repo stringlengths 7 90 | file_url stringlengths 81 315 | file_path stringlengths 4 228 | content stringlengths 0 32.8k | language stringclasses 1 value | license stringclasses 7 values | commit_sha stringlengths 40 40 | retrieved_at stringdate 2026-01-04 14:38:15 2026-01-05 02:33:18 | truncated bool 2 classes |
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TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/first_come_first_served.py | scheduling/first_come_first_served.py | # Implementation of First Come First Served scheduling algorithm
# In this Algorithm we just care about the order that the processes arrived
# without carring about their duration time
# https://en.wikipedia.org/wiki/Scheduling_(computing)#First_come,_first_served
from __future__ import annotations
def calculate_waiting_times(duration_times: list[int]) -> list[int]:
"""
This function calculates the waiting time of some processes that have a
specified duration time.
Return: The waiting time for each process.
>>> calculate_waiting_times([5, 10, 15])
[0, 5, 15]
>>> calculate_waiting_times([1, 2, 3, 4, 5])
[0, 1, 3, 6, 10]
>>> calculate_waiting_times([10, 3])
[0, 10]
"""
waiting_times = [0] * len(duration_times)
for i in range(1, len(duration_times)):
waiting_times[i] = duration_times[i - 1] + waiting_times[i - 1]
return waiting_times
def calculate_turnaround_times(
duration_times: list[int], waiting_times: list[int]
) -> list[int]:
"""
This function calculates the turnaround time of some processes.
Return: The time difference between the completion time and the
arrival time.
Practically waiting_time + duration_time
>>> calculate_turnaround_times([5, 10, 15], [0, 5, 15])
[5, 15, 30]
>>> calculate_turnaround_times([1, 2, 3, 4, 5], [0, 1, 3, 6, 10])
[1, 3, 6, 10, 15]
>>> calculate_turnaround_times([10, 3], [0, 10])
[10, 13]
"""
return [
duration_time + waiting_times[i]
for i, duration_time in enumerate(duration_times)
]
def calculate_average_turnaround_time(turnaround_times: list[int]) -> float:
"""
This function calculates the average of the turnaround times
Return: The average of the turnaround times.
>>> calculate_average_turnaround_time([0, 5, 16])
7.0
>>> calculate_average_turnaround_time([1, 5, 8, 12])
6.5
>>> calculate_average_turnaround_time([10, 24])
17.0
"""
return sum(turnaround_times) / len(turnaround_times)
def calculate_average_waiting_time(waiting_times: list[int]) -> float:
"""
This function calculates the average of the waiting times
Return: The average of the waiting times.
>>> calculate_average_waiting_time([0, 5, 16])
7.0
>>> calculate_average_waiting_time([1, 5, 8, 12])
6.5
>>> calculate_average_waiting_time([10, 24])
17.0
"""
return sum(waiting_times) / len(waiting_times)
if __name__ == "__main__":
# process id's
processes = [1, 2, 3]
# ensure that we actually have processes
if len(processes) == 0:
print("Zero amount of processes")
raise SystemExit(0)
# duration time of all processes
duration_times = [19, 8, 9]
# ensure we can match each id to a duration time
if len(duration_times) != len(processes):
print("Unable to match all id's with their duration time")
raise SystemExit(0)
# get the waiting times and the turnaround times
waiting_times = calculate_waiting_times(duration_times)
turnaround_times = calculate_turnaround_times(duration_times, waiting_times)
# get the average times
average_waiting_time = calculate_average_waiting_time(waiting_times)
average_turnaround_time = calculate_average_turnaround_time(turnaround_times)
# print all the results
print("Process ID\tDuration Time\tWaiting Time\tTurnaround Time")
for i, process in enumerate(processes):
print(
f"{process}\t\t{duration_times[i]}\t\t{waiting_times[i]}\t\t"
f"{turnaround_times[i]}"
)
print(f"Average waiting time = {average_waiting_time}")
print(f"Average turn around time = {average_turnaround_time}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/job_sequence_with_deadline.py | scheduling/job_sequence_with_deadline.py | """
Given a list of tasks, each with a deadline and reward, calculate which tasks can be
completed to yield the maximum reward. Each task takes one unit of time to complete,
and we can only work on one task at a time. Once a task has passed its deadline, it
can no longer be scheduled.
Example :
tasks_info = [(4, 20), (1, 10), (1, 40), (1, 30)]
max_tasks will return (2, [2, 0]) -
Scheduling these tasks would result in a reward of 40 + 20
This problem can be solved using the concept of "GREEDY ALGORITHM".
Time Complexity - O(n log n)
https://medium.com/@nihardudhat2000/job-sequencing-with-deadline-17ddbb5890b5
"""
from dataclasses import dataclass
from operator import attrgetter
@dataclass
class Task:
task_id: int
deadline: int
reward: int
def max_tasks(tasks_info: list[tuple[int, int]]) -> list[int]:
"""
Create a list of Task objects that are sorted so the highest rewards come first.
Return a list of those task ids that can be completed before i becomes too high.
>>> max_tasks([(4, 20), (1, 10), (1, 40), (1, 30)])
[2, 0]
>>> max_tasks([(1, 10), (2, 20), (3, 30), (2, 40)])
[3, 2]
>>> max_tasks([(9, 10)])
[0]
>>> max_tasks([(-9, 10)])
[]
>>> max_tasks([])
[]
>>> max_tasks([(0, 10), (0, 20), (0, 30), (0, 40)])
[]
>>> max_tasks([(-1, 10), (-2, 20), (-3, 30), (-4, 40)])
[]
"""
tasks = sorted(
(
Task(task_id, deadline, reward)
for task_id, (deadline, reward) in enumerate(tasks_info)
),
key=attrgetter("reward"),
reverse=True,
)
return [task.task_id for i, task in enumerate(tasks, start=1) if task.deadline >= i]
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{max_tasks([(4, 20), (1, 10), (1, 40), (1, 30)]) = }")
print(f"{max_tasks([(1, 10), (2, 20), (3, 30), (2, 40)]) = }")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/shortest_job_first.py | scheduling/shortest_job_first.py | """
Shortest job remaining first
Please note arrival time and burst
Please use spaces to separate times entered.
"""
from __future__ import annotations
import pandas as pd
def calculate_waitingtime(
arrival_time: list[int], burst_time: list[int], no_of_processes: int
) -> list[int]:
"""
Calculate the waiting time of each processes
Return: List of waiting times.
>>> calculate_waitingtime([1,2,3,4],[3,3,5,1],4)
[0, 3, 5, 0]
>>> calculate_waitingtime([1,2,3],[2,5,1],3)
[0, 2, 0]
>>> calculate_waitingtime([2,3],[5,1],2)
[1, 0]
"""
remaining_time = [0] * no_of_processes
waiting_time = [0] * no_of_processes
# Copy the burst time into remaining_time[]
for i in range(no_of_processes):
remaining_time[i] = burst_time[i]
complete = 0
increment_time = 0
minm = 999999999
short = 0
check = False
# Process until all processes are completed
while complete != no_of_processes:
for j in range(no_of_processes):
if (
arrival_time[j] <= increment_time
and remaining_time[j] > 0
and remaining_time[j] < minm
):
minm = remaining_time[j]
short = j
check = True
if not check:
increment_time += 1
continue
remaining_time[short] -= 1
minm = remaining_time[short]
if minm == 0:
minm = 999999999
if remaining_time[short] == 0:
complete += 1
check = False
# Find finish time of current process
finish_time = increment_time + 1
# Calculate waiting time
finar = finish_time - arrival_time[short]
waiting_time[short] = finar - burst_time[short]
waiting_time[short] = max(waiting_time[short], 0)
# Increment time
increment_time += 1
return waiting_time
def calculate_turnaroundtime(
burst_time: list[int], no_of_processes: int, waiting_time: list[int]
) -> list[int]:
"""
Calculate the turn around time of each Processes
Return: list of turn around times.
>>> calculate_turnaroundtime([3,3,5,1], 4, [0,3,5,0])
[3, 6, 10, 1]
>>> calculate_turnaroundtime([3,3], 2, [0,3])
[3, 6]
>>> calculate_turnaroundtime([8,10,1], 3, [1,0,3])
[9, 10, 4]
"""
turn_around_time = [0] * no_of_processes
for i in range(no_of_processes):
turn_around_time[i] = burst_time[i] + waiting_time[i]
return turn_around_time
def calculate_average_times(
waiting_time: list[int], turn_around_time: list[int], no_of_processes: int
) -> None:
"""
This function calculates the average of the waiting & turnaround times
Prints: Average Waiting time & Average Turn Around Time
>>> calculate_average_times([0,3,5,0],[3,6,10,1],4)
Average waiting time = 2.00000
Average turn around time = 5.0
>>> calculate_average_times([2,3],[3,6],2)
Average waiting time = 2.50000
Average turn around time = 4.5
>>> calculate_average_times([10,4,3],[2,7,6],3)
Average waiting time = 5.66667
Average turn around time = 5.0
"""
total_waiting_time = 0
total_turn_around_time = 0
for i in range(no_of_processes):
total_waiting_time = total_waiting_time + waiting_time[i]
total_turn_around_time = total_turn_around_time + turn_around_time[i]
print(f"Average waiting time = {total_waiting_time / no_of_processes:.5f}")
print("Average turn around time =", total_turn_around_time / no_of_processes)
if __name__ == "__main__":
print("Enter how many process you want to analyze")
no_of_processes = int(input())
burst_time = [0] * no_of_processes
arrival_time = [0] * no_of_processes
processes = list(range(1, no_of_processes + 1))
for i in range(no_of_processes):
print("Enter the arrival time and burst time for process:--" + str(i + 1))
arrival_time[i], burst_time[i] = map(int, input().split())
waiting_time = calculate_waitingtime(arrival_time, burst_time, no_of_processes)
bt = burst_time
n = no_of_processes
wt = waiting_time
turn_around_time = calculate_turnaroundtime(bt, n, wt)
calculate_average_times(waiting_time, turn_around_time, no_of_processes)
fcfs = pd.DataFrame(
list(zip(processes, burst_time, arrival_time, waiting_time, turn_around_time)),
columns=[
"Process",
"BurstTime",
"ArrivalTime",
"WaitingTime",
"TurnAroundTime",
],
)
# Printing the dataFrame
pd.set_option("display.max_rows", fcfs.shape[0] + 1)
print(fcfs)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/multi_level_feedback_queue.py | scheduling/multi_level_feedback_queue.py | from collections import deque
class Process:
def __init__(self, process_name: str, arrival_time: int, burst_time: int) -> None:
self.process_name = process_name # process name
self.arrival_time = arrival_time # arrival time of the process
# completion time of finished process or last interrupted time
self.stop_time = arrival_time
self.burst_time = burst_time # remaining burst time
self.waiting_time = 0 # total time of the process wait in ready queue
self.turnaround_time = 0 # time from arrival time to completion time
class MLFQ:
"""
MLFQ(Multi Level Feedback Queue)
https://en.wikipedia.org/wiki/Multilevel_feedback_queue
MLFQ has a lot of queues that have different priority
In this MLFQ,
The first Queue(0) to last second Queue(N-2) of MLFQ have Round Robin Algorithm
The last Queue(N-1) has First Come, First Served Algorithm
"""
def __init__(
self,
number_of_queues: int,
time_slices: list[int],
queue: deque[Process],
current_time: int,
) -> None:
# total number of mlfq's queues
self.number_of_queues = number_of_queues
# time slice of queues that round robin algorithm applied
self.time_slices = time_slices
# unfinished process is in this ready_queue
self.ready_queue = queue
# current time
self.current_time = current_time
# finished process is in this sequence queue
self.finish_queue: deque[Process] = deque()
def calculate_sequence_of_finish_queue(self) -> list[str]:
"""
This method returns the sequence of finished processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> _ = mlfq.multi_level_feedback_queue()
>>> mlfq.calculate_sequence_of_finish_queue()
['P2', 'P4', 'P1', 'P3']
"""
sequence = []
for i in range(len(self.finish_queue)):
sequence.append(self.finish_queue[i].process_name)
return sequence
def calculate_waiting_time(self, queue: list[Process]) -> list[int]:
"""
This method calculates waiting time of processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> _ = mlfq.multi_level_feedback_queue()
>>> mlfq.calculate_waiting_time([P1, P2, P3, P4])
[83, 17, 94, 101]
"""
waiting_times = []
for i in range(len(queue)):
waiting_times.append(queue[i].waiting_time)
return waiting_times
def calculate_turnaround_time(self, queue: list[Process]) -> list[int]:
"""
This method calculates turnaround time of processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> _ = mlfq.multi_level_feedback_queue()
>>> mlfq.calculate_turnaround_time([P1, P2, P3, P4])
[136, 34, 162, 125]
"""
turnaround_times = []
for i in range(len(queue)):
turnaround_times.append(queue[i].turnaround_time)
return turnaround_times
def calculate_completion_time(self, queue: list[Process]) -> list[int]:
"""
This method calculates completion time of processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> _ = mlfq.multi_level_feedback_queue()
>>> mlfq.calculate_turnaround_time([P1, P2, P3, P4])
[136, 34, 162, 125]
"""
completion_times = []
for i in range(len(queue)):
completion_times.append(queue[i].stop_time)
return completion_times
def calculate_remaining_burst_time_of_processes(
self, queue: deque[Process]
) -> list[int]:
"""
This method calculate remaining burst time of processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> finish_queue, ready_queue = mlfq.round_robin(deque([P1, P2, P3, P4]), 17)
>>> mlfq.calculate_remaining_burst_time_of_processes(mlfq.finish_queue)
[0]
>>> mlfq.calculate_remaining_burst_time_of_processes(ready_queue)
[36, 51, 7]
>>> finish_queue, ready_queue = mlfq.round_robin(ready_queue, 25)
>>> mlfq.calculate_remaining_burst_time_of_processes(mlfq.finish_queue)
[0, 0]
>>> mlfq.calculate_remaining_burst_time_of_processes(ready_queue)
[11, 26]
"""
return [q.burst_time for q in queue]
def update_waiting_time(self, process: Process) -> int:
"""
This method updates waiting times of unfinished processes
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> mlfq.current_time = 10
>>> P1.stop_time = 5
>>> mlfq.update_waiting_time(P1)
5
"""
process.waiting_time += self.current_time - process.stop_time
return process.waiting_time
def first_come_first_served(self, ready_queue: deque[Process]) -> deque[Process]:
"""
FCFS(First Come, First Served)
FCFS will be applied to MLFQ's last queue
A first came process will be finished at first
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> _ = mlfq.first_come_first_served(mlfq.ready_queue)
>>> mlfq.calculate_sequence_of_finish_queue()
['P1', 'P2', 'P3', 'P4']
"""
finished: deque[Process] = deque() # sequence deque of finished process
while len(ready_queue) != 0:
cp = ready_queue.popleft() # current process
# if process's arrival time is later than current time, update current time
if self.current_time < cp.arrival_time:
self.current_time += cp.arrival_time
# update waiting time of current process
self.update_waiting_time(cp)
# update current time
self.current_time += cp.burst_time
# finish the process and set the process's burst-time 0
cp.burst_time = 0
# set the process's turnaround time because it is finished
cp.turnaround_time = self.current_time - cp.arrival_time
# set the completion time
cp.stop_time = self.current_time
# add the process to queue that has finished queue
finished.append(cp)
self.finish_queue.extend(finished) # add finished process to finish queue
# FCFS will finish all remaining processes
return finished
def round_robin(
self, ready_queue: deque[Process], time_slice: int
) -> tuple[deque[Process], deque[Process]]:
"""
RR(Round Robin)
RR will be applied to MLFQ's all queues except last queue
All processes can't use CPU for time more than time_slice
If the process consume CPU up to time_slice, it will go back to ready queue
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> finish_queue, ready_queue = mlfq.round_robin(mlfq.ready_queue, 17)
>>> mlfq.calculate_sequence_of_finish_queue()
['P2']
"""
finished: deque[Process] = deque() # sequence deque of terminated process
# just for 1 cycle and unfinished processes will go back to queue
for _ in range(len(ready_queue)):
cp = ready_queue.popleft() # current process
# if process's arrival time is later than current time, update current time
if self.current_time < cp.arrival_time:
self.current_time += cp.arrival_time
# update waiting time of unfinished processes
self.update_waiting_time(cp)
# if the burst time of process is bigger than time-slice
if cp.burst_time > time_slice:
# use CPU for only time-slice
self.current_time += time_slice
# update remaining burst time
cp.burst_time -= time_slice
# update end point time
cp.stop_time = self.current_time
# locate the process behind the queue because it is not finished
ready_queue.append(cp)
else:
# use CPU for remaining burst time
self.current_time += cp.burst_time
# set burst time 0 because the process is finished
cp.burst_time = 0
# set the finish time
cp.stop_time = self.current_time
# update the process' turnaround time because it is finished
cp.turnaround_time = self.current_time - cp.arrival_time
# add the process to queue that has finished queue
finished.append(cp)
self.finish_queue.extend(finished) # add finished process to finish queue
# return finished processes queue and remaining processes queue
return finished, ready_queue
def multi_level_feedback_queue(self) -> deque[Process]:
"""
MLFQ(Multi Level Feedback Queue)
>>> P1 = Process("P1", 0, 53)
>>> P2 = Process("P2", 0, 17)
>>> P3 = Process("P3", 0, 68)
>>> P4 = Process("P4", 0, 24)
>>> mlfq = MLFQ(3, [17, 25], deque([P1, P2, P3, P4]), 0)
>>> finish_queue = mlfq.multi_level_feedback_queue()
>>> mlfq.calculate_sequence_of_finish_queue()
['P2', 'P4', 'P1', 'P3']
"""
# all queues except last one have round_robin algorithm
for i in range(self.number_of_queues - 1):
_finished, self.ready_queue = self.round_robin(
self.ready_queue, self.time_slices[i]
)
# the last queue has first_come_first_served algorithm
self.first_come_first_served(self.ready_queue)
return self.finish_queue
if __name__ == "__main__":
import doctest
P1 = Process("P1", 0, 53)
P2 = Process("P2", 0, 17)
P3 = Process("P3", 0, 68)
P4 = Process("P4", 0, 24)
number_of_queues = 3
time_slices = [17, 25]
queue = deque([P1, P2, P3, P4])
if len(time_slices) != number_of_queues - 1:
raise SystemExit(0)
doctest.testmod(extraglobs={"queue": deque([P1, P2, P3, P4])})
P1 = Process("P1", 0, 53)
P2 = Process("P2", 0, 17)
P3 = Process("P3", 0, 68)
P4 = Process("P4", 0, 24)
number_of_queues = 3
time_slices = [17, 25]
queue = deque([P1, P2, P3, P4])
mlfq = MLFQ(number_of_queues, time_slices, queue, 0)
finish_queue = mlfq.multi_level_feedback_queue()
# print total waiting times of processes(P1, P2, P3, P4)
print(
f"waiting time:\
\t\t\t{MLFQ.calculate_waiting_time(mlfq, [P1, P2, P3, P4])}"
)
# print completion times of processes(P1, P2, P3, P4)
print(
f"completion time:\
\t\t{MLFQ.calculate_completion_time(mlfq, [P1, P2, P3, P4])}"
)
# print total turnaround times of processes(P1, P2, P3, P4)
print(
f"turnaround time:\
\t\t{MLFQ.calculate_turnaround_time(mlfq, [P1, P2, P3, P4])}"
)
# print sequence of finished processes
print(
f"sequence of finished processes:\
{mlfq.calculate_sequence_of_finish_queue()}"
)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/non_preemptive_shortest_job_first.py | scheduling/non_preemptive_shortest_job_first.py | """
Non-preemptive Shortest Job First
Shortest execution time process is chosen for the next execution.
https://www.guru99.com/shortest-job-first-sjf-scheduling.html
https://en.wikipedia.org/wiki/Shortest_job_next
"""
from __future__ import annotations
from statistics import mean
def calculate_waitingtime(
arrival_time: list[int], burst_time: list[int], no_of_processes: int
) -> list[int]:
"""
Calculate the waiting time of each processes
Return: The waiting time for each process.
