Add lazy segment tree

[sak-codes]

References to other Issues or PRs or Relevant literature

Brief description of what is fixed or changed

Other comments

[codecov]

Codecov Report

Merging #539 (069b5df) into main (8f419fd) will decrease coverage by 1.743%.
Report is 15 commits behind head on main.
The diff coverage is 71.014%.

Additional details and impacted files

@@              Coverage Diff              @@
##              main      #539       +/-   ##
=============================================
- Coverage   98.528%   96.785%   -1.743%     
=============================================
  Files           32        34        +2     
  Lines         4010      4418      +408     
=============================================
+ Hits          3951      4276      +325     
- Misses          59       142       +83     

Files Changed	Coverage Δ
...ucts/miscellaneous_data_structures/segment_tree.py	82.327% <70.542%> (-14.869%)	⬇️
...tructs/miscellaneous_data_structures/algorithms.py	94.000% <77.777%> (-0.792%)	⬇️

... and 14 files with indirect coverage changes

[czgdp1807]

Run same tests of OneDimensionalArraySegmentTree with the new one. Put all tests into common function and pass objects of OneDimensionalArraySegmentTree and OneDimensionalArraySegmentTreeLazy to the common function.

[sak-codes]

I am trying to design the method parameters such that I can generalize the implementation but since lazy updates for each of the different applications have different implementation, I am unable to find a common design.

[czgdp1807]

lazy updates for each of the different applications have different implementation, I am unable to find a common design.

Share some examples so that we can figure something out.

[sak-codes]

Suppose we are solving an range sum update problem where we want to increment all the elements in the range $[i, j]$ with some number x. This is okay and well generalized for j != i. But when we want to change some element at index $i$, then if we use the same above approach then we need to pass by y=x-cur_value[i], then during the update we will have cur_value[i] += y. So user will get confuse when to use y and when to use x.

[czgdp1807]

Suggested change

	def update_range(self, start, end, value):
	def update(self, start, end, value):

[czgdp1807]

Suggested change

	def update(self, index, value):
	def __setitem__(self, index, value):

[czgdp1807]

Same for the parent class.

[czgdp1807]

I think right now the case is update for a single value and update_range for a range. I think we discussed to use __setitem__ to update a single value. However, for a range we will use update. So please do it.

[sak-codes]

So you want me to rename update_range to update?