TsingPig_Lab is a package for algorithm.
Project description
TsingPig - Lab
[TOC]
1. Introduction
This is a python package for simple algorithms and data structures which is developed by tsingpig.
Author: TsingPig
Repo: https://gitlab.com/tsingpig-code/tsingpig_lab
You can connect me by email: 1114196607@qq.com
Thanks for your support!
2. Features
2.1. DataStructures
2.1.1 Sparse Table (ST)
A data structure ST table (Sparse Table) that supports interval contribution problem queries.
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(nums: List, opt = lambda a, b: max(a, b)) |
$O(n \log n)$ | Initialize the Sparse Table (ST) data structure with the given list of numbers and an optional comparison function. |
qry(L: int, R: int) |
$O(1)$ | Query the opt value within the range [L, R]. |
**Example **
from tsingpig_lab.DataStructures import ST as ST
st = ST([1, 9, 0, 2, 4, 5])
print(st.qry(1, 3)) # 9
You can also customize comparison methods by passing function parameters. In default condition, the maximum value will be returned.
from tsingpig_lab.DataStructures import ST as ST
st = ST([1, 9, -99, 2, 4, 5], lambda a, b: min(a, b))
print(st.qry(1, 4)) # -99
Please note that the issue of contribution needs to be met. It means $Opt (x, x)=x$
2.1.2 Fenwick Tree
A data structure Fenwick Tree that supports range queries efficiently.
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(n: int, discretize: bool = False, nums: List[int] = None) |
$O(n \log n)$ | Initialize the Fenwick Tree data structure with the given array length n and optionally with discretized values. |
update(x: int, val: int = 1) |
$O(\log n)$ | Update the value at index x by adding val . |
query(lx: int, rx: int = None) |
$O(\log n)$ | If only lx is provided, query the number of elements less than or equal to lx . If both lx and rx are provided, query the number of elements between lx and rx inclusive. |
**Example **
Example without discretization
from tsingpig_lab.DataStructures import FenwickTree as FenwickTree
tr = FenwickTree(10)
tr.update(1, 1)
tr.update(2, 2)
tr.update(3, 5)
tr.update(1, 3)
# [0, 4, 2, 5, 0, 0, 0, 0, 0, 0]
print(tr.query(1, 10)) # 11
Example with discretization锛宨t allows the input array nums
has repeated elements.
from tsingpig_lab.DataStructures import FenwickTree as FenwickTree
nums = [1, 9, -99, 2, 4, 5, -99]
ft = FenwickTree(len(nums), discretize=True, nums=nums)
ft.update(2, 4)
ft.update(-99, 3)
# [0, 0, 3, 4, 0, 0]
print(ft.query(-99, 9)) # 7
2.1.3 SegmentTree
This type of segment tree is static, which means you need to predetermine the size of the input arrays. And during the whole usage of this tree, the size is fixed and can not be change.
This static nature can offer performance benefits in scenarios where the size of the dataset is known and fixed, avoiding the overhead associated with dynamic resizing.
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(nums, ops='sum') |
$O(n)$ | Initialize the Segment Tree data structure with the given array nums and operation type ops , defaulting to sum operation. |
build(idx=1, l=1, r=None) |
$O(n)$ | Build the Segment Tree. |
update(ul, ur, val, idx=1, l=1, r=None) |
$O(\log n)$ | Update the range [ul, ur] with the given value val . |
query(ql, qr, idx=1, l=1, r=None) |
$O(\log n)$ | Query the result value within the range [ql, qr]. |
Sample
from tsingpig_lab.DataStructures import SegmentTree as SegmentTree
tr = SegmentTree([1, 2, 3, 4, 5], 'sum')
tr.build()
print(tr.query(1, 5)) # 15
print(tr.query(2, 5)) # 14
tr.update(2, 4, 2) # 1 4 5 6 5
print(tr.query(2, 5)) # 20
tr = SegmentTree([8, 4, 5, 7, 9], 'min')
tr.build()
print(tr.query(1, 4)) # 4
tr.update(1, 4, 5) # [5, 4, 5, 5, 9]
print(tr.query(4, 5)) # 5
tr.update(3, 5, -10) # [5, 4, -10, -10, -10]
print(tr.query(1, 3)) # -10
Note: The index is start with 1.
2.1.4 SegmentTreeDynamic
This type of segment tree is dynamic, which means it supports dynamic allocation of nodes and efficient updates and queries on potentially very large ranges. This is beneficial when the range of possible indices is large, but the number of actual updates or queries is sparse.