>>> calculate_waitingtime([0,1,2], [10, 5, 8], 3)
[0, 9, 13]
>>> calculate_waitingtime([1,2,2,4], [4, 6, 3, 1], 4)
[0, 7, 4, 1]
>>> calculate_waitingtime([0,0,0], [12, 2, 10],3)
[12, 0, 2]
"""
waiting_time = [0] * no_of_processes
remaining_time = [0] * no_of_processes
# Initialize remaining_time to waiting_time.
for i in range(no_of_processes):
remaining_time[i] = burst_time[i]
ready_process: list[int] = []
completed = 0
total_time = 0
# When processes are not completed,
# A process whose arrival time has passed \
# and has remaining execution time is put into the ready_process.
# The shortest process in the ready_process, target_process is executed.
while completed != no_of_processes:
ready_process = []
target_process = -1
for i in range(no_of_processes):
if (arrival_time[i] <= total_time) and (remaining_time[i] > 0):
ready_process.append(i)
if len(ready_process) > 0:
target_process = ready_process[0]
for i in ready_process:
if remaining_time[i] < remaining_time[target_process]:
target_process = i
total_time += burst_time[target_process]
completed += 1
remaining_time[target_process] = 0
waiting_time[target_process] = (
total_time - arrival_time[target_process] - burst_time[target_process]
)
else:
total_time += 1
return waiting_time
def calculate_turnaroundtime(
burst_time: list[int], no_of_processes: int, waiting_time: list[int]
) -> list[int]:
"""
Calculate the turnaround time of each process.
Return: The turnaround time for each process.
>>> calculate_turnaroundtime([0,1,2], 3, [0, 10, 15])
[0, 11, 17]
>>> calculate_turnaroundtime([1,2,2,4], 4, [1, 8, 5, 4])
[2, 10, 7, 8]
>>> calculate_turnaroundtime([0,0,0], 3, [12, 0, 2])
[12, 0, 2]
"""
turn_around_time = [0] * no_of_processes
for i in range(no_of_processes):
turn_around_time[i] = burst_time[i] + waiting_time[i]
return turn_around_time
if __name__ == "__main__":
print("[TEST CASE 01]")
no_of_processes = 4
burst_time = [2, 5, 3, 7]
arrival_time = [0, 0, 0, 0]
waiting_time = calculate_waitingtime(arrival_time, burst_time, no_of_processes)
turn_around_time = calculate_turnaroundtime(
burst_time, no_of_processes, waiting_time
)
# Printing the Result
print("PID\tBurst Time\tArrival Time\tWaiting Time\tTurnaround Time")
for i, process_id in enumerate(list(range(1, 5))):
print(
f"{process_id}\t{burst_time[i]}\t\t\t{arrival_time[i]}\t\t\t\t"
f"{waiting_time[i]}\t\t\t\t{turn_around_time[i]}"
)
print(f"\nAverage waiting time = {mean(waiting_time):.5f}")
print(f"Average turnaround time = {mean(turn_around_time):.5f}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/highest_response_ratio_next.py | scheduling/highest_response_ratio_next.py | """
Highest response ratio next (HRRN) scheduling is a non-preemptive discipline.
It was developed as modification of shortest job next or shortest job first (SJN or SJF)
to mitigate the problem of process starvation.
https://en.wikipedia.org/wiki/Highest_response_ratio_next
"""
from statistics import mean
import numpy as np
def calculate_turn_around_time(
process_name: list, arrival_time: list, burst_time: list, no_of_process: int
) -> list:
"""
Calculate the turn around time of each processes
Return: The turn around time time for each process.
>>> calculate_turn_around_time(["A", "B", "C"], [3, 5, 8], [2, 4, 6], 3)
[2, 4, 7]
>>> calculate_turn_around_time(["A", "B", "C"], [0, 2, 4], [3, 5, 7], 3)
[3, 6, 11]
"""
current_time = 0
# Number of processes finished
finished_process_count = 0
# Displays the finished process.
# If it is 0, the performance is completed if it is 1, before the performance.
finished_process = [0] * no_of_process
# List to include calculation results
turn_around_time = [0] * no_of_process
# Sort by arrival time.
burst_time = [burst_time[i] for i in np.argsort(arrival_time)]
process_name = [process_name[i] for i in np.argsort(arrival_time)]
arrival_time.sort()
while no_of_process > finished_process_count:
"""
If the current time is less than the arrival time of
the process that arrives first among the processes that have not been performed,
change the current time.
"""
i = 0
while finished_process[i] == 1:
i += 1
current_time = max(current_time, arrival_time[i])
response_ratio = 0
# Index showing the location of the process being performed
loc = 0
# Saves the current response ratio.
temp = 0
for i in range(no_of_process):
if finished_process[i] == 0 and arrival_time[i] <= current_time:
temp = (burst_time[i] + (current_time - arrival_time[i])) / burst_time[
i
]
if response_ratio < temp:
response_ratio = temp
loc = i
# Calculate the turn around time
turn_around_time[loc] = current_time + burst_time[loc] - arrival_time[loc]
current_time += burst_time[loc]
# Indicates that the process has been performed.
finished_process[loc] = 1
# Increase finished_process_count by 1
finished_process_count += 1
return turn_around_time
def calculate_waiting_time(
process_name: list, # noqa: ARG001
turn_around_time: list,
burst_time: list,
no_of_process: int,
) -> list:
"""
Calculate the waiting time of each processes.
Return: The waiting time for each process.
>>> calculate_waiting_time(["A", "B", "C"], [2, 4, 7], [2, 4, 6], 3)
[0, 0, 1]
>>> calculate_waiting_time(["A", "B", "C"], [3, 6, 11], [3, 5, 7], 3)
[0, 1, 4]
"""
waiting_time = [0] * no_of_process
for i in range(no_of_process):
waiting_time[i] = turn_around_time[i] - burst_time[i]
return waiting_time
if __name__ == "__main__":
no_of_process = 5
process_name = ["A", "B", "C", "D", "E"]
arrival_time = [1, 2, 3, 4, 5]
burst_time = [1, 2, 3, 4, 5]
turn_around_time = calculate_turn_around_time(
process_name, arrival_time, burst_time, no_of_process
)
waiting_time = calculate_waiting_time(
process_name, turn_around_time, burst_time, no_of_process
)
print("Process name \tArrival time \tBurst time \tTurn around time \tWaiting time")
for i in range(no_of_process):
print(
f"{process_name[i]}\t\t{arrival_time[i]}\t\t{burst_time[i]}\t\t"
f"{turn_around_time[i]}\t\t\t{waiting_time[i]}"
)
print(f"average waiting time : {mean(waiting_time):.5f}")
print(f"average turn around time : {mean(turn_around_time):.5f}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/__init__.py | scheduling/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/scheduling/round_robin.py | scheduling/round_robin.py | """
Round Robin is a scheduling algorithm.
In Round Robin each process is assigned a fixed time slot in a cyclic way.
https://en.wikipedia.org/wiki/Round-robin_scheduling
"""
from __future__ import annotations
from statistics import mean
def calculate_waiting_times(burst_times: list[int]) -> list[int]:
"""
Calculate the waiting times of a list of processes that have a specified duration.
Return: The waiting time for each process.
>>> calculate_waiting_times([10, 5, 8])
[13, 10, 13]
>>> calculate_waiting_times([4, 6, 3, 1])
[5, 8, 9, 6]
>>> calculate_waiting_times([12, 2, 10])
[12, 2, 12]
"""
quantum = 2
rem_burst_times = list(burst_times)
waiting_times = [0] * len(burst_times)
t = 0
while True:
done = True
for i, burst_time in enumerate(burst_times):
if rem_burst_times[i] > 0:
done = False
if rem_burst_times[i] > quantum:
t += quantum
rem_burst_times[i] -= quantum
else:
t += rem_burst_times[i]
waiting_times[i] = t - burst_time
rem_burst_times[i] = 0
if done is True:
return waiting_times
def calculate_turn_around_times(
burst_times: list[int], waiting_times: list[int]
) -> list[int]:
"""
>>> calculate_turn_around_times([1, 2, 3, 4], [0, 1, 3])
[1, 3, 6]
>>> calculate_turn_around_times([10, 3, 7], [10, 6, 11])
[20, 9, 18]
"""
return [burst + waiting for burst, waiting in zip(burst_times, waiting_times)]
if __name__ == "__main__":
burst_times = [3, 5, 7]
waiting_times = calculate_waiting_times(burst_times)
turn_around_times = calculate_turn_around_times(burst_times, waiting_times)
print("Process ID \tBurst Time \tWaiting Time \tTurnaround Time")
for i, burst_time in enumerate(burst_times):
print(
f" {i + 1}\t\t {burst_time}\t\t {waiting_times[i]}\t\t "
f"{turn_around_times[i]}"
)
print(f"\nAverage waiting time = {mean(waiting_times):.5f}")
print(f"Average turn around time = {mean(turn_around_times):.5f}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/burrows_wheeler.py | data_compression/burrows_wheeler.py | """
https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform
The Burrows-Wheeler transform (BWT, also called block-sorting compression)
rearranges a character string into runs of similar characters. This is useful
for compression, since it tends to be easy to compress a string that has runs
of repeated characters by techniques such as move-to-front transform and
run-length encoding. More importantly, the transformation is reversible,
without needing to store any additional data except the position of the first
original character. The BWT is thus a "free" method of improving the efficiency
of text compression algorithms, costing only some extra computation.
"""
from __future__ import annotations
from typing import TypedDict
class BWTTransformDict(TypedDict):
bwt_string: str
idx_original_string: int
def all_rotations(s: str) -> list[str]:
"""
:param s: The string that will be rotated len(s) times.
:return: A list with the rotations.
:raises TypeError: If s is not an instance of str.
Examples:
>>> all_rotations("^BANANA|") # doctest: +NORMALIZE_WHITESPACE
['^BANANA|', 'BANANA|^', 'ANANA|^B', 'NANA|^BA', 'ANA|^BAN', 'NA|^BANA',
'A|^BANAN', '|^BANANA']
>>> all_rotations("a_asa_da_casa") # doctest: +NORMALIZE_WHITESPACE
['a_asa_da_casa', '_asa_da_casaa', 'asa_da_casaa_', 'sa_da_casaa_a',
'a_da_casaa_as', '_da_casaa_asa', 'da_casaa_asa_', 'a_casaa_asa_d',
'_casaa_asa_da', 'casaa_asa_da_', 'asaa_asa_da_c', 'saa_asa_da_ca',
'aa_asa_da_cas']
>>> all_rotations("panamabanana") # doctest: +NORMALIZE_WHITESPACE
['panamabanana', 'anamabananap', 'namabananapa', 'amabananapan',
'mabananapana', 'abananapanam', 'bananapanama', 'ananapanamab',
'nanapanamaba', 'anapanamaban', 'napanamabana', 'apanamabanan']
>>> all_rotations(5)
Traceback (most recent call last):
...
TypeError: The parameter s type must be str.
"""
if not isinstance(s, str):
raise TypeError("The parameter s type must be str.")
return [s[i:] + s[:i] for i in range(len(s))]
def bwt_transform(s: str) -> BWTTransformDict:
"""
:param s: The string that will be used at bwt algorithm
:return: the string composed of the last char of each row of the ordered
rotations and the index of the original string at ordered rotations list
:raises TypeError: If the s parameter type is not str
:raises ValueError: If the s parameter is empty
Examples:
>>> bwt_transform("^BANANA")
{'bwt_string': 'BNN^AAA', 'idx_original_string': 6}
>>> bwt_transform("a_asa_da_casa")
{'bwt_string': 'aaaadss_c__aa', 'idx_original_string': 3}
>>> bwt_transform("panamabanana")
{'bwt_string': 'mnpbnnaaaaaa', 'idx_original_string': 11}
>>> bwt_transform(4)
Traceback (most recent call last):
...
TypeError: The parameter s type must be str.
>>> bwt_transform('')
Traceback (most recent call last):
...
ValueError: The parameter s must not be empty.
"""
if not isinstance(s, str):
raise TypeError("The parameter s type must be str.")
if not s:
raise ValueError("The parameter s must not be empty.")
rotations = all_rotations(s)
rotations.sort() # sort the list of rotations in alphabetically order
# make a string composed of the last char of each rotation
response: BWTTransformDict = {
"bwt_string": "".join([word[-1] for word in rotations]),
"idx_original_string": rotations.index(s),
}
return response
def reverse_bwt(bwt_string: str, idx_original_string: int) -> str:
"""
:param bwt_string: The string returned from bwt algorithm execution
:param idx_original_string: A 0-based index of the string that was used to
generate bwt_string at ordered rotations list
:return: The string used to generate bwt_string when bwt was executed
:raises TypeError: If the bwt_string parameter type is not str
:raises ValueError: If the bwt_string parameter is empty
:raises TypeError: If the idx_original_string type is not int or if not
possible to cast it to int
:raises ValueError: If the idx_original_string value is lower than 0 or
greater than len(bwt_string) - 1
>>> reverse_bwt("BNN^AAA", 6)
'^BANANA'
>>> reverse_bwt("aaaadss_c__aa", 3)
'a_asa_da_casa'
>>> reverse_bwt("mnpbnnaaaaaa", 11)
'panamabanana'
>>> reverse_bwt(4, 11)
Traceback (most recent call last):
...
TypeError: The parameter bwt_string type must be str.
>>> reverse_bwt("", 11)
Traceback (most recent call last):
...
ValueError: The parameter bwt_string must not be empty.
>>> reverse_bwt("mnpbnnaaaaaa", "asd") # doctest: +NORMALIZE_WHITESPACE
Traceback (most recent call last):
...
TypeError: The parameter idx_original_string type must be int or passive
of cast to int.
>>> reverse_bwt("mnpbnnaaaaaa", -1)
Traceback (most recent call last):
...
ValueError: The parameter idx_original_string must not be lower than 0.
>>> reverse_bwt("mnpbnnaaaaaa", 12) # doctest: +NORMALIZE_WHITESPACE
Traceback (most recent call last):
...
ValueError: The parameter idx_original_string must be lower than
len(bwt_string).
>>> reverse_bwt("mnpbnnaaaaaa", 11.0)
'panamabanana'
>>> reverse_bwt("mnpbnnaaaaaa", 11.4)
'panamabanana'
"""
if not isinstance(bwt_string, str):
raise TypeError("The parameter bwt_string type must be str.")
if not bwt_string:
raise ValueError("The parameter bwt_string must not be empty.")
try:
idx_original_string = int(idx_original_string)
except ValueError:
raise TypeError(
"The parameter idx_original_string type must be int or passive"
" of cast to int."
)
if idx_original_string < 0:
raise ValueError("The parameter idx_original_string must not be lower than 0.")
if idx_original_string >= len(bwt_string):
raise ValueError(
"The parameter idx_original_string must be lower than len(bwt_string)."
)
ordered_rotations = [""] * len(bwt_string)
for _ in range(len(bwt_string)):
for i in range(len(bwt_string)):
ordered_rotations[i] = bwt_string[i] + ordered_rotations[i]
ordered_rotations.sort()
return ordered_rotations[idx_original_string]
if __name__ == "__main__":
entry_msg = "Provide a string that I will generate its BWT transform: "
s = input(entry_msg).strip()
result = bwt_transform(s)
print(
f"Burrows Wheeler transform for string '{s}' results "
f"in '{result['bwt_string']}'"
)
original_string = reverse_bwt(result["bwt_string"], result["idx_original_string"])
print(
f"Reversing Burrows Wheeler transform for entry '{result['bwt_string']}' "
f"we get original string '{original_string}'"
)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/huffman.py | data_compression/huffman.py | from __future__ import annotations
import sys
class Letter:
def __init__(self, letter: str, freq: int):
self.letter: str = letter
self.freq: int = freq
self.bitstring: dict[str, str] = {}
def __repr__(self) -> str:
return f"{self.letter}:{self.freq}"
class TreeNode:
def __init__(self, freq: int, left: Letter | TreeNode, right: Letter | TreeNode):
self.freq: int = freq
self.left: Letter | TreeNode = left
self.right: Letter | TreeNode = right
def parse_file(file_path: str) -> list[Letter]:
"""
Read the file and build a dict of all letters and their
frequencies, then convert the dict into a list of Letters.
"""
chars: dict[str, int] = {}
with open(file_path) as f:
while True:
c = f.read(1)
if not c:
break
chars[c] = chars[c] + 1 if c in chars else 1
return sorted((Letter(c, f) for c, f in chars.items()), key=lambda x: x.freq)
def build_tree(letters: list[Letter]) -> Letter | TreeNode:
"""
Run through the list of Letters and build the min heap
for the Huffman Tree.
