Create longest_increasing_subsequence_iterative.py

dynamic_programming/longest_increasing_subsequence_iterative.py

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+"""
+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()