The dynamic nature of this segment tree allows it to handle large datasets efficiently without requiring a fixed size at initialization, making it suitable for scenarios with unknown or very large ranges.
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(ops='sum', max_val=1e9) |
$O(1)$ | Initialize the Segment Tree data structure with the operation type ops , defaulting to sum operation, and a maximum value for the range. |
update(ul, ur, val, node=None, l=1, r=None) |
$O(\log n)$ | Update the range [ul, ur] with the given value val . |
query(ql, qr, node=None, l=1, r=None) |
$O(\log n)$ | Query the result value within the range [ql, qr]. |
Sample
Import the SegmentTreeDynamic class
from your_module import SegmentTreeDynamic
# Initialize the segment tree for sum operation with a maximum value of 1e15
tr = SegmentTreeDynamic('sum', int(1e15))
tr.update(1, 5, 99)
tr.update(1, 5, 1)
print(tr.query(1, 1)) # 100
print(tr.query(1, 5)) # 500
# Initialize the segment tree for min operation
tr = SegmentTreeDynamic(ops='min')
tr.update(1, 5, 10)
print(tr.query(1, 4)) # 10
tr.update(2, 4, 5) # [10, 5, 5, 5, 10]
print(tr.query(4, 5)) # 5
tr.update(3, 5, -10) # [10, 5, -10, -10, -10]
print(tr.query(1, 3)) # -10
Note: The index starts at 1.
2.2. Algorithms
2.2.1 BaseConverter
Using for convert input number with base-a to result number with base-b.
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(a: int, b: int) |
N/A | Initialize the BaseConverter with base a to convert numbers to base b . The bases must be within the range [2, 16]. |
convert(num: str) -> str |
$O(\log n)$ | Convert a number in base a (given as a string) to its representation in base b . |
**Example **
As shown below, you create a base converter from base-10 to base-2.
from tsingpig_lab.Algorithms import BaseConverter
baseCon = BaseConverter(10, 2)
print(baseCon.convert("123")) # 1111011
As shown below, you create a base converter from base-16 to base-10.
All of the input and output string should not contain any prefix string or suffix string, for example you should not input like '1BF52H' or '0x1BF52', which may bring wrong results or errors.
from tsingpig_lab.Algorithms import BaseConverter
baseCon = BaseConverter(16, 10)
print(baseCon.convert("1BF52")) # 114514
2.2.2 Bin
Usage
Method | Time Complexity | Description |
---|---|---|
__init__(num: str, b: int = 2) |
N/A | Initialize the Bin object with a number string num in base b (default is binary). If b is not 2, it converts the number from base b to base 2. |
grey_to_bin() -> str |
$O(n)$ | Converts the stored binary string, treated as a Gray code, to its corresponding binary code. $n$ is the length of the binary representation of $num$ . |
bin_to_grey() -> str |
$O(n)$ | Converts the stored binary string, treated as a binary code, to its corresponding Gray code. |
**Example **
As shown below, you initialize a binary object base on 2.
from tsingpig_lab.Algorithms import Bin
b = Bin('1111')
You can also initialize a binary object base on any number.
from tsingpig_lab.Algorithms import Bin
b = Bin("11", 10) # 1011
Calculate the binary num string which is treated as a normal binary code to Gray Code as below.
from tsingpig_lab.Algorithms import Bin
b = Bin("11", 10) # 1011
print(b.grey_to_bin()) # 1101
Calculate the binary num string which is treated as Gray Code code to normal binary code as below.
from tsingpig_lab.Algorithms import Bin
b = Bin("1100")
print(b.bin_to_grey()) # 1010
3. Note for Pypi
How to upload your own package
Firstly, open your package folder and type this command in its' corresponding cmd:
python setup.py sdist
Then:
twine upload dist/*
And then it works, users can download your package by this line in conda:
pip install TsingPig-Lab==0.1.7 -i https://www.pypi.org/simple/
API
pypi-AgEIcHlwaS5vcmcCJGYxZWEwMjY0LWJmMGUtNGMwMS1hMjM4LTVhZTA2N2EwMDA3MAACKlszLCI3NDRkODY1Ni02ODE3LTRiNjEtYTliMi1kZThmOTI0YjQ5ZWEiXQAABiC-6w2Qs90CFAe8UE5e9oYxb5RbBaRY0KXngikzxWfPcQ
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