Create longest_increasing_subsequence_iterative.py (#12524)

* Create longest_increasing_subsequence_iterative.py

* Update longest_increasing_subsequence_iterative.py

* Update longest_increasing_subsequence_iterative.py

---------

Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

dynamic_programming/longest_increasing_subsequence_iterative.py

@@ -0,0 +1,72 @@
+"""
+Author  : Sanjay Muthu <https://github.com/XenoBytesX>
+
+This is a pure Python implementation of Dynamic Programming solution to the longest
+increasing subsequence of a given sequence.
+
+The problem is:
+    Given an array, to find the longest and increasing sub-array in that given array and
+    return it.
+
+Example:
+    ``[10, 22, 9, 33, 21, 50, 41, 60, 80]`` as input will return
+    ``[10, 22, 33, 50, 60, 80]`` as output
+"""
+
+from __future__ import annotations
+
+import copy
+
+
+def longest_subsequence(array: list[int]) -> list[int]:
+    """
+    Some examples
+
+    >>> longest_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80])
+    [10, 22, 33, 50, 60, 80]
+    >>> longest_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9])
+    [1, 2, 3, 9]
+    >>> longest_subsequence([9, 8, 7, 6, 5, 7])
+    [7, 7]
+    >>> longest_subsequence([28, 26, 12, 23, 35, 39])
+    [12, 23, 35, 39]
+    >>> longest_subsequence([1, 1, 1])
+    [1, 1, 1]
+    >>> longest_subsequence([])
+    []
+    """
+    n = len(array)
+    # The longest increasing subsequence ending at array[i]
+    longest_increasing_subsequence = []
+    for i in range(n):
+        longest_increasing_subsequence.append([array[i]])
+
+    for i in range(1, n):
+        for prev in range(i):
+            # If array[prev] is less than or equal to array[i], then
+            # longest_increasing_subsequence[prev] + array[i]
+            # is a valid increasing subsequence
+
+            # longest_increasing_subsequence[i] is only set to
+            # longest_increasing_subsequence[prev] + array[i] if the length is longer.
+
+            if array[prev] <= array[i] and len(
+                longest_increasing_subsequence[prev]
+            ) + 1 > len(longest_increasing_subsequence[i]):
+                longest_increasing_subsequence[i] = copy.copy(
+                    longest_increasing_subsequence[prev]
+                )
+                longest_increasing_subsequence[i].append(array[i])
+
+    result: list[int] = []
+    for i in range(n):
+        if len(longest_increasing_subsequence[i]) > len(result):
+            result = longest_increasing_subsequence[i]
+
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()