You are given a list of n integers. Your task is to count how many longest increasing subsequences the list has.
For example, in the list [4,1,5,6,3,4,3,8], a longest increasing subsequence contains 4 numbers. The possible subsequences are [1,3,4,8], [1,5,6,8] and [4,5,6,8]. Thus the answer is 3 in this case.
In a file countlis.py
, implement the function count_sequences
that takes a list of integers as a parameter. The function should return the number of longest increasing subsequences.
The function should be efficient when 1 \le n \le 100.
def count_sequences(numbers): # TODO if __name__ == "__main__": print(count_sequences([1, 2, 3])) # 1 print(count_sequences([3, 2, 1])) # 3 print(count_sequences([1, 1, 1, 1, 1])) # 5 print(count_sequences([1, 8, 2, 7, 3, 6])) # 1 print(count_sequences([1, 1, 2, 2, 3, 3])) # 8 print(count_sequences([4, 1, 5, 6, 3, 4, 3, 8])) # 3