Longest increasing subsequence added (#364)

Author: sHiVaNgI821

pydatastructs/linear_data_structures/__init__.py

@@ -35,6 +35,7 @@
     longest_common_subsequence,
     is_ordered,
     upper_bound,
-    lower_bound
+    lower_bound,
+    longest_increasing_subsequence
 )
 __all__.extend(algorithms.__all__)

pydatastructs/linear_data_structures/algorithms.py

@@ -15,9 +15,10 @@
     'cocktail_shaker_sort',
     'quick_sort',
     'longest_common_subsequence',
+    'is_ordered',
     'upper_bound',
     'lower_bound',
-    'is_ordered'
+    'longest_increasing_subsequence'
 ]
 
 def _merge(array, sl, el, sr, er, end, comp):
@@ -978,3 +979,62 @@ def lower_bound(array, value, **kwargs):
             index = mid
             inclusive_end = mid - 1
     return index
+
+def longest_increasing_subsequence(array):
+    """
+    Returns the longest increasing subsequence (as a OneDimensionalArray) that
+    can be obtained from a given OneDimensionalArray. A subsequence
+    of an array is an ordered subset of the array's elements having the same
+    sequential ordering as the original array. Here, an increasing
+    sequence stands for a strictly increasing sequence of numbers.
+
+    Parameters
+    ==========
+
+    array: OneDimensionalArray
+        The given array in the form of a OneDimensionalArray
+
+    Returns
+    =======
+
+    output: OneDimensionalArray
+        Returns the longest increasing subsequence that can be obtained
+        from the given array
+
+    Examples
+    ========
+
+    >>> from pydatastructs import lower_bound, OneDimensionalArray as ODA
+    >>> from pydatastructs import longest_increasing_subsequence as LIS
+    >>> array = ODA(int, [2, 5, 3, 7, 11, 8, 10, 13, 6])
+    >>> longest_inc_subsequence = LIS(array)
+    >>> longest_inc_subsequence
+    [2, 3, 7, 8, 10, 13]
+    >>> array2 = ODA(int, [3, 4, -1, 5, 8, 2, 2 ,2, 3, 12, 7, 9, 10])
+    >>> longest_inc_subsequence = LIS(array2)
+    >>> longest_inc_subsequence
+    [-1, 2, 3, 7, 9, 10]
+    """
+    n = len(array)
+    dp = [0]*n
+    parent = [-1]*n
+    length = 0
+    for i in range(1, n):
+        if array[i] <= array[dp[0]]:
+            dp[0] = i
+        elif array[dp[length]] < array[i]:
+            length += 1
+            dp[length] = i
+            parent[i] = dp[length - 1]
+        else:
+            curr_array = [array[dp[i]] for i in range(length)]
+            ceil = lower_bound(curr_array, array[i])
+            dp[ceil] = i
+            parent[i] = dp[ceil - 1]
+    ans = []
+
+    last_index = dp[length]
+    while last_index != -1:
+        ans[:0] = [array[last_index]]
+        last_index = parent[last_index]
+    return ans

pydatastructs/linear_data_structures/tests/test_algorithms.py

@@ -1,8 +1,10 @@
 from pydatastructs import (
     merge_sort_parallel, DynamicOneDimensionalArray,
     OneDimensionalArray, brick_sort, brick_sort_parallel,
-    heapsort, matrix_multiply_parallel, counting_sort, bucket_sort, cocktail_shaker_sort, quick_sort, longest_common_subsequence,
-    is_ordered, upper_bound, lower_bound)
+    heapsort, matrix_multiply_parallel, counting_sort, bucket_sort,
+    cocktail_shaker_sort, quick_sort, longest_common_subsequence, is_ordered,
+    upper_bound, lower_bound, longest_increasing_subsequence)
+
 
 from pydatastructs.utils.raises_util import raises
 import random
@@ -241,3 +243,31 @@ def test_lower_bound():
     output = lower_bound(arr8, 6, end=3, comp=lambda x, y: x > y)
     expected_result = 1
     assert expected_result == output
+
+def test_longest_increasing_subsequence():
+    ODA = OneDimensionalArray
+
+    arr1 = ODA(int, [2, 5, 3, 7, 11, 8, 10, 13, 6])
+    output = longest_increasing_subsequence(arr1)
+    expected_result = [2, 3, 7, 8, 10, 13]
+    assert expected_result == output
+
+    arr2 = ODA(int, [3, 4, -1, 5, 8, 2, 2, 2, 3, 12, 7, 9, 10])
+    output = longest_increasing_subsequence(arr2)
+    expected_result = [-1, 2, 3, 7, 9, 10]
+    assert expected_result == output
+
+    arr3 = ODA(int, [6, 6, 6, 19, 9])
+    output = longest_increasing_subsequence(arr3)
+    expected_result = [6, 9]
+    assert expected_result == output
+
+    arr4 = ODA(int, [5, 4, 4, 3, 3, 6, 6, 8])
+    output = longest_increasing_subsequence(arr4)
+    expected_result = [3, 6, 8]
+    assert expected_result == output
+
+    arr5 = ODA(int, [7, 6, 6, 6, 5, 4, 3])
+    output = longest_increasing_subsequence(arr5)
+    expected_result = [3]
+    assert expected_result == output