"""
response: list[Letter | TreeNode] = list(letters)
while len(response) > 1:
left = response.pop(0)
right = response.pop(0)
total_freq = left.freq + right.freq
node = TreeNode(total_freq, left, right)
response.append(node)
response.sort(key=lambda x: x.freq)
return response[0]
def traverse_tree(root: Letter | TreeNode, bitstring: str) -> list[Letter]:
"""
Recursively traverse the Huffman Tree to set each
Letter's bitstring dictionary, and return the list of Letters
"""
if isinstance(root, Letter):
root.bitstring[root.letter] = bitstring
return [root]
treenode: TreeNode = root
letters = []
letters += traverse_tree(treenode.left, bitstring + "0")
letters += traverse_tree(treenode.right, bitstring + "1")
return letters
def huffman(file_path: str) -> None:
"""
Parse the file, build the tree, then run through the file
again, using the letters dictionary to find and print out the
bitstring for each letter.
"""
letters_list = parse_file(file_path)
root = build_tree(letters_list)
letters = {
k: v for letter in traverse_tree(root, "") for k, v in letter.bitstring.items()
}
print(f"Huffman Coding of {file_path}: ")
with open(file_path) as f:
while True:
c = f.read(1)
if not c:
break
print(letters[c], end=" ")
print()
if __name__ == "__main__":
# pass the file path to the huffman function
huffman(sys.argv[1])
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/peak_signal_to_noise_ratio.py | data_compression/peak_signal_to_noise_ratio.py | """
Peak signal-to-noise ratio - PSNR
https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
Source:
https://tutorials.techonical.com/how-to-calculate-psnr-value-of-two-images-using-python
"""
import math
import os
import cv2
import numpy as np
PIXEL_MAX = 255.0
def peak_signal_to_noise_ratio(original: float, contrast: float) -> float:
mse = np.mean((original - contrast) ** 2)
if mse == 0:
return 100
return 20 * math.log10(PIXEL_MAX / math.sqrt(mse))
def main() -> None:
dir_path = os.path.dirname(os.path.realpath(__file__))
# Loading images (original image and compressed image)
original = cv2.imread(os.path.join(dir_path, "image_data/original_image.png"))
contrast = cv2.imread(os.path.join(dir_path, "image_data/compressed_image.png"), 1)
original2 = cv2.imread(os.path.join(dir_path, "image_data/PSNR-example-base.png"))
contrast2 = cv2.imread(
os.path.join(dir_path, "image_data/PSNR-example-comp-10.jpg"), 1
)
# Value expected: 29.73dB
print("-- First Test --")
print(f"PSNR value is {peak_signal_to_noise_ratio(original, contrast)} dB")
# # Value expected: 31.53dB (Wikipedia Example)
print("\n-- Second Test --")
print(f"PSNR value is {peak_signal_to_noise_ratio(original2, contrast2)} dB")
if __name__ == "__main__":
main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/coordinate_compression.py | data_compression/coordinate_compression.py | """
Assumption:
- The values to compress are assumed to be comparable,
values can be sorted and compared with '<' and '>' operators.
"""
class CoordinateCompressor:
"""
A class for coordinate compression.
This class allows you to compress and decompress a list of values.
Mapping:
In addition to compression and decompression, this class maintains a mapping
between original values and their compressed counterparts using two data
structures: a dictionary `coordinate_map` and a list `reverse_map`:
- `coordinate_map`: A dictionary that maps original values to their compressed
coordinates. Keys are original values, and values are compressed coordinates.
- `reverse_map`: A list used for reverse mapping, where each index corresponds
to a compressed coordinate, and the value at that index is the original value.
Example of mapping:
Original: 10, Compressed: 0
Original: 52, Compressed: 1
Original: 83, Compressed: 2
Original: 100, Compressed: 3
This mapping allows for efficient compression and decompression of values within
the list.
"""
def __init__(self, arr: list[int | float | str]) -> None:
"""
Initialize the CoordinateCompressor with a list.
Args:
arr: The list of values to be compressed.
>>> arr = [100, 10, 52, 83]
>>> cc = CoordinateCompressor(arr)
>>> cc.compress(100)
3
>>> cc.compress(52)
1
>>> cc.decompress(1)
52
"""
# A dictionary to store compressed coordinates
self.coordinate_map: dict[int | float | str, int] = {}
# A list to store reverse mapping
self.reverse_map: list[int | float | str] = [-1] * len(arr)
self.arr = sorted(arr) # The input list
self.n = len(arr) # The length of the input list
self.compress_coordinates()
def compress_coordinates(self) -> None:
"""
Compress the coordinates in the input list.
>>> arr = [100, 10, 52, 83]
>>> cc = CoordinateCompressor(arr)
>>> cc.coordinate_map[83]
2
>>> cc.coordinate_map[80] # Value not in the original list
Traceback (most recent call last):
...
KeyError: 80
>>> cc.reverse_map[2]
83
"""
key = 0
for val in self.arr:
if val not in self.coordinate_map:
self.coordinate_map[val] = key
self.reverse_map[key] = val
key += 1
def compress(self, original: float | str) -> int:
"""
Compress a single value.
Args:
original: The value to compress.
Returns:
The compressed integer, or -1 if not found in the original list.
>>> arr = [100, 10, 52, 83]
>>> cc = CoordinateCompressor(arr)
>>> cc.compress(100)
3
>>> cc.compress(7) # Value not in the original list
-1
"""
return self.coordinate_map.get(original, -1)
def decompress(self, num: int) -> int | float | str:
"""
Decompress a single integer.
Args:
num: The compressed integer to decompress.
Returns:
The original value.
>>> arr = [100, 10, 52, 83]
>>> cc = CoordinateCompressor(arr)
>>> cc.decompress(0)
10
>>> cc.decompress(5) # Compressed coordinate out of range
-1
"""
return self.reverse_map[num] if 0 <= num < len(self.reverse_map) else -1
if __name__ == "__main__":
from doctest import testmod
testmod()
arr: list[int | float | str] = [100, 10, 52, 83]
cc = CoordinateCompressor(arr)
for original in arr:
compressed = cc.compress(original)
decompressed = cc.decompress(compressed)
print(f"Original: {decompressed}, Compressed: {compressed}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/lempel_ziv.py | data_compression/lempel_ziv.py | """
One of the several implementations of Lempel-Ziv-Welch compression algorithm
https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch
"""
import math
import os
import sys
def read_file_binary(file_path: str) -> str:
"""
Reads given file as bytes and returns them as a long string
"""
result = ""
try:
with open(file_path, "rb") as binary_file:
data = binary_file.read()
for dat in data:
curr_byte = f"{dat:08b}"
result += curr_byte
return result
except OSError:
print("File not accessible")
sys.exit()
def add_key_to_lexicon(
lexicon: dict[str, str], curr_string: str, index: int, last_match_id: str
) -> None:
"""
Adds new strings (curr_string + "0", curr_string + "1") to the lexicon
"""
lexicon.pop(curr_string)
lexicon[curr_string + "0"] = last_match_id
if math.log2(index).is_integer():
for curr_key, value in lexicon.items():
lexicon[curr_key] = f"0{value}"
lexicon[curr_string + "1"] = bin(index)[2:]
def compress_data(data_bits: str) -> str:
"""
Compresses given data_bits using Lempel-Ziv-Welch compression algorithm
and returns the result as a string
"""
lexicon = {"0": "0", "1": "1"}
result, curr_string = "", ""
index = len(lexicon)
for i in range(len(data_bits)):
curr_string += data_bits[i]
if curr_string not in lexicon:
continue
last_match_id = lexicon[curr_string]
result += last_match_id
add_key_to_lexicon(lexicon, curr_string, index, last_match_id)
index += 1
curr_string = ""
while curr_string != "" and curr_string not in lexicon:
curr_string += "0"
if curr_string != "":
last_match_id = lexicon[curr_string]
result += last_match_id
return result
def add_file_length(source_path: str, compressed: str) -> str:
"""
Adds given file's length in front (using Elias gamma coding) of the compressed
string
"""
file_length = os.path.getsize(source_path)
file_length_binary = bin(file_length)[2:]
length_length = len(file_length_binary)
return "0" * (length_length - 1) + file_length_binary + compressed
def write_file_binary(file_path: str, to_write: str) -> None:
"""
Writes given to_write string (should only consist of 0's and 1's) as bytes in the
file
"""
byte_length = 8
try:
with open(file_path, "wb") as opened_file:
result_byte_array = [
to_write[i : i + byte_length]
for i in range(0, len(to_write), byte_length)
]
if len(result_byte_array[-1]) % byte_length == 0:
result_byte_array.append("10000000")
else:
result_byte_array[-1] += "1" + "0" * (
byte_length - len(result_byte_array[-1]) - 1
)
for elem in result_byte_array:
opened_file.write(int(elem, 2).to_bytes(1, byteorder="big"))
except OSError:
print("File not accessible")
sys.exit()
def compress(source_path: str, destination_path: str) -> None:
"""
Reads source file, compresses it and writes the compressed result in destination
file
"""
data_bits = read_file_binary(source_path)
compressed = compress_data(data_bits)
compressed = add_file_length(source_path, compressed)
write_file_binary(destination_path, compressed)
if __name__ == "__main__":
compress(sys.argv[1], sys.argv[2])
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/__init__.py | data_compression/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/run_length_encoding.py | data_compression/run_length_encoding.py | # https://en.wikipedia.org/wiki/Run-length_encoding
def run_length_encode(text: str) -> list:
"""
Performs Run Length Encoding
>>> run_length_encode("AAAABBBCCDAA")
[('A', 4), ('B', 3), ('C', 2), ('D', 1), ('A', 2)]
>>> run_length_encode("A")
[('A', 1)]
>>> run_length_encode("AA")
[('A', 2)]
>>> run_length_encode("AAADDDDDDFFFCCCAAVVVV")
[('A', 3), ('D', 6), ('F', 3), ('C', 3), ('A', 2), ('V', 4)]
"""
encoded = []
count = 1
for i in range(len(text)):
if i + 1 < len(text) and text[i] == text[i + 1]:
count += 1
else:
encoded.append((text[i], count))
count = 1
return encoded
def run_length_decode(encoded: list) -> str:
"""
Performs Run Length Decoding
>>> run_length_decode([('A', 4), ('B', 3), ('C', 2), ('D', 1), ('A', 2)])
'AAAABBBCCDAA'
>>> run_length_decode([('A', 1)])
'A'
>>> run_length_decode([('A', 2)])
'AA'
>>> run_length_decode([('A', 3), ('D', 6), ('F', 3), ('C', 3), ('A', 2), ('V', 4)])
'AAADDDDDDFFFCCCAAVVVV'
"""
return "".join(char * length for char, length in encoded)
if __name__ == "__main__":
from doctest import testmod
testmod(name="run_length_encode", verbose=True)
testmod(name="run_length_decode", verbose=True)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/lz77.py | data_compression/lz77.py | """
LZ77 compression algorithm
- lossless data compression published in papers by Abraham Lempel and Jacob Ziv in 1977
- also known as LZ1 or sliding-window compression
- form the basis for many variations including LZW, LZSS, LZMA and others
It uses a “sliding window” method. Within the sliding window we have:
- search buffer
- look ahead buffer
len(sliding_window) = len(search_buffer) + len(look_ahead_buffer)
LZ77 manages a dictionary that uses triples composed of:
- Offset into search buffer, it's the distance between the start of a phrase and
the beginning of a file.
- Length of the match, it's the number of characters that make up a phrase.
- The indicator is represented by a character that is going to be encoded next.
As a file is parsed, the dictionary is dynamically updated to reflect the compressed
data contents and size.
Examples:
"cabracadabrarrarrad" <-> [(0, 0, 'c'), (0, 0, 'a'), (0, 0, 'b'), (0, 0, 'r'),
(3, 1, 'c'), (2, 1, 'd'), (7, 4, 'r'), (3, 5, 'd')]
"ababcbababaa" <-> [(0, 0, 'a'), (0, 0, 'b'), (2, 2, 'c'), (4, 3, 'a'), (2, 2, 'a')]
"aacaacabcabaaac" <-> [(0, 0, 'a'), (1, 1, 'c'), (3, 4, 'b'), (3, 3, 'a'), (1, 2, 'c')]
Sources:
en.wikipedia.org/wiki/LZ77_and_LZ78
"""
from dataclasses import dataclass
__version__ = "0.1"
__author__ = "Lucia Harcekova"
@dataclass
class Token:
"""
Dataclass representing triplet called token consisting of length, offset
and indicator. This triplet is used during LZ77 compression.
"""
offset: int
length: int
indicator: str
def __repr__(self) -> str:
"""
>>> token = Token(1, 2, "c")
>>> repr(token)
'(1, 2, c)'
>>> str(token)
'(1, 2, c)'
"""
return f"({self.offset}, {self.length}, {self.indicator})"
class LZ77Compressor:
"""
Class containing compress and decompress methods using LZ77 compression algorithm.
"""
def __init__(self, window_size: int = 13, lookahead_buffer_size: int = 6) -> None:
self.window_size = window_size
self.lookahead_buffer_size = lookahead_buffer_size
self.search_buffer_size = self.window_size - self.lookahead_buffer_size
def compress(self, text: str) -> list[Token]:
"""
Compress the given string text using LZ77 compression algorithm.
Args:
text: string to be compressed
Returns:
output: the compressed text as a list of Tokens
>>> lz77_compressor = LZ77Compressor()
>>> str(lz77_compressor.compress("ababcbababaa"))
'[(0, 0, a), (0, 0, b), (2, 2, c), (4, 3, a), (2, 2, a)]'
>>> str(lz77_compressor.compress("aacaacabcabaaac"))
'[(0, 0, a), (1, 1, c), (3, 4, b), (3, 3, a), (1, 2, c)]'
"""
output = []
search_buffer = ""
# while there are still characters in text to compress
while text:
# find the next encoding phrase
# - triplet with offset, length, indicator (the next encoding character)
token = self._find_encoding_token(text, search_buffer)
# update the search buffer:
# - add new characters from text into it
# - check if size exceed the max search buffer size, if so, drop the
# oldest elements
search_buffer += text[: token.length + 1]
if len(search_buffer) > self.search_buffer_size:
search_buffer = search_buffer[-self.search_buffer_size :]
# update the text
text = text[token.length + 1 :]
# append the token to output
output.append(token)
return output
def decompress(self, tokens: list[Token]) -> str:
"""
Convert the list of tokens into an output string.
Args:
tokens: list containing triplets (offset, length, char)
Returns:
output: decompressed text
Tests:
>>> lz77_compressor = LZ77Compressor()
>>> lz77_compressor.decompress([Token(0, 0, 'c'), Token(0, 0, 'a'),
... Token(0, 0, 'b'), Token(0, 0, 'r'), Token(3, 1, 'c'),
... Token(2, 1, 'd'), Token(7, 4, 'r'), Token(3, 5, 'd')])
'cabracadabrarrarrad'
>>> lz77_compressor.decompress([Token(0, 0, 'a'), Token(0, 0, 'b'),
... Token(2, 2, 'c'), Token(4, 3, 'a'), Token(2, 2, 'a')])
'ababcbababaa'
>>> lz77_compressor.decompress([Token(0, 0, 'a'), Token(1, 1, 'c'),
... Token(3, 4, 'b'), Token(3, 3, 'a'), Token(1, 2, 'c')])
'aacaacabcabaaac'
"""
output = ""
for token in tokens:
for _ in range(token.length):
output += output[-token.offset]
output += token.indicator
return output
def _find_encoding_token(self, text: str, search_buffer: str) -> Token:
"""Finds the encoding token for the first character in the text.
Tests:
>>> lz77_compressor = LZ77Compressor()
>>> lz77_compressor._find_encoding_token("abrarrarrad", "abracad").offset
7
>>> lz77_compressor._find_encoding_token("adabrarrarrad", "cabrac").length
1
>>> lz77_compressor._find_encoding_token("abc", "xyz").offset
0
>>> lz77_compressor._find_encoding_token("", "xyz").offset
Traceback (most recent call last):
...
ValueError: We need some text to work with.
>>> lz77_compressor._find_encoding_token("abc", "").offset
0
"""
if not text:
raise ValueError("We need some text to work with.")
# Initialise result parameters to default values
length, offset = 0, 0
if not search_buffer:
return Token(offset, length, text[length])
for i, character in enumerate(search_buffer):
found_offset = len(search_buffer) - i
if character == text[0]:
found_length = self._match_length_from_index(text, search_buffer, 0, i)
# if the found length is bigger than the current or if it's equal,
# which means it's offset is smaller: update offset and length
if found_length >= length:
offset, length = found_offset, found_length
return Token(offset, length, text[length])
def _match_length_from_index(
self, text: str, window: str, text_index: int, window_index: int
) -> int:
"""Calculate the longest possible match of text and window characters from
text_index in text and window_index in window.
Args:
text: _description_
window: sliding window
text_index: index of character in text
window_index: index of character in sliding window
Returns:
The maximum match between text and window, from given indexes.
Tests:
>>> lz77_compressor = LZ77Compressor(13, 6)
>>> lz77_compressor._match_length_from_index("rarrad", "adabrar", 0, 4)
5
>>> lz77_compressor._match_length_from_index("adabrarrarrad",
... "cabrac", 0, 1)
1
"""
if not text or text[text_index] != window[window_index]:
return 0
return 1 + self._match_length_from_index(
text, window + text[text_index], text_index + 1, window_index + 1
)
if __name__ == "__main__":
from doctest import testmod
testmod()
# Initialize compressor class
lz77_compressor = LZ77Compressor(window_size=13, lookahead_buffer_size=6)
# Example
TEXT = "cabracadabrarrarrad"
compressed_text = lz77_compressor.compress(TEXT)
print(lz77_compressor.compress("ababcbababaa"))
decompressed_text = lz77_compressor.decompress(compressed_text)
assert decompressed_text == TEXT, "The LZ77 algorithm returned the invalid result."
