|
| 1 | +""" |
| 2 | +Author : Sanjay Muthu <https://github.com/XenoBytesX> |
| 3 | + |
| 4 | +This is a pure Python implementation of Dynamic Programming solution to the longest |
| 5 | +increasing subsequence of a given sequence. |
| 6 | + |
| 7 | +The problem is: |
| 8 | + Given an array, to find the longest and increasing sub-array in that given array and |
| 9 | + return it. |
| 10 | + |
| 11 | +Example: |
| 12 | + ``[10, 22, 9, 33, 21, 50, 41, 60, 80]`` as input will return |
| 13 | + ``[10, 22, 33, 50, 60, 80]`` as output |
| 14 | +""" |
| 15 | + |
| 16 | +from __future__ import annotations |
| 17 | + |
| 18 | +import copy |
| 19 | + |
| 20 | + |
| 21 | +def longest_subsequence(array: list[int]) -> list[int]: |
| 22 | + """ |
| 23 | + Some examples |
| 24 | + |
| 25 | + >>> longest_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80]) |
| 26 | + [10, 22, 33, 50, 60, 80] |
| 27 | + >>> longest_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9]) |
| 28 | + [1, 2, 3, 9] |
| 29 | + >>> longest_subsequence([9, 8, 7, 6, 5, 7]) |
| 30 | + [7, 7] |
| 31 | + >>> longest_subsequence([28, 26, 12, 23, 35, 39]) |
| 32 | + [12, 23, 35, 39] |
| 33 | + >>> longest_subsequence([1, 1, 1]) |
| 34 | + [1, 1, 1] |
| 35 | + >>> longest_subsequence([]) |
| 36 | + [] |
| 37 | + """ |
| 38 | + n = len(array) |
| 39 | + # The longest increasing subsequence ending at array[i] |
| 40 | + longest_increasing_subsequence = [] |
| 41 | + for i in range(n): |
| 42 | + longest_increasing_subsequence.append([array[i]]) |
| 43 | + |
| 44 | + for i in range(1, n): |
| 45 | + for prev in range(i): |
| 46 | + # If array[prev] is less than or equal to array[i], then |
| 47 | + # longest_increasing_subsequence[prev] + array[i] |
| 48 | + # is a valid increasing subsequence |
| 49 | + |
| 50 | + # longest_increasing_subsequence[i] is only set to |
| 51 | + # longest_increasing_subsequence[prev] + array[i] if the length is longer. |
| 52 | + |
| 53 | + if array[prev] <= array[i] and len( |
| 54 | + longest_increasing_subsequence[prev] |
| 55 | + ) + 1 > len(longest_increasing_subsequence[i]): |
| 56 | + longest_increasing_subsequence[i] = copy.copy( |
| 57 | + longest_increasing_subsequence[prev] |
| 58 | + ) |
| 59 | + longest_increasing_subsequence[i].append(array[i]) |
| 60 | + |
| 61 | + result: list[int] = [] |
| 62 | + for i in range(n): |
| 63 | + if len(longest_increasing_subsequence[i]) > len(result): |
| 64 | + result = longest_increasing_subsequence[i] |
| 65 | + |
| 66 | + return result |
| 67 | + |
| 68 | + |
| 69 | +if __name__ == "__main__": |
| 70 | + import doctest |
| 71 | + |
| 72 | + doctest.testmod() |
0 commit comments