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55 lines
1.2 KiB
Python
55 lines
1.2 KiB
Python
#############################
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# Author: Aravind Kashyap
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# File: lis.py
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# comments: This programme outputs the Longest Strictly Increasing Subsequence in O(NLogN)
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# Where N is the Number of elements in the list
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#############################
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from typing import List
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def CeilIndex(v, l, r, key):
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while r - l > 1:
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m = (l + r) // 2
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if v[m] >= key:
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r = m
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else:
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l = m
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return r
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def LongestIncreasingSubsequenceLength(v: List[int]) -> int:
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"""
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>>> LongestIncreasingSubsequenceLength([2, 5, 3, 7, 11, 8, 10, 13, 6])
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6
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>>> LongestIncreasingSubsequenceLength([])
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0
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>>> LongestIncreasingSubsequenceLength([0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15])
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6
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>>> LongestIncreasingSubsequenceLength([5, 4, 3, 2, 1])
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1
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"""
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if len(v) == 0:
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return 0
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tail = [0] * len(v)
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length = 1
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tail[0] = v[0]
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for i in range(1, len(v)):
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if v[i] < tail[0]:
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tail[0] = v[i]
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elif v[i] > tail[length - 1]:
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tail[length] = v[i]
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length += 1
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else:
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tail[CeilIndex(tail, -1, length - 1, v[i])] = v[i]
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return length
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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