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/data_compression/lempel_ziv_decompress.py | data_compression/lempel_ziv_decompress.py | """
One of the several implementations of Lempel-Ziv-Welch decompression algorithm
https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch
"""
import math
import sys
def read_file_binary(file_path: str) -> str:
"""
Reads given file as bytes and returns them as a long string
"""
result = ""
try:
with open(file_path, "rb") as binary_file:
data = binary_file.read()
for dat in data:
curr_byte = f"{dat:08b}"
result += curr_byte
return result
except OSError:
print("File not accessible")
sys.exit()
def decompress_data(data_bits: str) -> str:
"""
Decompresses given data_bits using Lempel-Ziv-Welch compression algorithm
and returns the result as a string
"""
lexicon = {"0": "0", "1": "1"}
result, curr_string = "", ""
index = len(lexicon)
for i in range(len(data_bits)):
curr_string += data_bits[i]
if curr_string not in lexicon:
continue
last_match_id = lexicon[curr_string]
result += last_match_id
lexicon[curr_string] = last_match_id + "0"
if math.log2(index).is_integer():
new_lex = {}
for curr_key in list(lexicon):
new_lex["0" + curr_key] = lexicon.pop(curr_key)
lexicon = new_lex
lexicon[bin(index)[2:]] = last_match_id + "1"
index += 1
curr_string = ""
return result
def write_file_binary(file_path: str, to_write: str) -> None:
"""
Writes given to_write string (should only consist of 0's and 1's) as bytes in the
file
"""
byte_length = 8
try:
with open(file_path, "wb") as opened_file:
result_byte_array = [
to_write[i : i + byte_length]
for i in range(0, len(to_write), byte_length)
]
if len(result_byte_array[-1]) % byte_length == 0:
result_byte_array.append("10000000")
else:
result_byte_array[-1] += "1" + "0" * (
byte_length - len(result_byte_array[-1]) - 1
)
for elem in result_byte_array[:-1]:
opened_file.write(int(elem, 2).to_bytes(1, byteorder="big"))
except OSError:
print("File not accessible")
sys.exit()
def remove_prefix(data_bits: str) -> str:
"""
Removes size prefix, that compressed file should have
Returns the result
"""
counter = 0
for letter in data_bits:
if letter == "1":
break
counter += 1
data_bits = data_bits[counter:]
data_bits = data_bits[counter + 1 :]
return data_bits
def compress(source_path: str, destination_path: str) -> None:
"""
Reads source file, decompresses it and writes the result in destination file
"""
data_bits = read_file_binary(source_path)
data_bits = remove_prefix(data_bits)
decompressed = decompress_data(data_bits)
write_file_binary(destination_path, decompressed)
if __name__ == "__main__":
compress(sys.argv[1], sys.argv[2])
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/file_transfer/send_file.py | file_transfer/send_file.py | def send_file(filename: str = "mytext.txt", testing: bool = False) -> None:
import socket
port = 12312 # Reserve a port for your service.
sock = socket.socket() # Create a socket object
host = socket.gethostname() # Get local machine name
sock.bind((host, port)) # Bind to the port
sock.listen(5) # Now wait for client connection.
print("Server listening....")
while True:
conn, addr = sock.accept() # Establish connection with client.
print(f"Got connection from {addr}")
data = conn.recv(1024)
print(f"Server received: {data = }")
with open(filename, "rb") as in_file:
data = in_file.read(1024)
while data:
conn.send(data)
print(f"Sent {data!r}")
data = in_file.read(1024)
print("Done sending")
conn.close()
if testing: # Allow the test to complete
break
sock.shutdown(1)
sock.close()
if __name__ == "__main__":
send_file()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/file_transfer/__init__.py | file_transfer/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/file_transfer/receive_file.py | file_transfer/receive_file.py | import socket
def main():
sock = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
host = socket.gethostname()
port = 12312
sock.connect((host, port))
sock.send(b"Hello server!")
with open("Received_file", "wb") as out_file:
print("File opened")
print("Receiving data...")
while True:
data = sock.recv(1024)
if not data:
break
out_file.write(data)
print("Successfully received the file")
sock.close()
print("Connection closed")
if __name__ == "__main__":
main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/file_transfer/tests/test_send_file.py | file_transfer/tests/test_send_file.py | from unittest.mock import Mock, patch
from file_transfer.send_file import send_file
@patch("socket.socket")
@patch("builtins.open")
def test_send_file_running_as_expected(file, sock):
# ===== initialization =====
conn = Mock()
sock.return_value.accept.return_value = conn, Mock()
f = iter([1, None])
file.return_value.__enter__.return_value.read.side_effect = lambda _: next(f)
# ===== invoke =====
send_file(filename="mytext.txt", testing=True)
# ===== ensurance =====
sock.assert_called_once()
sock.return_value.bind.assert_called_once()
sock.return_value.listen.assert_called_once()
sock.return_value.accept.assert_called_once()
conn.recv.assert_called_once()
file.return_value.__enter__.assert_called_once()
file.return_value.__enter__.return_value.read.assert_called()
conn.send.assert_called_once()
conn.close.assert_called_once()
sock.return_value.shutdown.assert_called_once()
sock.return_value.close.assert_called_once()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/file_transfer/tests/__init__.py | file_transfer/tests/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/fractional_cover_problem.py | greedy_methods/fractional_cover_problem.py | # https://en.wikipedia.org/wiki/Set_cover_problem
from dataclasses import dataclass
from operator import attrgetter
@dataclass
class Item:
weight: int
value: int
@property
def ratio(self) -> float:
"""
Return the value-to-weight ratio for the item.
Returns:
float: The value-to-weight ratio for the item.
Examples:
>>> Item(10, 65).ratio
6.5
>>> Item(20, 100).ratio
5.0
>>> Item(30, 120).ratio
4.0
"""
return self.value / self.weight
def fractional_cover(items: list[Item], capacity: int) -> float:
"""
Solve the Fractional Cover Problem.
Args:
items: A list of items, where each item has weight and value attributes.
capacity: The maximum weight capacity of the knapsack.
Returns:
The maximum value that can be obtained by selecting fractions of items to cover
the knapsack's capacity.
Raises:
ValueError: If capacity is negative.
Examples:
>>> fractional_cover((Item(10, 60), Item(20, 100), Item(30, 120)), capacity=50)
240.0
>>> fractional_cover([Item(20, 100), Item(30, 120), Item(10, 60)], capacity=25)
135.0
>>> fractional_cover([Item(10, 60), Item(20, 100), Item(30, 120)], capacity=60)
280.0
>>> fractional_cover(items=[Item(5, 30), Item(10, 60), Item(15, 90)], capacity=30)
180.0
>>> fractional_cover(items=[], capacity=50)
0.0
>>> fractional_cover(items=[Item(10, 60)], capacity=5)
30.0
>>> fractional_cover(items=[Item(10, 60)], capacity=1)
6.0
>>> fractional_cover(items=[Item(10, 60)], capacity=0)
0.0
>>> fractional_cover(items=[Item(10, 60)], capacity=-1)
Traceback (most recent call last):
...
ValueError: Capacity cannot be negative
"""
if capacity < 0:
raise ValueError("Capacity cannot be negative")
total_value = 0.0
remaining_capacity = capacity
# Sort the items by their value-to-weight ratio in descending order
for item in sorted(items, key=attrgetter("ratio"), reverse=True):
if remaining_capacity == 0:
break
weight_taken = min(item.weight, remaining_capacity)
total_value += weight_taken * item.ratio
remaining_capacity -= weight_taken
return total_value
if __name__ == "__main__":
import doctest
if result := doctest.testmod().failed:
print(f"{result} test(s) failed")
else:
print("All tests passed")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/smallest_range.py | greedy_methods/smallest_range.py | """
smallest_range function takes a list of sorted integer lists and finds the smallest
range that includes at least one number from each list, using a min heap for efficiency.
"""
from heapq import heappop, heappush
from sys import maxsize
def smallest_range(nums: list[list[int]]) -> list[int]:
"""
Find the smallest range from each list in nums.
Uses min heap for efficiency. The range includes at least one number from each list.
Args:
`nums`: List of k sorted integer lists.
Returns:
list: Smallest range as a two-element list.
Examples:
>>> smallest_range([[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]])
[20, 24]
>>> smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
[1, 1]
>>> smallest_range(((1, 2, 3), (1, 2, 3), (1, 2, 3)))
[1, 1]
>>> smallest_range(((-3, -2, -1), (0, 0, 0), (1, 2, 3)))
[-1, 1]
>>> smallest_range([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
[3, 7]
>>> smallest_range([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
[0, 0]
>>> smallest_range([[], [], []])
Traceback (most recent call last):
...
IndexError: list index out of range
"""
min_heap: list[tuple[int, int, int]] = []
current_max = -maxsize - 1
for i, items in enumerate(nums):
heappush(min_heap, (items[0], i, 0))
current_max = max(current_max, items[0])
# Initialize smallest_range with large integer values
smallest_range = [-maxsize - 1, maxsize]
while min_heap:
current_min, list_index, element_index = heappop(min_heap)
if current_max - current_min < smallest_range[1] - smallest_range[0]:
smallest_range = [current_min, current_max]
if element_index == len(nums[list_index]) - 1:
break
next_element = nums[list_index][element_index + 1]
heappush(min_heap, (next_element, list_index, element_index + 1))
current_max = max(current_max, next_element)
return smallest_range
if __name__ == "__main__":
from doctest import testmod
testmod()
print(f"{smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])}") # Output: [1, 1]
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/optimal_merge_pattern.py | greedy_methods/optimal_merge_pattern.py | """
This is a pure Python implementation of the greedy-merge-sort algorithm
reference: https://www.geeksforgeeks.org/optimal-file-merge-patterns/
For doctests run following command:
python3 -m doctest -v greedy_merge_sort.py
Objective
Merge a set of sorted files of different length into a single sorted file.
We need to find an optimal solution, where the resultant file
will be generated in minimum time.
Approach
If the number of sorted files are given, there are many ways
to merge them into a single sorted file.
This merge can be performed pair wise.
To merge a m-record file and a n-record file requires possibly m+n record moves
the optimal choice being,
merge the two smallest files together at each step (greedy approach).
"""
def optimal_merge_pattern(files: list) -> float:
"""Function to merge all the files with optimum cost
Args:
files [list]: A list of sizes of different files to be merged
Returns:
optimal_merge_cost [int]: Optimal cost to merge all those files
Examples:
>>> optimal_merge_pattern([2, 3, 4])
14
>>> optimal_merge_pattern([5, 10, 20, 30, 30])
205
>>> optimal_merge_pattern([8, 8, 8, 8, 8])
96
"""
optimal_merge_cost = 0
while len(files) > 1:
temp = 0
# Consider two files with minimum cost to be merged
for _ in range(2):
min_index = files.index(min(files))
temp += files[min_index]
files.pop(min_index)
files.append(temp)
optimal_merge_cost += temp
return optimal_merge_cost
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/best_time_to_buy_and_sell_stock.py | greedy_methods/best_time_to_buy_and_sell_stock.py | """
Given a list of stock prices calculate the maximum profit that can be made from a
single buy and sell of one share of stock. We only allowed to complete one buy
transaction and one sell transaction but must buy before we sell.
Example : prices = [7, 1, 5, 3, 6, 4]
max_profit will return 5 - which is by buying at price 1 and selling at price 6.
This problem can be solved using the concept of "GREEDY ALGORITHM".
We iterate over the price array once, keeping track of the lowest price point
(buy) and the maximum profit we can get at each point. The greedy choice at each point
is to either buy at the current price if it's less than our current buying price, or
sell at the current price if the profit is more than our current maximum profit.
"""
def max_profit(prices: list[int]) -> int:
"""
>>> max_profit([7, 1, 5, 3, 6, 4])
5
>>> max_profit([7, 6, 4, 3, 1])
0
"""
if not prices:
return 0
min_price = prices[0]
max_profit: int = 0
for price in prices:
min_price = min(price, min_price)
max_profit = max(price - min_price, max_profit)
return max_profit
if __name__ == "__main__":
import doctest
doctest.testmod()
print(max_profit([7, 1, 5, 3, 6, 4]))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/minimum_coin_change.py | greedy_methods/minimum_coin_change.py | """
Test cases:
Do you want to enter your denominations ? (Y/N) :N
Enter the change you want to make in Indian Currency: 987
Following is minimal change for 987 :
500 100 100 100 100 50 20 10 5 2
Do you want to enter your denominations ? (Y/N) :Y
Enter number of denomination:10
1
5
10
20
50
100
200
500
1000
2000
Enter the change you want to make: 18745
Following is minimal change for 18745 :
2000 2000 2000 2000 2000 2000 2000 2000 2000 500 200 20 20 5
Do you want to enter your denominations ? (Y/N) :N
Enter the change you want to make: 0
The total value cannot be zero or negative.
Do you want to enter your denominations ? (Y/N) :N
Enter the change you want to make: -98
The total value cannot be zero or negative.
Do you want to enter your denominations ? (Y/N) :Y
Enter number of denomination:5
1
5
100
500
1000
Enter the change you want to make: 456
Following is minimal change for 456 :
100 100 100 100 5 5 5 5 5 5 5 5 5 5 5 1
"""
def find_minimum_change(denominations: list[int], value: str) -> list[int]:
"""
Find the minimum change from the given denominations and value
>>> find_minimum_change([1, 5, 10, 20, 50, 100, 200, 500, 1000,2000], 18745)
[2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 500, 200, 20, 20, 5]
>>> find_minimum_change([1, 2, 5, 10, 20, 50, 100, 500, 2000], 987)
[500, 100, 100, 100, 100, 50, 20, 10, 5, 2]
>>> find_minimum_change([1, 2, 5, 10, 20, 50, 100, 500, 2000], 0)
[]
>>> find_minimum_change([1, 2, 5, 10, 20, 50, 100, 500, 2000], -98)
[]
>>> find_minimum_change([1, 5, 100, 500, 1000], 456)
[100, 100, 100, 100, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1]
"""
total_value = int(value)
# Initialize Result
answer = []
# Traverse through all denomination
for denomination in reversed(denominations):
# Find denominations
while int(total_value) >= int(denomination):
total_value -= int(denomination)
answer.append(denomination) # Append the "answers" array
return answer
# Driver Code
if __name__ == "__main__":
denominations = []
value = "0"
if (
input("Do you want to enter your denominations ? (yY/n): ").strip().lower()
== "y"
):
n = int(input("Enter the number of denominations you want to add: ").strip())
for i in range(n):
denominations.append(int(input(f"Denomination {i}: ").strip()))
value = input("Enter the change you want to make in Indian Currency: ").strip()
else:
# All denominations of Indian Currency if user does not enter
denominations = [1, 2, 5, 10, 20, 50, 100, 500, 2000]
value = input("Enter the change you want to make: ").strip()
if int(value) == 0 or int(value) < 0:
print("The total value cannot be zero or negative.")
else:
print(f"Following is minimal change for {value}: ")
answer = find_minimum_change(denominations, value)
# Print result
for i in range(len(answer)):
print(answer[i], end=" ")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/fractional_knapsack.py | greedy_methods/fractional_knapsack.py | from bisect import bisect
from itertools import accumulate
def frac_knapsack(vl, wt, w, n):
"""
>>> frac_knapsack([60, 100, 120], [10, 20, 30], 50, 3)
240.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 10, 4)
105.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 4)
95.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6], 8, 4)
60.0
>>> frac_knapsack([10, 40, 30], [5, 4, 6, 3], 8, 4)
60.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 0, 4)
0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 0)
95.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], -8, 4)
0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, -4)
95.0
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 800, 4)
130
>>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 400)
95.0
>>> frac_knapsack("ABCD", [5, 4, 6, 3], 8, 400)
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for /: 'str' and 'int'
"""
r = sorted(zip(vl, wt), key=lambda x: x[0] / x[1], reverse=True)
vl, wt = [i[0] for i in r], [i[1] for i in r]
acc = list(accumulate(wt))
k = bisect(acc, w)
return (
0
if k == 0
else sum(vl[:k]) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
if k != n
else sum(vl[:k])
)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/__init__.py | greedy_methods/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/gas_station.py | greedy_methods/gas_station.py | """
Task:
There are n gas stations along a circular route, where the amount of gas
at the ith station is gas_quantities[i].
You have a car with an unlimited gas tank and it costs costs[i] of gas
to travel from the ith station to its next (i + 1)th station.
You begin the journey with an empty tank at one of the gas stations.
Given two integer arrays gas_quantities and costs, return the starting
gas station's index if you can travel around the circuit once
in the clockwise direction otherwise, return -1.
If there exists a solution, it is guaranteed to be unique
Reference: https://leetcode.com/problems/gas-station/description
Implementation notes:
First, check whether the total gas is enough to complete the journey. If not, return -1.
However, if there is enough gas, it is guaranteed that there is a valid
starting index to reach the end of the journey.
Greedily calculate the net gain (gas_quantity - cost) at each station.
If the net gain ever goes below 0 while iterating through the stations,
start checking from the next station.
"""
from dataclasses import dataclass
@dataclass
class GasStation:
gas_quantity: int
cost: int
def get_gas_stations(
gas_quantities: list[int], costs: list[int]
) -> tuple[GasStation, ...]:
"""
This function returns a tuple of gas stations.
Args:
gas_quantities: Amount of gas available at each station
costs: The cost of gas required to move from one station to the next
Returns:
A tuple of gas stations
>>> gas_stations = get_gas_stations([1, 2, 3, 4, 5], [3, 4, 5, 1, 2])
>>> len(gas_stations)
5
>>> gas_stations[0]
GasStation(gas_quantity=1, cost=3)
>>> gas_stations[-1]
GasStation(gas_quantity=5, cost=2)
"""
return tuple(
GasStation(quantity, cost) for quantity, cost in zip(gas_quantities, costs)
)
def can_complete_journey(gas_stations: tuple[GasStation, ...]) -> int:
"""
This function returns the index from which to start the journey
in order to reach the end.
Args:
gas_quantities [list]: Amount of gas available at each station
cost [list]: The cost of gas required to move from one station to the next
Returns:
start [int]: start index needed to complete the journey
Examples:
>>> can_complete_journey(get_gas_stations([1, 2, 3, 4, 5], [3, 4, 5, 1, 2]))
3
>>> can_complete_journey(get_gas_stations([2, 3, 4], [3, 4, 3]))
-1
"""
total_gas = sum(gas_station.gas_quantity for gas_station in gas_stations)
total_cost = sum(gas_station.cost for gas_station in gas_stations)
if total_gas < total_cost:
return -1
start = 0
net = 0
for i, gas_station in enumerate(gas_stations):
net += gas_station.gas_quantity - gas_station.cost
if net < 0:
start = i + 1
net = 0
return start
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/fractional_knapsack_2.py | greedy_methods/fractional_knapsack_2.py | # https://en.wikipedia.org/wiki/Continuous_knapsack_problem
# https://www.guru99.com/fractional-knapsack-problem-greedy.html
# https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93
from __future__ import annotations
def fractional_knapsack(
value: list[int], weight: list[int], capacity: int
) -> tuple[float, list[float]]:
"""
>>> value = [1, 3, 5, 7, 9]
>>> weight = [0.9, 0.7, 0.5, 0.3, 0.1]
>>> fractional_knapsack(value, weight, 5)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 15)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 25)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, 26)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack(value, weight, -1)
(-90.0, [0, 0, 0, 0, -10.0])
>>> fractional_knapsack([1, 3, 5, 7], weight, 30)
(16, [1, 1, 1, 1])
>>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30)
(25, [1, 1, 1, 1, 1])
>>> fractional_knapsack([], [], 30)
(0, [])
"""
index = list(range(len(value)))
ratio = [v / w for v, w in zip(value, weight)]
index.sort(key=lambda i: ratio[i], reverse=True)
max_value: float = 0
fractions: list[float] = [0] * len(value)
for i in index:
if weight[i] <= capacity:
fractions[i] = 1
max_value += value[i]
capacity -= weight[i]
else:
fractions[i] = capacity / weight[i]
max_value += value[i] * capacity / weight[i]
break
return max_value, fractions
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/greedy_methods/minimum_waiting_time.py | greedy_methods/minimum_waiting_time.py | """
Calculate the minimum waiting time using a greedy algorithm.
reference: https://www.youtube.com/watch?v=Sf3eiO12eJs
For doctests run following command:
python -m doctest -v minimum_waiting_time.py
The minimum_waiting_time function uses a greedy algorithm to calculate the minimum
time for queries to complete. It sorts the list in non-decreasing order, calculates
the waiting time for each query by multiplying its position in the list with the
sum of all remaining query times, and returns the total waiting time. A doctest
ensures that the function produces the correct output.
