that appears in both of them. A subsequence appears in the
+same relative order but not necessarily continuously.
+Example: "programming" and "gaming" -> "gaming"
+"""
+
+from __future__ import annotations
+
+
+# Longest Increasing Subsequence (LIS)
+def longest_increasing_subsequence(array: list[int]) -> list[int]:
+    """
+    Finds the longest increasing subsequence in the given array using dynamic programming.
+
+    Parameters:
+    ----------
+    array: list[int]
+        The input array of integers.
+
+    Returns:
+    -------
+    list[int]
+        The longest increasing subsequence (LIS) as a list.
+
+    Examples:
+    --------
+    >>> longest_increasing_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80])
+    [10, 22, 33, 41, 60, 80]
+    >>> longest_increasing_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9])
+    [1, 2, 3, 9]
+    >>> longest_increasing_subsequence([9, 8, 7, 6, 5, 7])
+    [5, 7]
+    >>> longest_increasing_subsequence([1, 1, 1])
+    [1]
+    >>> longest_increasing_subsequence([])
+    []
+    """
+    if not array:
+        return []
+
+    n = len(array)
+    dp = [1] * n  # dp[i] stores the length of the LIS ending at index i
+    prev = [-1] * n  # prev[i] stores the index of the previous element in the LIS
+
+    max_length = 1  # Length of the longest increasing subsequence found
+    max_index = 0  # Index of the last element of the longest increasing subsequence
+
+    # Compute lengths of LIS for all elements
+    for i in range(1, n):
+        for j in range(i):
+            if array[i] > array[j] and dp[i] < dp[j] + 1:
+                dp[i] = dp[j] + 1
+                prev[i] = j
+        if dp[i] > max_length:
+            max_length = dp[i]
+            max_index = i
+
+    # Reconstructing the longest increasing subsequence
+    lis = []
+    while max_index != -1:
+        lis.append(array[max_index])
+        max_index = prev[max_index]
+
+    return lis[::-1]  # The LIS is constructed in reverse order, so reverse it
+
+
+# Longest Common Subsequence (LCS)
+def longest_common_subsequence(x: str, y: str) -> tuple[int, str]:
+    """
+    Finds the longest common subsequence between two strings and its length.
+
+    Examples:
+    >>> longest_common_subsequence("programming", "gaming")
+    (6, 'gaming')
+    >>> longest_common_subsequence("physics", "smartphone")
+    (2, 'ph')
+    >>> longest_common_subsequence("computer", "food")
+    (1, 'o')
+    >>> longest_common_subsequence("", "abc")
+    (0, '')
+    >>> longest_common_subsequence("abc", "")
+    (0, '')
+    >>> longest_common_subsequence("abcdef", "ace")
+    (3, 'ace')
+    """
+    m, n = len(x), len(y)
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            if x[i - 1] == y[j - 1]:
+                dp[i][j] = dp[i - 1][j - 1] + 1
+            else:
+                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+
+    # Reconstructing the longest common subsequence
+    i, j = m, n
+    lcs = []
+    while i > 0 and j > 0:
+        if x[i - 1] == y[j - 1]:
+            lcs.append(x[i - 1])
+            i -= 1
+            j -= 1
+        elif dp[i - 1][j] > dp[i][j - 1]:
+            i -= 1
+        else:
+            j -= 1
+
+    return dp[m][n], "".join(reversed(lcs))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example usage for LIS
+    arr = [10, 22, 9, 33, 21, 50, 41, 60, 80]
+    lis = longest_increasing_subsequence(arr)
+    print(f"Longest Increasing Subsequence: {lis}")
+
+    # Example usage for LCS
+    str1 = "AGGTAB"
+    str2 = "GXTXAYB"
+    length, lcs = longest_common_subsequence(str1, str2)
+    print(f"Longest Common Subsequence: '{lcs}' with length {length}")