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"""

Problem Statement

=================

Given an array of n positive integers. Write a program to find the sum of maximum sum subsequence of the given array

such that the integers in the subsequence are in increasing order.

Complexity

----------

* Time Complexity: O(n^2)

* Space Complexity: O(n)

Video

-----

* https://youtu.be/99ssGWhLPUE

Reference

---------

* http://www.geeksforgeeks.org/dynamic-programming-set-14-maximum-sum-increasing-subsequence/

"""

def maximum_sum_subsequence(sequence):

sequence_length = len(sequence)

T = [sequence[i] for i in range(sequence_length)]

for index_i in range(1, sequence_length):

for index_j in range(0, index_i):

if sequence[index_j] < sequence[index_i]:

T[index_i] = max(T[index_i], T[index_j] + sequence[index_i])

return max(T)

if __name__ == '__main__':

sequence = [1, 101, 10, 2, 3, 100, 4]

assert 111 == maximum_sum_subsequence(sequence)