"""
def minimum_waiting_time(queries: list[int]) -> int:
"""
This function takes a list of query times and returns the minimum waiting time
for all queries to be completed.
Args:
queries: A list of queries measured in picoseconds
Returns:
total_waiting_time: Minimum waiting time measured in picoseconds
Examples:
>>> minimum_waiting_time([3, 2, 1, 2, 6])
17
>>> minimum_waiting_time([3, 2, 1])
4
>>> minimum_waiting_time([1, 2, 3, 4])
10
>>> minimum_waiting_time([5, 5, 5, 5])
30
>>> minimum_waiting_time([])
0
"""
n = len(queries)
if n in (0, 1):
return 0
return sum(query * (n - i - 1) for i, query in enumerate(sorted(queries)))
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/gaussian_elimination.py | linear_algebra/gaussian_elimination.py | """
| Gaussian elimination method for solving a system of linear equations.
| Gaussian elimination - https://en.wikipedia.org/wiki/Gaussian_elimination
"""
import numpy as np
from numpy import float64
from numpy.typing import NDArray
def retroactive_resolution(
coefficients: NDArray[float64], vector: NDArray[float64]
) -> NDArray[float64]:
"""
This function performs a retroactive linear system resolution
for triangular matrix
Examples:
1.
* 2x1 + 2x2 - 1x3 = 5
* 0x1 - 2x2 - 1x3 = -7
* 0x1 + 0x2 + 5x3 = 15
2.
* 2x1 + 2x2 = -1
* 0x1 - 2x2 = -1
>>> gaussian_elimination([[2, 2, -1], [0, -2, -1], [0, 0, 5]], [[5], [-7], [15]])
array([[2.],
[2.],
[3.]])
>>> gaussian_elimination([[2, 2], [0, -2]], [[-1], [-1]])
array([[-1. ],
[ 0.5]])
"""
rows, _columns = np.shape(coefficients)
x: NDArray[float64] = np.zeros((rows, 1), dtype=float)
for row in reversed(range(rows)):
total = np.dot(coefficients[row, row + 1 :], x[row + 1 :])
x[row, 0] = (vector[row][0] - total[0]) / coefficients[row, row]
return x
def gaussian_elimination(
coefficients: NDArray[float64], vector: NDArray[float64]
) -> NDArray[float64]:
"""
This function performs Gaussian elimination method
Examples:
1.
* 1x1 - 4x2 - 2x3 = -2
* 5x1 + 2x2 - 2x3 = -3
* 1x1 - 1x2 + 0x3 = 4
2.
* 1x1 + 2x2 = 5
* 5x1 + 2x2 = 5
>>> gaussian_elimination([[1, -4, -2], [5, 2, -2], [1, -1, 0]], [[-2], [-3], [4]])
array([[ 2.3 ],
[-1.7 ],
[ 5.55]])
>>> gaussian_elimination([[1, 2], [5, 2]], [[5], [5]])
array([[0. ],
[2.5]])
"""
# coefficients must to be a square matrix so we need to check first
rows, columns = np.shape(coefficients)
if rows != columns:
return np.array((), dtype=float)
# augmented matrix
augmented_mat: NDArray[float64] = np.concatenate((coefficients, vector), axis=1)
augmented_mat = augmented_mat.astype("float64")
# scale the matrix leaving it triangular
for row in range(rows - 1):
pivot = augmented_mat[row, row]
for col in range(row + 1, columns):
factor = augmented_mat[col, row] / pivot
augmented_mat[col, :] -= factor * augmented_mat[row, :]
x = retroactive_resolution(
augmented_mat[:, 0:columns], augmented_mat[:, columns : columns + 1]
)
return x
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/jacobi_iteration_method.py | linear_algebra/jacobi_iteration_method.py | """
Jacobi Iteration Method - https://en.wikipedia.org/wiki/Jacobi_method
"""
from __future__ import annotations
import numpy as np
from numpy import float64
from numpy.typing import NDArray
# Method to find solution of system of linear equations
def jacobi_iteration_method(
coefficient_matrix: NDArray[float64],
constant_matrix: NDArray[float64],
init_val: list[float],
iterations: int,
) -> list[float]:
"""
Jacobi Iteration Method:
An iterative algorithm to determine the solutions of strictly diagonally dominant
system of linear equations
4x1 + x2 + x3 = 2
x1 + 5x2 + 2x3 = -6
x1 + 2x2 + 4x3 = -4
x_init = [0.5, -0.5 , -0.5]
Examples:
>>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
>>> constant = np.array([[2], [-6], [-4]])
>>> init_val = [0.5, -0.5, -0.5]
>>> iterations = 3
>>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
[0.909375, -1.14375, -0.7484375]
>>> coefficient = np.array([[4, 1, 1], [1, 5, 2]])
>>> constant = np.array([[2], [-6], [-4]])
>>> init_val = [0.5, -0.5, -0.5]
>>> iterations = 3
>>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
Traceback (most recent call last):
...
ValueError: Coefficient matrix dimensions must be nxn but received 2x3
>>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
>>> constant = np.array([[2], [-6]])
>>> init_val = [0.5, -0.5, -0.5]
>>> iterations = 3
>>> jacobi_iteration_method(
... coefficient, constant, init_val, iterations
... ) # doctest: +NORMALIZE_WHITESPACE
Traceback (most recent call last):
...
ValueError: Coefficient and constant matrices dimensions must be nxn and nx1 but
received 3x3 and 2x1
>>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
>>> constant = np.array([[2], [-6], [-4]])
>>> init_val = [0.5, -0.5]
>>> iterations = 3
>>> jacobi_iteration_method(
... coefficient, constant, init_val, iterations
... ) # doctest: +NORMALIZE_WHITESPACE
Traceback (most recent call last):
...
ValueError: Number of initial values must be equal to number of rows in coefficient
matrix but received 2 and 3
>>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
>>> constant = np.array([[2], [-6], [-4]])
>>> init_val = [0.5, -0.5, -0.5]
>>> iterations = 0
>>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
Traceback (most recent call last):
...
ValueError: Iterations must be at least 1
"""
rows1, cols1 = coefficient_matrix.shape
rows2, cols2 = constant_matrix.shape
if rows1 != cols1:
msg = f"Coefficient matrix dimensions must be nxn but received {rows1}x{cols1}"
raise ValueError(msg)
if cols2 != 1:
msg = f"Constant matrix must be nx1 but received {rows2}x{cols2}"
raise ValueError(msg)
if rows1 != rows2:
msg = (
"Coefficient and constant matrices dimensions must be nxn and nx1 but "
f"received {rows1}x{cols1} and {rows2}x{cols2}"
)
raise ValueError(msg)
if len(init_val) != rows1:
msg = (
"Number of initial values must be equal to number of rows in coefficient "
f"matrix but received {len(init_val)} and {rows1}"
)
raise ValueError(msg)
if iterations <= 0:
raise ValueError("Iterations must be at least 1")
table: NDArray[float64] = np.concatenate(
(coefficient_matrix, constant_matrix), axis=1
)
rows, _cols = table.shape
strictly_diagonally_dominant(table)
"""
# Iterates the whole matrix for given number of times
for _ in range(iterations):
new_val = []
for row in range(rows):
temp = 0
for col in range(cols):
if col == row:
denom = table[row][col]
elif col == cols - 1:
val = table[row][col]
else:
temp += (-1) * table[row][col] * init_val[col]
temp = (temp + val) / denom
new_val.append(temp)
init_val = new_val
"""
# denominator - a list of values along the diagonal
denominator = np.diag(coefficient_matrix)
# val_last - values of the last column of the table array
val_last = table[:, -1]
# masks - boolean mask of all strings without diagonal
# elements array coefficient_matrix
masks = ~np.eye(coefficient_matrix.shape[0], dtype=bool)
# no_diagonals - coefficient_matrix array values without diagonal elements
no_diagonals = coefficient_matrix[masks].reshape(-1, rows - 1)
# Here we get 'i_col' - these are the column numbers, for each row
# without diagonal elements, except for the last column.
_i_row, i_col = np.where(masks)
ind = i_col.reshape(-1, rows - 1)
#'i_col' is converted to a two-dimensional list 'ind', which will be
# used to make selections from 'init_val' ('arr' array see below).
# Iterates the whole matrix for given number of times
for _ in range(iterations):
arr = np.take(init_val, ind)
sum_product_rows = np.sum((-1) * no_diagonals * arr, axis=1)
new_val = (sum_product_rows + val_last) / denominator
init_val = new_val
return new_val.tolist()
# Checks if the given matrix is strictly diagonally dominant
def strictly_diagonally_dominant(table: NDArray[float64]) -> bool:
"""
>>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 4, -4]])
>>> strictly_diagonally_dominant(table)
True
>>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 3, -4]])
>>> strictly_diagonally_dominant(table)
Traceback (most recent call last):
...
ValueError: Coefficient matrix is not strictly diagonally dominant
"""
rows, cols = table.shape
is_diagonally_dominant = True
for i in range(rows):
total = 0
for j in range(cols - 1):
if i == j:
continue
else:
total += table[i][j]
if table[i][i] <= total:
raise ValueError("Coefficient matrix is not strictly diagonally dominant")
return is_diagonally_dominant
# Test Cases
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/matrix_inversion.py | linear_algebra/matrix_inversion.py | import numpy as np
def invert_matrix(matrix: list[list[float]]) -> list[list[float]]:
"""
Returns the inverse of a square matrix using NumPy.
Parameters:
matrix (list[list[float]]): A square matrix.
Returns:
list[list[float]]: Inverted matrix if invertible, else raises error.
>>> invert_matrix([[4.0, 7.0], [2.0, 6.0]])
[[0.6000000000000001, -0.7000000000000001], [-0.2, 0.4]]
>>> invert_matrix([[1.0, 2.0], [0.0, 0.0]])
Traceback (most recent call last):
...
ValueError: Matrix is not invertible
"""
np_matrix = np.array(matrix)
try:
inv_matrix = np.linalg.inv(np_matrix)
except np.linalg.LinAlgError:
raise ValueError("Matrix is not invertible")
return inv_matrix.tolist()
if __name__ == "__main__":
mat = [[4.0, 7.0], [2.0, 6.0]]
print("Original Matrix:")
print(mat)
print("Inverted Matrix:")
print(invert_matrix(mat))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/__init__.py | linear_algebra/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/lu_decomposition.py | linear_algebra/lu_decomposition.py | """
Lower-upper (LU) decomposition factors a matrix as a product of a lower
triangular matrix and an upper triangular matrix. A square matrix has an LU
decomposition under the following conditions:
- If the matrix is invertible, then it has an LU decomposition if and only
if all of its leading principal minors are non-zero (see
https://en.wikipedia.org/wiki/Minor_(linear_algebra) for an explanation of
leading principal minors of a matrix).
- If the matrix is singular (i.e., not invertible) and it has a rank of k
(i.e., it has k linearly independent columns), then it has an LU
decomposition if its first k leading principal minors are non-zero.
This algorithm will simply attempt to perform LU decomposition on any square
matrix and raise an error if no such decomposition exists.
Reference: https://en.wikipedia.org/wiki/LU_decomposition
"""
from __future__ import annotations
import numpy as np
def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
"""
Perform LU decomposition on a given matrix and raises an error if the matrix
isn't square or if no such decomposition exists
>>> matrix = np.array([[2, -2, 1], [0, 1, 2], [5, 3, 1]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
>>> lower_mat
array([[1. , 0. , 0. ],
[0. , 1. , 0. ],
[2.5, 8. , 1. ]])
>>> upper_mat
array([[ 2. , -2. , 1. ],
[ 0. , 1. , 2. ],
[ 0. , 0. , -17.5]])
>>> matrix = np.array([[4, 3], [6, 3]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
>>> lower_mat
array([[1. , 0. ],
[1.5, 1. ]])
>>> upper_mat
array([[ 4. , 3. ],
[ 0. , -1.5]])
>>> # Matrix is not square
>>> matrix = np.array([[2, -2, 1], [0, 1, 2]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
Traceback (most recent call last):
...
ValueError: 'table' has to be of square shaped array but got a 2x3 array:
[[ 2 -2 1]
[ 0 1 2]]
>>> # Matrix is invertible, but its first leading principal minor is 0
>>> matrix = np.array([[0, 1], [1, 0]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
Traceback (most recent call last):
...
ArithmeticError: No LU decomposition exists
>>> # Matrix is singular, but its first leading principal minor is 1
>>> matrix = np.array([[1, 0], [1, 0]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
>>> lower_mat
array([[1., 0.],
[1., 1.]])
>>> upper_mat
array([[1., 0.],
[0., 0.]])
>>> # Matrix is singular, but its first leading principal minor is 0
>>> matrix = np.array([[0, 1], [0, 1]])
>>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
Traceback (most recent call last):
...
ArithmeticError: No LU decomposition exists
"""
# Ensure that table is a square array
rows, columns = np.shape(table)
if rows != columns:
msg = (
"'table' has to be of square shaped array but got a "
f"{rows}x{columns} array:\n{table}"
)
raise ValueError(msg)
lower = np.zeros((rows, columns))
upper = np.zeros((rows, columns))
# in 'total', the necessary data is extracted through slices
# and the sum of the products is obtained.
for i in range(columns):
for j in range(i):
total = np.sum(lower[i, :i] * upper[:i, j])
if upper[j][j] == 0:
raise ArithmeticError("No LU decomposition exists")
lower[i][j] = (table[i][j] - total) / upper[j][j]
lower[i][i] = 1
for j in range(i, columns):
total = np.sum(lower[i, :i] * upper[:i, j])
upper[i][j] = table[i][j] - total
return lower, upper
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/lib.py | linear_algebra/src/lib.py | """
Created on Mon Feb 26 14:29:11 2018
@author: Christian Bender
@license: MIT-license
This module contains some useful classes and functions for dealing
with linear algebra in python.
Overview:
- class Vector
- function zero_vector(dimension)
- function unit_basis_vector(dimension, pos)
- function axpy(scalar, vector1, vector2)
- function random_vector(N, a, b)
- class Matrix
- function square_zero_matrix(N)
- function random_matrix(W, H, a, b)
"""
from __future__ import annotations
import math
import random
from collections.abc import Collection
from typing import overload
class Vector:
"""
This class represents a vector of arbitrary size.
You need to give the vector components.
Overview of the methods:
__init__(components: Collection[float] | None): init the vector
__len__(): gets the size of the vector (number of components)
__str__(): returns a string representation
__add__(other: Vector): vector addition
__sub__(other: Vector): vector subtraction
__mul__(other: float): scalar multiplication
__mul__(other: Vector): dot product
copy(): copies this vector and returns it
component(i): gets the i-th component (0-indexed)
change_component(pos: int, value: float): changes specified component
euclidean_length(): returns the euclidean length of the vector
angle(other: Vector, deg: bool): returns the angle between two vectors
"""
def __init__(self, components: Collection[float] | None = None) -> None:
"""
input: components or nothing
simple constructor for init the vector
"""
if components is None:
components = []
self.__components = list(components)
def __len__(self) -> int:
"""
returns the size of the vector
"""
return len(self.__components)
def __str__(self) -> str:
"""
returns a string representation of the vector
"""
return "(" + ",".join(map(str, self.__components)) + ")"
def __add__(self, other: Vector) -> Vector:
"""
input: other vector
assumes: other vector has the same size
returns a new vector that represents the sum.
"""
size = len(self)
if size == len(other):
result = [self.__components[i] + other.component(i) for i in range(size)]
return Vector(result)
else:
raise Exception("must have the same size")
def __sub__(self, other: Vector) -> Vector:
"""
input: other vector
assumes: other vector has the same size
returns a new vector that represents the difference.
"""
size = len(self)
if size == len(other):
result = [self.__components[i] - other.component(i) for i in range(size)]
return Vector(result)
else: # error case
raise Exception("must have the same size")
def __eq__(self, other: object) -> bool:
"""
performs the comparison between two vectors
"""
if not isinstance(other, Vector):
return NotImplemented
if len(self) != len(other):
return False
return all(self.component(i) == other.component(i) for i in range(len(self)))
@overload
def __mul__(self, other: float) -> Vector: ...
@overload
def __mul__(self, other: Vector) -> float: ...
def __mul__(self, other: float | Vector) -> float | Vector:
"""
mul implements the scalar multiplication
and the dot-product
"""
if isinstance(other, (float, int)):
ans = [c * other for c in self.__components]
return Vector(ans)
elif isinstance(other, Vector) and len(self) == len(other):
size = len(self)
prods = [self.__components[i] * other.component(i) for i in range(size)]
return sum(prods)
else: # error case
raise Exception("invalid operand!")
def copy(self) -> Vector:
"""
copies this vector and returns it.
"""
return Vector(self.__components)
def component(self, i: int) -> float:
"""
input: index (0-indexed)
output: the i-th component of the vector.
"""
if isinstance(i, int) and -len(self.__components) <= i < len(self.__components):
return self.__components[i]
else:
raise Exception("index out of range")
def change_component(self, pos: int, value: float) -> None:
"""
input: an index (pos) and a value
changes the specified component (pos) with the
'value'
"""
# precondition
assert -len(self.__components) <= pos < len(self.__components)
self.__components[pos] = value
def euclidean_length(self) -> float:
"""
returns the euclidean length of the vector
>>> Vector([2, 3, 4]).euclidean_length()
5.385164807134504
>>> Vector([1]).euclidean_length()
1.0
>>> Vector([0, -1, -2, -3, 4, 5, 6]).euclidean_length()
9.539392014169456
>>> Vector([]).euclidean_length()
Traceback (most recent call last):
...
Exception: Vector is empty
"""
if len(self.__components) == 0:
raise Exception("Vector is empty")
squares = [c**2 for c in self.__components]
return math.sqrt(sum(squares))
def angle(self, other: Vector, deg: bool = False) -> float:
"""
find angle between two Vector (self, Vector)
>>> Vector([3, 4, -1]).angle(Vector([2, -1, 1]))
1.4906464636572374
>>> Vector([3, 4, -1]).angle(Vector([2, -1, 1]), deg = True)
85.40775111366095
>>> Vector([3, 4, -1]).angle(Vector([2, -1]))
Traceback (most recent call last):
...
Exception: invalid operand!
"""
num = self * other
den = self.euclidean_length() * other.euclidean_length()
if deg:
return math.degrees(math.acos(num / den))
else:
return math.acos(num / den)
def zero_vector(dimension: int) -> Vector:
"""
returns a zero-vector of size 'dimension'
"""
# precondition
assert isinstance(dimension, int)
return Vector([0] * dimension)
def unit_basis_vector(dimension: int, pos: int) -> Vector:
"""
returns a unit basis vector with a One
at index 'pos' (indexing at 0)
"""
# precondition
assert isinstance(dimension, int)
assert isinstance(pos, int)
ans = [0] * dimension
ans[pos] = 1
return Vector(ans)
def axpy(scalar: float, x: Vector, y: Vector) -> Vector:
"""
input: a 'scalar' and two vectors 'x' and 'y'
output: a vector
computes the axpy operation
"""
# precondition
assert isinstance(x, Vector)
assert isinstance(y, Vector)
assert isinstance(scalar, (int, float))
return x * scalar + y
def random_vector(n: int, a: int, b: int) -> Vector:
"""
input: size (N) of the vector.
random range (a,b)
output: returns a random vector of size N, with
random integer components between 'a' and 'b'.
"""
random.seed(None)
ans = [random.randint(a, b) for _ in range(n)]
return Vector(ans)
class Matrix:
"""
class: Matrix
This class represents an arbitrary matrix.
Overview of the methods:
__init__():
__str__(): returns a string representation
__add__(other: Matrix): matrix addition
__sub__(other: Matrix): matrix subtraction
__mul__(other: float): scalar multiplication
__mul__(other: Vector): vector multiplication
height() : returns height
width() : returns width
component(x: int, y: int): returns specified component
change_component(x: int, y: int, value: float): changes specified component
minor(x: int, y: int): returns minor along (x, y)
cofactor(x: int, y: int): returns cofactor along (x, y)
determinant() : returns determinant
"""
def __init__(self, matrix: list[list[float]], w: int, h: int) -> None:
"""
simple constructor for initializing the matrix with components.
"""
self.__matrix = matrix
self.__width = w
self.__height = h
def __str__(self) -> str:
"""
returns a string representation of this matrix.
"""
ans = ""
for i in range(self.__height):
ans += "|"
for j in range(self.__width):
if j < self.__width - 1:
ans += str(self.__matrix[i][j]) + ","
else:
ans += str(self.__matrix[i][j]) + "|\n"
return ans
def __add__(self, other: Matrix) -> Matrix:
"""
implements matrix addition.
"""
if self.__width == other.width() and self.__height == other.height():
matrix = []
for i in range(self.__height):
row = [
self.__matrix[i][j] + other.component(i, j)
for j in range(self.__width)
]
matrix.append(row)
return Matrix(matrix, self.__width, self.__height)
else:
raise Exception("matrix must have the same dimension!")
def __sub__(self, other: Matrix) -> Matrix:
"""
implements matrix subtraction.
"""
if self.__width == other.width() and self.__height == other.height():
matrix = []
for i in range(self.__height):
row = [
self.__matrix[i][j] - other.component(i, j)
for j in range(self.__width)
]
matrix.append(row)
return Matrix(matrix, self.__width, self.__height)
else:
raise Exception("matrices must have the same dimension!")
@overload
def __mul__(self, other: float) -> Matrix: ...
@overload
def __mul__(self, other: Vector) -> Vector: ...
def __mul__(self, other: float | Vector) -> Vector | Matrix:
"""
implements the matrix-vector multiplication.
implements the matrix-scalar multiplication
"""
if isinstance(other, Vector): # matrix-vector
if len(other) == self.__width:
ans = zero_vector(self.__height)
for i in range(self.__height):
prods = [
self.__matrix[i][j] * other.component(j)
for j in range(self.__width)
]
ans.change_component(i, sum(prods))
return ans
else:
raise Exception(
"vector must have the same size as the "
"number of columns of the matrix!"
)
elif isinstance(other, (int, float)): # matrix-scalar
matrix = [
[self.__matrix[i][j] * other for j in range(self.__width)]
for i in range(self.__height)
]
return Matrix(matrix, self.__width, self.__height)
return None
def height(self) -> int:
"""
getter for the height
"""
return self.__height
def width(self) -> int:
"""
getter for the width
"""
return self.__width
def component(self, x: int, y: int) -> float:
"""
returns the specified (x,y) component
"""
if 0 <= x < self.__height and 0 <= y < self.__width:
return self.__matrix[x][y]
else:
raise Exception("change_component: indices out of bounds")
def change_component(self, x: int, y: int, value: float) -> None:
"""
changes the x-y component of this matrix
"""
if 0 <= x < self.__height and 0 <= y < self.__width:
self.__matrix[x][y] = value
else:
raise Exception("change_component: indices out of bounds")
def minor(self, x: int, y: int) -> float:
"""
returns the minor along (x, y)
"""
if self.__height != self.__width:
raise Exception("Matrix is not square")
minor = self.__matrix[:x] + self.__matrix[x + 1 :]
for i in range(len(minor)):
minor[i] = minor[i][:y] + minor[i][y + 1 :]
return Matrix(minor, self.__width - 1, self.__height - 1).determinant()
def cofactor(self, x: int, y: int) -> float:
"""
returns the cofactor (signed minor) along (x, y)
"""
if self.__height != self.__width:
raise Exception("Matrix is not square")
if 0 <= x < self.__height and 0 <= y < self.__width:
return (-1) ** (x + y) * self.minor(x, y)
else:
raise Exception("Indices out of bounds")
def determinant(self) -> float:
"""
returns the determinant of an nxn matrix using Laplace expansion
"""
if self.__height != self.__width:
raise Exception("Matrix is not square")
if self.__height < 1:
raise Exception("Matrix has no element")
elif self.__height == 1:
return self.__matrix[0][0]
elif self.__height == 2:
return (
self.__matrix[0][0] * self.__matrix[1][1]
- self.__matrix[0][1] * self.__matrix[1][0]
)
else:
cofactor_prods = [
self.__matrix[0][y] * self.cofactor(0, y) for y in range(self.__width)
]
return sum(cofactor_prods)
def square_zero_matrix(n: int) -> Matrix:
"""
returns a square zero-matrix of dimension NxN
"""
ans: list[list[float]] = [[0] * n for _ in range(n)]
return Matrix(ans, n, n)
def random_matrix(width: int, height: int, a: int, b: int) -> Matrix:
"""
returns a random matrix WxH with integer components
between 'a' and 'b'
"""
random.seed(None)
matrix: list[list[float]] = [
[random.randint(a, b) for _ in range(width)] for _ in range(height)
]
return Matrix(matrix, width, height)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/rayleigh_quotient.py | linear_algebra/src/rayleigh_quotient.py | """
https://en.wikipedia.org/wiki/Rayleigh_quotient
"""
from typing import Any
import numpy as np
def is_hermitian(matrix: np.ndarray) -> bool:
"""
Checks if a matrix is Hermitian.
>>> import numpy as np
>>> A = np.array([
... [2, 2+1j, 4],
... [2-1j, 3, 1j],
... [4, -1j, 1]])
>>> is_hermitian(A)
True
>>> A = np.array([
... [2, 2+1j, 4+1j],
... [2-1j, 3, 1j],
... [4, -1j, 1]])
>>> is_hermitian(A)
False
"""
return np.array_equal(matrix, matrix.conjugate().T)
def rayleigh_quotient(a: np.ndarray, v: np.ndarray) -> Any:
"""
Returns the Rayleigh quotient of a Hermitian matrix A and
vector v.
>>> import numpy as np
>>> A = np.array([
... [1, 2, 4],
... [2, 3, -1],
... [4, -1, 1]
... ])
>>> v = np.array([
... [1],
... [2],
... [3]
... ])
>>> rayleigh_quotient(A, v)
array([[3.]])
"""
v_star = v.conjugate().T
v_star_dot = v_star.dot(a)
assert isinstance(v_star_dot, np.ndarray)
return (v_star_dot.dot(v)) / (v_star.dot(v))
def tests() -> None:
a = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]])
v = np.array([[1], [2], [3]])
assert is_hermitian(a), f"{a} is not hermitian."
print(rayleigh_quotient(a, v))
a = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]])
assert is_hermitian(a), f"{a} is not hermitian."
assert rayleigh_quotient(a, v) == float(3)
if __name__ == "__main__":
import doctest
doctest.testmod()
tests()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/power_iteration.py | linear_algebra/src/power_iteration.py | import numpy as np
def power_iteration(
input_matrix: np.ndarray,
vector: np.ndarray,
error_tol: float = 1e-12,
max_iterations: int = 100,
) -> tuple[float, np.ndarray]:
"""
Power Iteration.
Find the largest eigenvalue and corresponding eigenvector
of matrix input_matrix given a random vector in the same space.
Will work so long as vector has component of largest eigenvector.
input_matrix must be either real or Hermitian.
Input
input_matrix: input matrix whose largest eigenvalue we will find.
Numpy array. np.shape(input_matrix) == (N,N).
vector: random initial vector in same space as matrix.
Numpy array. np.shape(vector) == (N,) or (N,1)
Output
largest_eigenvalue: largest eigenvalue of the matrix input_matrix.
Float. Scalar.
largest_eigenvector: eigenvector corresponding to largest_eigenvalue.
Numpy array. np.shape(largest_eigenvector) == (N,) or (N,1).
>>> import numpy as np
>>> input_matrix = np.array([
... [41, 4, 20],
... [ 4, 26, 30],
... [20, 30, 50]
... ])
>>> vector = np.array([41,4,20])
>>> power_iteration(input_matrix,vector)
(79.66086378788381, array([0.44472726, 0.46209842, 0.76725662]))
"""
# Ensure matrix is square.
assert np.shape(input_matrix)[0] == np.shape(input_matrix)[1]
# Ensure proper dimensionality.
assert np.shape(input_matrix)[0] == np.shape(vector)[0]
# Ensure inputs are either both complex or both real
assert np.iscomplexobj(input_matrix) == np.iscomplexobj(vector)
is_complex = np.iscomplexobj(input_matrix)
if is_complex:
# Ensure complex input_matrix is Hermitian
assert np.array_equal(input_matrix, input_matrix.conj().T)
# Set convergence to False. Will define convergence when we exceed max_iterations
# or when we have small changes from one iteration to next.
convergence = False
lambda_previous = 0
iterations = 0
error = 1e12
while not convergence:
# Multiple matrix by the vector.
w = np.dot(input_matrix, vector)
# Normalize the resulting output vector.
vector = w / np.linalg.norm(w)
# Find rayleigh quotient
# (faster than usual b/c we know vector is normalized already)
vector_h = vector.conj().T if is_complex else vector.T
lambda_ = np.dot(vector_h, np.dot(input_matrix, vector))
# Check convergence.
error = np.abs(lambda_ - lambda_previous) / lambda_
iterations += 1
if error <= error_tol or iterations >= max_iterations:
convergence = True
lambda_previous = lambda_
if is_complex:
lambda_ = np.real(lambda_)
return float(lambda_), vector
def test_power_iteration() -> None:
"""
>>> test_power_iteration() # self running tests
"""
real_input_matrix = np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]])
real_vector = np.array([41, 4, 20])
complex_input_matrix = real_input_matrix.astype(np.complex128)
imag_matrix = np.triu(1j * complex_input_matrix, 1)
complex_input_matrix += imag_matrix
complex_input_matrix += -1 * imag_matrix.T
complex_vector = np.array([41, 4, 20]).astype(np.complex128)
for problem_type in ["real", "complex"]:
if problem_type == "real":
input_matrix = real_input_matrix
vector = real_vector
elif problem_type == "complex":
input_matrix = complex_input_matrix
vector = complex_vector
# Our implementation.
eigen_value, eigen_vector = power_iteration(input_matrix, vector)
# Numpy implementation.
# Get eigenvalues and eigenvectors using built-in numpy
# eigh (eigh used for symmetric or hermetian matrices).
eigen_values, eigen_vectors = np.linalg.eigh(input_matrix)
# Last eigenvalue is the maximum one.
eigen_value_max = eigen_values[-1]
# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
eigen_vector_max = eigen_vectors[:, -1]
# Check our implementation and numpy gives close answers.
assert np.abs(eigen_value - eigen_value_max) <= 1e-6
# Take absolute values element wise of each eigenvector.
# as they are only unique to a minus sign.
assert np.linalg.norm(np.abs(eigen_vector) - np.abs(eigen_vector_max)) <= 1e-6
if __name__ == "__main__":
import doctest
doctest.testmod()
test_power_iteration()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/conjugate_gradient.py | linear_algebra/src/conjugate_gradient.py | """
Resources:
- https://en.wikipedia.org/wiki/Conjugate_gradient_method
- https://en.wikipedia.org/wiki/Definite_symmetric_matrix
"""
from typing import Any
import numpy as np
def _is_matrix_spd(matrix: np.ndarray) -> bool:
"""
Returns True if input matrix is symmetric positive definite.
Returns False otherwise.
For a matrix to be SPD, all eigenvalues must be positive.
>>> import numpy as np
>>> matrix = np.array([
... [4.12401784, -5.01453636, -0.63865857],
... [-5.01453636, 12.33347422, -3.40493586],
... [-0.63865857, -3.40493586, 5.78591885]])
>>> _is_matrix_spd(matrix)
True
>>> matrix = np.array([
... [0.34634879, 1.96165514, 2.18277744],
... [0.74074469, -1.19648894, -1.34223498],
... [-0.7687067 , 0.06018373, -1.16315631]])
>>> _is_matrix_spd(matrix)
False
"""
# Ensure matrix is square.
assert np.shape(matrix)[0] == np.shape(matrix)[1]
# If matrix not symmetric, exit right away.
if np.allclose(matrix, matrix.T) is False:
return False
# Get eigenvalues and eignevectors for a symmetric matrix.
eigen_values, _ = np.linalg.eigh(matrix)
# Check sign of all eigenvalues.
# np.all returns a value of type np.bool_
return bool(np.all(eigen_values > 0))
def _create_spd_matrix(dimension: int) -> Any:
"""
Returns a symmetric positive definite matrix given a dimension.
Input:
dimension gives the square matrix dimension.
Output:
spd_matrix is an diminesion x dimensions symmetric positive definite (SPD) matrix.
>>> import numpy as np
>>> dimension = 3
>>> spd_matrix = _create_spd_matrix(dimension)
>>> _is_matrix_spd(spd_matrix)
True
"""
rng = np.random.default_rng()
random_matrix = rng.normal(size=(dimension, dimension))
spd_matrix = np.dot(random_matrix, random_matrix.T)
assert _is_matrix_spd(spd_matrix)
return spd_matrix
def conjugate_gradient(
spd_matrix: np.ndarray,
load_vector: np.ndarray,
max_iterations: int = 1000,
tol: float = 1e-8,
) -> Any:
"""
Returns solution to the linear system np.dot(spd_matrix, x) = b.
Input:
spd_matrix is an NxN Symmetric Positive Definite (SPD) matrix.
load_vector is an Nx1 vector.
Output:
x is an Nx1 vector that is the solution vector.
>>> import numpy as np
>>> spd_matrix = np.array([
... [8.73256573, -5.02034289, -2.68709226],
... [-5.02034289, 3.78188322, 0.91980451],
... [-2.68709226, 0.91980451, 1.94746467]])
>>> b = np.array([
... [-5.80872761],
... [ 3.23807431],
... [ 1.95381422]])
>>> conjugate_gradient(spd_matrix, b)
array([[-0.63114139],
[-0.01561498],
[ 0.13979294]])
"""
# Ensure proper dimensionality.
assert np.shape(spd_matrix)[0] == np.shape(spd_matrix)[1]
assert np.shape(load_vector)[0] == np.shape(spd_matrix)[0]
assert _is_matrix_spd(spd_matrix)
# Initialize solution guess, residual, search direction.
x0 = np.zeros((np.shape(load_vector)[0], 1))
r0 = np.copy(load_vector)
p0 = np.copy(r0)
# Set initial errors in solution guess and residual.
error_residual = 1e9
error_x_solution = 1e9
error = 1e9
# Set iteration counter to threshold number of iterations.
iterations = 0
while error > tol:
# Save this value so we only calculate the matrix-vector product once.
w = np.dot(spd_matrix, p0)
# The main algorithm.
# Update search direction magnitude.
alpha = np.dot(r0.T, r0) / np.dot(p0.T, w)
# Update solution guess.
x = x0 + alpha * p0
# Calculate new residual.
r = r0 - alpha * w
# Calculate new Krylov subspace scale.
beta = np.dot(r.T, r) / np.dot(r0.T, r0)
# Calculate new A conjuage search direction.
p = r + beta * p0
# Calculate errors.
error_residual = np.linalg.norm(r - r0)
error_x_solution = np.linalg.norm(x - x0)
error = np.maximum(error_residual, error_x_solution)
# Update variables.
x0 = np.copy(x)
r0 = np.copy(r)
p0 = np.copy(p)
# Update number of iterations.
iterations += 1
if iterations > max_iterations:
break
return x
def test_conjugate_gradient() -> None:
"""
>>> test_conjugate_gradient() # self running tests
"""
# Create linear system with SPD matrix and known solution x_true.
dimension = 3
spd_matrix = _create_spd_matrix(dimension)
rng = np.random.default_rng()
x_true = rng.normal(size=(dimension, 1))
b = np.dot(spd_matrix, x_true)
# Numpy solution.
x_numpy = np.linalg.solve(spd_matrix, b)
# Our implementation.
x_conjugate_gradient = conjugate_gradient(spd_matrix, b)
# Ensure both solutions are close to x_true (and therefore one another).
assert np.linalg.norm(x_numpy - x_true) <= 1e-6
assert np.linalg.norm(x_conjugate_gradient - x_true) <= 1e-6
if __name__ == "__main__":
import doctest
doctest.testmod()
test_conjugate_gradient()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/schur_complement.py | linear_algebra/src/schur_complement.py | import unittest
import numpy as np
import pytest
def schur_complement(
mat_a: np.ndarray,
mat_b: np.ndarray,
mat_c: np.ndarray,
pseudo_inv: np.ndarray | None = None,
) -> np.ndarray:
"""
Schur complement of a symmetric matrix X given as a 2x2 block matrix
consisting of matrices `A`, `B` and `C`.
Matrix `A` must be quadratic and non-singular.
In case `A` is singular, a pseudo-inverse may be provided using
the `pseudo_inv` argument.
| Link to Wiki: https://en.wikipedia.org/wiki/Schur_complement
| See also Convex Optimization - Boyd and Vandenberghe, A.5.5
>>> import numpy as np
>>> a = np.array([[1, 2], [2, 1]])
>>> b = np.array([[0, 3], [3, 0]])
>>> c = np.array([[2, 1], [6, 3]])
>>> schur_complement(a, b, c)
array([[ 5., -5.],
[ 0., 6.]])
"""
shape_a = np.shape(mat_a)
shape_b = np.shape(mat_b)
shape_c = np.shape(mat_c)
if shape_a[0] != shape_b[0]:
msg = (
"Expected the same number of rows for A and B. "
f"Instead found A of size {shape_a} and B of size {shape_b}"
)
raise ValueError(msg)
if shape_b[1] != shape_c[1]:
msg = (
"Expected the same number of columns for B and C. "
f"Instead found B of size {shape_b} and C of size {shape_c}"
)
raise ValueError(msg)
a_inv = pseudo_inv
if a_inv is None:
try:
a_inv = np.linalg.inv(mat_a)
except np.linalg.LinAlgError:
raise ValueError(
"Input matrix A is not invertible. Cannot compute Schur complement."
)
return mat_c - mat_b.T @ a_inv @ mat_b
class TestSchurComplement(unittest.TestCase):
def test_schur_complement(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1], [6, 3]])
s = schur_complement(a, b, c)
input_matrix = np.block([[a, b], [b.T, c]])
det_x = np.linalg.det(input_matrix)
det_a = np.linalg.det(a)
det_s = np.linalg.det(s)
assert np.is_close(det_x, det_a * det_s)
def test_improper_a_b_dimensions(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1], [6, 3]])
with pytest.raises(ValueError):
schur_complement(a, b, c)
def test_improper_b_c_dimensions(self) -> None:
a = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
b = np.array([[0, 3], [3, 0], [2, 3]])
c = np.array([[2, 1, 3], [6, 3, 5]])
with pytest.raises(ValueError):
schur_complement(a, b, c)
if __name__ == "__main__":
import doctest
doctest.testmod()
unittest.main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/rank_of_matrix.py | linear_algebra/src/rank_of_matrix.py | """
Calculate the rank of a matrix.
See: https://en.wikipedia.org/wiki/Rank_(linear_algebra)
"""
def rank_of_matrix(matrix: list[list[int | float]]) -> int:
"""
Finds the rank of a matrix.
Args:
`matrix`: The matrix as a list of lists.
Returns:
The rank of the matrix.
Example:
>>> matrix1 = [[1, 2, 3],
... [4, 5, 6],
... [7, 8, 9]]
>>> rank_of_matrix(matrix1)
2
>>> matrix2 = [[1, 0, 0],
... [0, 1, 0],
... [0, 0, 0]]
>>> rank_of_matrix(matrix2)
2
>>> matrix3 = [[1, 2, 3, 4],
... [5, 6, 7, 8],
... [9, 10, 11, 12]]
>>> rank_of_matrix(matrix3)
2
>>> rank_of_matrix([[2,3,-1,-1],
... [1,-1,-2,4],
... [3,1,3,-2],
... [6,3,0,-7]])
4
>>> rank_of_matrix([[2,1,-3,-6],
... [3,-3,1,2],
... [1,1,1,2]])
3
>>> rank_of_matrix([[2,-1,0],
... [1,3,4],
... [4,1,-3]])
3
>>> rank_of_matrix([[3,2,1],
... [-6,-4,-2]])
1
>>> rank_of_matrix([[],[]])
0
>>> rank_of_matrix([[1]])
1
>>> rank_of_matrix([[]])
0
"""
rows = len(matrix)
columns = len(matrix[0])
rank = min(rows, columns)
for row in range(rank):
# Check if diagonal element is not zero
if matrix[row][row] != 0:
# Eliminate all the elements below the diagonal
for col in range(row + 1, rows):
multiplier = matrix[col][row] / matrix[row][row]
for i in range(row, columns):
matrix[col][i] -= multiplier * matrix[row][i]
else:
# Find a non-zero diagonal element to swap rows
reduce = True
for i in range(row + 1, rows):
if matrix[i][row] != 0:
matrix[row], matrix[i] = matrix[i], matrix[row]
reduce = False
break
if reduce:
rank -= 1
for i in range(rows):
matrix[i][row] = matrix[i][rank]
# Reduce the row pointer by one to stay on the same row
row -= 1
return rank
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/test_linear_algebra.py | linear_algebra/src/test_linear_algebra.py | """
Created on Mon Feb 26 15:40:07 2018
@author: Christian Bender
@license: MIT-license
This file contains the test-suite for the linear algebra library.
"""
import unittest
import pytest
from .lib import (
Matrix,
Vector,
axpy,
square_zero_matrix,
unit_basis_vector,
zero_vector,
)
class Test(unittest.TestCase):
def test_component(self) -> None:
"""
test for method component()
"""
x = Vector([1, 2, 3])
assert x.component(0) == 1
assert x.component(2) == 3
_ = Vector()
def test_str(self) -> None:
"""
test for method toString()
"""
x = Vector([0, 0, 0, 0, 0, 1])
assert str(x) == "(0,0,0,0,0,1)"
def test_size(self) -> None:
"""
test for method size()
"""
x = Vector([1, 2, 3, 4])
assert len(x) == 4
def test_euclidean_length(self) -> None:
"""
test for method euclidean_length()
"""
x = Vector([1, 2])
y = Vector([1, 2, 3, 4, 5])
z = Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
w = Vector([1, -1, 1, -1, 2, -3, 4, -5])
assert x.euclidean_length() == pytest.approx(2.236, abs=1e-3)
assert y.euclidean_length() == pytest.approx(7.416, abs=1e-3)
assert z.euclidean_length() == 0
assert w.euclidean_length() == pytest.approx(7.616, abs=1e-3)
def test_add(self) -> None:
"""
test for + operator
"""
x = Vector([1, 2, 3])
y = Vector([1, 1, 1])
assert (x + y).component(0) == 2
assert (x + y).component(1) == 3
assert (x + y).component(2) == 4
def test_sub(self) -> None:
"""
test for - operator
"""
x = Vector([1, 2, 3])
y = Vector([1, 1, 1])
assert (x - y).component(0) == 0
assert (x - y).component(1) == 1
assert (x - y).component(2) == 2
def test_mul(self) -> None:
"""
test for * operator
"""
x = Vector([1, 2, 3])
a = Vector([2, -1, 4]) # for test of dot product
b = Vector([1, -2, -1])
assert str(x * 3.0) == "(3.0,6.0,9.0)"
assert a * b == 0
def test_zero_vector(self) -> None:
"""
test for global function zero_vector()
"""
assert str(zero_vector(10)).count("0") == 10
def test_unit_basis_vector(self) -> None:
"""
test for global function unit_basis_vector()
"""
assert str(unit_basis_vector(3, 1)) == "(0,1,0)"
def test_axpy(self) -> None:
"""
test for global function axpy() (operation)
"""
x = Vector([1, 2, 3])
y = Vector([1, 0, 1])
assert str(axpy(2, x, y)) == "(3,4,7)"
def test_copy(self) -> None:
"""
test for method copy()
"""
x = Vector([1, 0, 0, 0, 0, 0])
y = x.copy()
assert str(x) == str(y)
def test_change_component(self) -> None:
"""
test for method change_component()
"""
x = Vector([1, 0, 0])
x.change_component(0, 0)
x.change_component(1, 1)
assert str(x) == "(0,1,0)"
def test_str_matrix(self) -> None:
"""
test for Matrix method str()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
assert str(a) == "|1,2,3|\n|2,4,5|\n|6,7,8|\n"
def test_minor(self) -> None:
"""
test for Matrix method minor()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
minors = [[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
for x in range(a.height()):
for y in range(a.width()):
assert minors[x][y] == a.minor(x, y)
def test_cofactor(self) -> None:
"""
test for Matrix method cofactor()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
cofactors = [[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
for x in range(a.height()):
for y in range(a.width()):
assert cofactors[x][y] == a.cofactor(x, y)
def test_determinant(self) -> None:
"""
test for Matrix method determinant()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
assert a.determinant() == -5
def test__mul__matrix(self) -> None:
"""
test for Matrix * operator
"""
a = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 3, 3)
x = Vector([1, 2, 3])
assert str(a * x) == "(14,32,50)"
assert str(a * 2) == "|2,4,6|\n|8,10,12|\n|14,16,18|\n"
def test_change_component_matrix(self) -> None:
"""
test for Matrix method change_component()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
a.change_component(0, 2, 5)
assert str(a) == "|1,2,5|\n|2,4,5|\n|6,7,8|\n"
def test_component_matrix(self) -> None:
"""
test for Matrix method component()
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
assert a.component(2, 1) == 7, "0.01"
def test__add__matrix(self) -> None:
"""
test for Matrix + operator
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
b = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]], 3, 3)
assert str(a + b) == "|2,4,10|\n|4,8,10|\n|12,14,18|\n"
def test__sub__matrix(self) -> None:
"""
test for Matrix - operator
"""
a = Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]], 3, 3)
b = Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]], 3, 3)
assert str(a - b) == "|0,0,-4|\n|0,0,0|\n|0,0,-2|\n"
def test_square_zero_matrix(self) -> None:
"""
test for global function square_zero_matrix()
"""
assert str(square_zero_matrix(5)) == (
"|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n"
)
if __name__ == "__main__":
unittest.main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/transformations_2d.py | linear_algebra/src/transformations_2d.py | """
2D Transformations are regularly used in Linear Algebra.
I have added the codes for reflection, projection, scaling and rotation 2D matrices.
.. code-block:: python
scaling(5) = [[5.0, 0.0], [0.0, 5.0]]
rotation(45) = [[0.5253219888177297, -0.8509035245341184],
[0.8509035245341184, 0.5253219888177297]]
projection(45) = [[0.27596319193541496, 0.446998331800279],
[0.446998331800279, 0.7240368080645851]]
reflection(45) = [[0.05064397763545947, 0.893996663600558],
[0.893996663600558, 0.7018070490682369]]
"""
from math import cos, sin
def scaling(scaling_factor: float) -> list[list[float]]:
"""
>>> scaling(5)
[[5.0, 0.0], [0.0, 5.0]]
"""
scaling_factor = float(scaling_factor)
return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]
def rotation(angle: float) -> list[list[float]]:
"""
>>> rotation(45) # doctest: +NORMALIZE_WHITESPACE
[[0.5253219888177297, -0.8509035245341184],
[0.8509035245341184, 0.5253219888177297]]
"""
c, s = cos(angle), sin(angle)
return [[c, -s], [s, c]]
def projection(angle: float) -> list[list[float]]:
"""
>>> projection(45) # doctest: +NORMALIZE_WHITESPACE
[[0.27596319193541496, 0.446998331800279],
[0.446998331800279, 0.7240368080645851]]
"""
c, s = cos(angle), sin(angle)
cs = c * s
return [[c * c, cs], [cs, s * s]]
def reflection(angle: float) -> list[list[float]]:
"""
>>> reflection(45) # doctest: +NORMALIZE_WHITESPACE
[[0.05064397763545947, 0.893996663600558],
[0.893996663600558, 0.7018070490682369]]
"""
c, s = cos(angle), sin(angle)
cs = c * s
return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
print(f" {scaling(5) = }")
print(f" {rotation(45) = }")
print(f"{projection(45) = }")
print(f"{reflection(45) = }")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/polynom_for_points.py | linear_algebra/src/polynom_for_points.py | def points_to_polynomial(coordinates: list[list[int]]) -> str:
"""
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
number of points you want to use
>>> points_to_polynomial([])
Traceback (most recent call last):
...
ValueError: The program cannot work out a fitting polynomial.
>>> points_to_polynomial([[]])
Traceback (most recent call last):
...
ValueError: The program cannot work out a fitting polynomial.
>>> points_to_polynomial([[1, 0], [2, 0], [3, 0]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*0.0'
>>> points_to_polynomial([[1, 1], [2, 1], [3, 1]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*1.0'
>>> points_to_polynomial([[1, 3], [2, 3], [3, 3]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*3.0'
>>> points_to_polynomial([[1, 1], [2, 2], [3, 3]])
'f(x)=x^2*0.0+x^1*1.0+x^0*0.0'
>>> points_to_polynomial([[1, 1], [2, 4], [3, 9]])
'f(x)=x^2*1.0+x^1*-0.0+x^0*0.0'
>>> points_to_polynomial([[1, 3], [2, 6], [3, 11]])
'f(x)=x^2*1.0+x^1*-0.0+x^0*2.0'
>>> points_to_polynomial([[1, -3], [2, -6], [3, -11]])
'f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0'
>>> points_to_polynomial([[1, 5], [2, 2], [3, 9]])
'f(x)=x^2*5.0+x^1*-18.0+x^0*18.0'
>>> points_to_polynomial([[1, 1], [1, 2], [1, 3]])
'x=1'
>>> points_to_polynomial([[1, 1], [2, 2], [2, 2]])
Traceback (most recent call last):
...
ValueError: The program cannot work out a fitting polynomial.
"""
if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
if len({tuple(pair) for pair in coordinates}) != len(coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
set_x = {x for x, _ in coordinates}
if len(set_x) == 1:
return f"x={coordinates[0][0]}"
if len(set_x) != len(coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
x = len(coordinates)
# put the x and x to the power values in a matrix
matrix: list[list[float]] = [
[
coordinates[count_of_line][0] ** (x - (count_in_line + 1))
for count_in_line in range(x)
]
for count_of_line in range(x)
]
# put the y values into a vector
vector: list[float] = [coordinates[count_of_line][1] for count_of_line in range(x)]
for count in range(x):
for number in range(x):
if count == number:
continue
fraction = matrix[number][count] / matrix[count][count]
for counting_columns, item in enumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[number][counting_columns] -= item * fraction
# manipulating the values in the vector
vector[number] -= vector[count] * fraction
# make solutions
solution: list[str] = [
str(vector[count] / matrix[count][count]) for count in range(x)
]
solved = "f(x)="
for count in range(x):
remove_e: list[str] = solution[count].split("E")
if len(remove_e) > 1:
solution[count] = f"{remove_e[0]}*10^{remove_e[1]}"
solved += f"x^{x - (count + 1)}*{solution[count]}"
if count + 1 != x:
solved += "+"
return solved
if __name__ == "__main__":
print(points_to_polynomial([]))
print(points_to_polynomial([[]]))
print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/__init__.py | linear_algebra/src/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/linear_algebra/src/gaussian_elimination_pivoting.py | linear_algebra/src/gaussian_elimination_pivoting.py | import numpy as np
def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
"""
Solve a linear system of equations using Gaussian elimination with partial pivoting
Args:
- `matrix`: Coefficient matrix with the last column representing the constants.
Returns:
- Solution vector.
Raises:
- ``ValueError``: If the matrix is not correct (i.e., singular).
https://courses.engr.illinois.edu/cs357/su2013/lect.htm Lecture 7
Example:
>>> A = np.array([[2, 1, -1], [-3, -1, 2], [-2, 1, 2]], dtype=float)
>>> B = np.array([8, -11, -3], dtype=float)
>>> solution = solve_linear_system(np.column_stack((A, B)))
>>> np.allclose(solution, np.array([2., 3., -1.]))
True
>>> solve_linear_system(np.array([[0, 0, 0]], dtype=float))
Traceback (most recent call last):
...
ValueError: Matrix is not square
>>> solve_linear_system(np.array([[0, 0, 0], [0, 0, 0]], dtype=float))
Traceback (most recent call last):
...
ValueError: Matrix is singular
"""
ab = np.copy(matrix)
num_of_rows = ab.shape[0]
num_of_columns = ab.shape[1] - 1
x_lst: list[float] = []
if num_of_rows != num_of_columns:
raise ValueError("Matrix is not square")
for column_num in range(num_of_rows):
# Lead element search
for i in range(column_num, num_of_columns):
if abs(ab[i][column_num]) > abs(ab[column_num][column_num]):
ab[[column_num, i]] = ab[[i, column_num]]
# Upper triangular matrix
if abs(ab[column_num, column_num]) < 1e-8:
raise ValueError("Matrix is singular")
if column_num != 0:
for i in range(column_num, num_of_rows):
ab[i, :] -= (
ab[i, column_num - 1]
/ ab[column_num - 1, column_num - 1]
* ab[column_num - 1, :]
)
# Find x vector (Back Substitution)
for column_num in range(num_of_rows - 1, -1, -1):
x = ab[column_num, -1] / ab[column_num, column_num]
x_lst.insert(0, x)
for i in range(column_num - 1, -1, -1):
ab[i, -1] -= ab[i, column_num] * x
# Return the solution vector
return np.asarray(x_lst)
if __name__ == "__main__":
from doctest import testmod
testmod()
example_matrix = np.array(
[
[5.0, -5.0, -3.0, 4.0, -11.0],
[1.0, -4.0, 6.0, -4.0, -10.0],
[-2.0, -5.0, 4.0, -5.0, -12.0],
[-3.0, -3.0, 5.0, -5.0, 8.0],
],
dtype=float,
)
print(f"Matrix:\n{example_matrix}")
print(f"{solve_linear_system(example_matrix) = }")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/sherman_morrison.py | matrix/sherman_morrison.py | from __future__ import annotations
from typing import Any
class Matrix:
"""
<class Matrix>
Matrix structure.
"""
def __init__(self, row: int, column: int, default_value: float = 0) -> None:
"""
<method Matrix.__init__>
Initialize matrix with given size and default value.
Example:
>>> a = Matrix(2, 3, 1)
>>> a
Matrix consist of 2 rows and 3 columns
[1, 1, 1]
[1, 1, 1]
"""
self.row, self.column = row, column
self.array = [[default_value for _ in range(column)] for _ in range(row)]
def __str__(self) -> str:
"""
<method Matrix.__str__>
Return string representation of this matrix.
"""
# Prefix
s = f"Matrix consist of {self.row} rows and {self.column} columns\n"
# Make string identifier
max_element_length = 0
for row_vector in self.array:
for obj in row_vector:
max_element_length = max(max_element_length, len(str(obj)))
string_format_identifier = f"%{max_element_length}s"
# Make string and return
def single_line(row_vector: list[float]) -> str:
nonlocal string_format_identifier
line = "["
line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
line += "]"
return line
s += "\n".join(single_line(row_vector) for row_vector in self.array)
return s
def __repr__(self) -> str:
return str(self)
def validate_indices(self, loc: tuple[int, int]) -> bool:
"""
<method Matrix.validate_indicies>
Check if given indices are valid to pick element from matrix.
Example:
>>> a = Matrix(2, 6, 0)
>>> a.validate_indices((2, 7))
False
>>> a.validate_indices((0, 0))
True
"""
if not (isinstance(loc, (list, tuple)) and len(loc) == 2): # noqa: SIM114
return False
elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
return False
else:
return True
def __getitem__(self, loc: tuple[int, int]) -> Any:
"""
<method Matrix.__getitem__>
Return array[row][column] where loc = (row, column).
Example:
>>> a = Matrix(3, 2, 7)
>>> a[1, 0]
7
"""
assert self.validate_indices(loc)
return self.array[loc[0]][loc[1]]
def __setitem__(self, loc: tuple[int, int], value: float) -> None:
"""
<method Matrix.__setitem__>
Set array[row][column] = value where loc = (row, column).
Example:
>>> a = Matrix(2, 3, 1)
>>> a[1, 2] = 51
>>> a
Matrix consist of 2 rows and 3 columns
[ 1, 1, 1]
[ 1, 1, 51]
"""
assert self.validate_indices(loc)
self.array[loc[0]][loc[1]] = value
def __add__(self, another: Matrix) -> Matrix:
"""
<method Matrix.__add__>
Return self + another.
Example:
>>> a = Matrix(2, 1, -4)
>>> b = Matrix(2, 1, 3)
>>> a+b
Matrix consist of 2 rows and 1 columns
[-1]
[-1]
"""
# Validation
assert isinstance(another, Matrix)
assert self.row == another.row
assert self.column == another.column
# Add
result = Matrix(self.row, self.column)
for r in range(self.row):
for c in range(self.column):
result[r, c] = self[r, c] + another[r, c]
return result
def __neg__(self) -> Matrix:
"""
<method Matrix.__neg__>
Return -self.
Example:
>>> a = Matrix(2, 2, 3)
>>> a[0, 1] = a[1, 0] = -2
>>> -a
Matrix consist of 2 rows and 2 columns
[-3, 2]
[ 2, -3]
"""
result = Matrix(self.row, self.column)
for r in range(self.row):
for c in range(self.column):
result[r, c] = -self[r, c]
return result
def __sub__(self, another: Matrix) -> Matrix:
return self + (-another)
def __mul__(self, another: float | Matrix) -> Matrix:
"""
<method Matrix.__mul__>
Return self * another.
Example:
>>> a = Matrix(2, 3, 1)
>>> a[0,2] = a[1,2] = 3
>>> a * -2
Matrix consist of 2 rows and 3 columns
[-2, -2, -6]
[-2, -2, -6]
"""
if isinstance(another, (int, float)): # Scalar multiplication
result = Matrix(self.row, self.column)
for r in range(self.row):
for c in range(self.column):
result[r, c] = self[r, c] * another
return result
elif isinstance(another, Matrix): # Matrix multiplication
assert self.column == another.row
result = Matrix(self.row, another.column)
for r in range(self.row):
for c in range(another.column):
for i in range(self.column):
result[r, c] += self[r, i] * another[i, c]
return result
else:
msg = f"Unsupported type given for another ({type(another)})"
raise TypeError(msg)
def transpose(self) -> Matrix:
"""
<method Matrix.transpose>
Return self^T.
Example:
>>> a = Matrix(2, 3)
>>> for r in range(2):
... for c in range(3):
... a[r,c] = r*c
...
>>> a.transpose()
Matrix consist of 3 rows and 2 columns
[0, 0]
[0, 1]
[0, 2]
"""
result = Matrix(self.column, self.row)
for r in range(self.row):
for c in range(self.column):
result[c, r] = self[r, c]
return result
def sherman_morrison(self, u: Matrix, v: Matrix) -> Any:
"""
<method Matrix.sherman_morrison>
Apply Sherman-Morrison formula in O(n^2).
To learn this formula, please look this:
https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula
This method returns (A + uv^T)^(-1) where A^(-1) is self. Returns None if it's
impossible to calculate.
Warning: This method doesn't check if self is invertible.
Make sure self is invertible before execute this method.
Example:
>>> ainv = Matrix(3, 3, 0)
>>> for i in range(3): ainv[i,i] = 1
...
>>> u = Matrix(3, 1, 0)
>>> u[0,0], u[1,0], u[2,0] = 1, 2, -3
>>> v = Matrix(3, 1, 0)
>>> v[0,0], v[1,0], v[2,0] = 4, -2, 5
>>> ainv.sherman_morrison(u, v)
Matrix consist of 3 rows and 3 columns
[ 1.2857142857142856, -0.14285714285714285, 0.3571428571428571]
[ 0.5714285714285714, 0.7142857142857143, 0.7142857142857142]
[ -0.8571428571428571, 0.42857142857142855, -0.0714285714285714]
"""
# Size validation
assert isinstance(u, Matrix)
assert isinstance(v, Matrix)
assert self.row == self.column == u.row == v.row # u, v should be column vector
assert u.column == v.column == 1 # u, v should be column vector
# Calculate
v_t = v.transpose()
numerator_factor = (v_t * self * u)[0, 0] + 1
if numerator_factor == 0:
return None # It's not invertible
return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))
# Testing
if __name__ == "__main__":
def test1() -> None:
# a^(-1)
ainv = Matrix(3, 3, 0)
for i in range(3):
ainv[i, i] = 1
print(f"a^(-1) is {ainv}")
# u, v
u = Matrix(3, 1, 0)
u[0, 0], u[1, 0], u[2, 0] = 1, 2, -3
v = Matrix(3, 1, 0)
v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5
print(f"u is {u}")
print(f"v is {v}")
print(f"uv^T is {u * v.transpose()}")
# Sherman Morrison
print(f"(a + uv^T)^(-1) is {ainv.sherman_morrison(u, v)}")
def test2() -> None:
import doctest
doctest.testmod()
test2()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/largest_square_area_in_matrix.py | matrix/largest_square_area_in_matrix.py | """
Question:
Given a binary matrix mat of size n * m, find out the maximum size square
sub-matrix with all 1s.
---
Example 1:
Input:
n = 2, m = 2
mat = [[1, 1],
[1, 1]]
Output:
2
Explanation: The maximum size of the square
sub-matrix is 2. The matrix itself is the
maximum sized sub-matrix in this case.
---
Example 2
Input:
n = 2, m = 2
mat = [[0, 0],
[0, 0]]
Output: 0
Explanation: There is no 1 in the matrix.
Approach:
We initialize another matrix (dp) with the same dimensions
as the original one initialized with all 0's.
dp_array(i,j) represents the side length of the maximum square whose
bottom right corner is the cell with index (i,j) in the original matrix.
Starting from index (0,0), for every 1 found in the original matrix,
we update the value of the current element as
dp_array(i,j)=dp_array(dp(i-1,j),dp_array(i-1,j-1),dp_array(i,j-1)) + 1.
"""
def largest_square_area_in_matrix_top_down_approch(
rows: int, cols: int, mat: list[list[int]]
) -> int:
"""
Function updates the largest_square_area[0], if recursive call found
square with maximum area.
We aren't using dp_array here, so the time complexity would be exponential.
>>> largest_square_area_in_matrix_top_down_approch(2, 2, [[1,1], [1,1]])
2
>>> largest_square_area_in_matrix_top_down_approch(2, 2, [[0,0], [0,0]])
0
"""
def update_area_of_max_square(row: int, col: int) -> int:
# BASE CASE
if row >= rows or col >= cols:
return 0
right = update_area_of_max_square(row, col + 1)
diagonal = update_area_of_max_square(row + 1, col + 1)
down = update_area_of_max_square(row + 1, col)
if mat[row][col]:
sub_problem_sol = 1 + min([right, diagonal, down])
largest_square_area[0] = max(largest_square_area[0], sub_problem_sol)
return sub_problem_sol
else:
return 0
largest_square_area = [0]
update_area_of_max_square(0, 0)
return largest_square_area[0]
def largest_square_area_in_matrix_top_down_approch_with_dp(
rows: int, cols: int, mat: list[list[int]]
) -> int:
"""
Function updates the largest_square_area[0], if recursive call found
square with maximum area.
We are using dp_array here, so the time complexity would be O(N^2).
>>> largest_square_area_in_matrix_top_down_approch_with_dp(2, 2, [[1,1], [1,1]])
2
>>> largest_square_area_in_matrix_top_down_approch_with_dp(2, 2, [[0,0], [0,0]])
0
"""
def update_area_of_max_square_using_dp_array(
row: int, col: int, dp_array: list[list[int]]
) -> int:
if row >= rows or col >= cols:
return 0
if dp_array[row][col] != -1:
return dp_array[row][col]
right = update_area_of_max_square_using_dp_array(row, col + 1, dp_array)
diagonal = update_area_of_max_square_using_dp_array(row + 1, col + 1, dp_array)
down = update_area_of_max_square_using_dp_array(row + 1, col, dp_array)
if mat[row][col]:
sub_problem_sol = 1 + min([right, diagonal, down])
largest_square_area[0] = max(largest_square_area[0], sub_problem_sol)
dp_array[row][col] = sub_problem_sol
return sub_problem_sol
else:
return 0
largest_square_area = [0]
dp_array = [[-1] * cols for _ in range(rows)]
update_area_of_max_square_using_dp_array(0, 0, dp_array)
return largest_square_area[0]
def largest_square_area_in_matrix_bottom_up(
rows: int, cols: int, mat: list[list[int]]
) -> int:
"""
Function updates the largest_square_area, using bottom up approach.
>>> largest_square_area_in_matrix_bottom_up(2, 2, [[1,1], [1,1]])
2
>>> largest_square_area_in_matrix_bottom_up(2, 2, [[0,0], [0,0]])
0
"""
dp_array = [[0] * (cols + 1) for _ in range(rows + 1)]
largest_square_area = 0
for row in range(rows - 1, -1, -1):
for col in range(cols - 1, -1, -1):
right = dp_array[row][col + 1]
diagonal = dp_array[row + 1][col + 1]
bottom = dp_array[row + 1][col]
if mat[row][col] == 1:
dp_array[row][col] = 1 + min(right, diagonal, bottom)
largest_square_area = max(dp_array[row][col], largest_square_area)
else:
dp_array[row][col] = 0
return largest_square_area
def largest_square_area_in_matrix_bottom_up_space_optimization(
rows: int, cols: int, mat: list[list[int]]
) -> int:
"""
Function updates the largest_square_area, using bottom up
approach. with space optimization.
>>> largest_square_area_in_matrix_bottom_up_space_optimization(2, 2, [[1,1], [1,1]])
2
>>> largest_square_area_in_matrix_bottom_up_space_optimization(2, 2, [[0,0], [0,0]])
0
"""
current_row = [0] * (cols + 1)
next_row = [0] * (cols + 1)
largest_square_area = 0
for row in range(rows - 1, -1, -1):
for col in range(cols - 1, -1, -1):
right = current_row[col + 1]
diagonal = next_row[col + 1]
bottom = next_row[col]
if mat[row][col] == 1:
current_row[col] = 1 + min(right, diagonal, bottom)
largest_square_area = max(current_row[col], largest_square_area)
else:
current_row[col] = 0
next_row = current_row
return largest_square_area
if __name__ == "__main__":
import doctest
doctest.testmod()
print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/max_area_of_island.py | matrix/max_area_of_island.py | """
Given an two dimensional binary matrix grid. An island is a group of 1's (representing
land) connected 4-directionally (horizontal or vertical.) You may assume all four edges
of the grid are surrounded by water. The area of an island is the number of cells with
a value 1 in the island. Return the maximum area of an island in a grid. If there is no
island, return 0.
"""
matrix = [
[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
]
def is_safe(row: int, col: int, rows: int, cols: int) -> bool:
"""
Checking whether coordinate (row, col) is valid or not.
>>> is_safe(0, 0, 5, 5)
True
>>> is_safe(-1,-1, 5, 5)
False
"""
return 0 <= row < rows and 0 <= col < cols
def depth_first_search(row: int, col: int, seen: set, mat: list[list[int]]) -> int:
"""
Returns the current area of the island
>>> depth_first_search(0, 0, set(), matrix)
0
"""
rows = len(mat)
cols = len(mat[0])
if is_safe(row, col, rows, cols) and (row, col) not in seen and mat[row][col] == 1:
seen.add((row, col))
return (
1
+ depth_first_search(row + 1, col, seen, mat)
+ depth_first_search(row - 1, col, seen, mat)
+ depth_first_search(row, col + 1, seen, mat)
+ depth_first_search(row, col - 1, seen, mat)
)
else:
return 0
def find_max_area(mat: list[list[int]]) -> int:
"""
Finds the area of all islands and returns the maximum area.
>>> find_max_area(matrix)
6
"""
seen: set = set()
max_area = 0
for row, line in enumerate(mat):
for col, item in enumerate(line):
if item == 1 and (row, col) not in seen:
# Maximizing the area
max_area = max(max_area, depth_first_search(row, col, seen, mat))
return max_area
if __name__ == "__main__":
import doctest
print(find_max_area(matrix)) # Output -> 6
"""
Explanation:
We are allowed to move in four directions (horizontal or vertical) so the possible
in a matrix if we are at x and y position the possible moving are
Directions are [(x, y+1), (x, y-1), (x+1, y), (x-1, y)] but we need to take care of
boundary cases as well which are x and y can not be smaller than 0 and greater than
the number of rows and columns respectively.
Visualization
mat = [
[0,0,A,0,0,0,0,B,0,0,0,0,0],
[0,0,0,0,0,0,0,B,B,B,0,0,0],
[0,C,C,0,D,0,0,0,0,0,0,0,0],
[0,C,0,0,D,D,0,0,E,0,E,0,0],
[0,C,0,0,D,D,0,0,E,E,E,0,0],
[0,0,0,0,0,0,0,0,0,0,E,0,0],
[0,0,0,0,0,0,0,F,F,F,0,0,0],
[0,0,0,0,0,0,0,F,F,0,0,0,0]
]
For visualization, I have defined the connected island with letters
by observation, we can see that
A island is of area 1
B island is of area 4
C island is of area 4
D island is of area 5
E island is of area 6 and
F island is of area 5
it has 6 unique islands of mentioned areas
and the maximum of all of them is 6 so we return 6.
"""
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/pascal_triangle.py | matrix/pascal_triangle.py | """
This implementation demonstrates how to generate the elements of a Pascal's triangle.
The element havingva row index of r and column index of c can be derivedvas follows:
triangle[r][c] = triangle[r-1][c-1]+triangle[r-1][c]
A Pascal's triangle is a triangular array containing binomial coefficients.
https://en.wikipedia.org/wiki/Pascal%27s_triangle
"""
def print_pascal_triangle(num_rows: int) -> None:
"""
Print Pascal's triangle for different number of rows
>>> print_pascal_triangle(5)
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
"""
triangle = generate_pascal_triangle(num_rows)
for row_idx in range(num_rows):
# Print left spaces
for _ in range(num_rows - row_idx - 1):
print(end=" ")
# Print row values
for col_idx in range(row_idx + 1):
if col_idx != row_idx:
print(triangle[row_idx][col_idx], end=" ")
else:
print(triangle[row_idx][col_idx], end="")
print()
def generate_pascal_triangle(num_rows: int) -> list[list[int]]:
"""
Create Pascal's triangle for different number of rows
>>> generate_pascal_triangle(0)
[]
>>> generate_pascal_triangle(1)
[[1]]
>>> generate_pascal_triangle(2)
[[1], [1, 1]]
>>> generate_pascal_triangle(3)
[[1], [1, 1], [1, 2, 1]]
>>> generate_pascal_triangle(4)
[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
>>> generate_pascal_triangle(5)
[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]
>>> generate_pascal_triangle(-5)
Traceback (most recent call last):
...
ValueError: The input value of 'num_rows' should be greater than or equal to 0
>>> generate_pascal_triangle(7.89)
Traceback (most recent call last):
...
TypeError: The input value of 'num_rows' should be 'int'
"""
if not isinstance(num_rows, int):
raise TypeError("The input value of 'num_rows' should be 'int'")
if num_rows == 0:
return []
elif num_rows < 0:
raise ValueError(
"The input value of 'num_rows' should be greater than or equal to 0"
)
triangle: list[list[int]] = []
for current_row_idx in range(num_rows):
current_row = populate_current_row(triangle, current_row_idx)
triangle.append(current_row)
return triangle
def populate_current_row(triangle: list[list[int]], current_row_idx: int) -> list[int]:
"""
>>> triangle = [[1]]
>>> populate_current_row(triangle, 1)
[1, 1]
"""
current_row = [-1] * (current_row_idx + 1)
# first and last elements of current row are equal to 1
current_row[0], current_row[-1] = 1, 1
for current_col_idx in range(1, current_row_idx):
calculate_current_element(
triangle, current_row, current_row_idx, current_col_idx
)
return current_row
def calculate_current_element(
triangle: list[list[int]],
current_row: list[int],
current_row_idx: int,
current_col_idx: int,
) -> None:
"""
>>> triangle = [[1], [1, 1]]
>>> current_row = [1, -1, 1]
>>> calculate_current_element(triangle, current_row, 2, 1)
>>> current_row
[1, 2, 1]
"""
above_to_left_elt = triangle[current_row_idx - 1][current_col_idx - 1]
above_to_right_elt = triangle[current_row_idx - 1][current_col_idx]
current_row[current_col_idx] = above_to_left_elt + above_to_right_elt
def generate_pascal_triangle_optimized(num_rows: int) -> list[list[int]]:
"""
This function returns a matrix representing the corresponding pascal's triangle
according to the given input of number of rows of Pascal's triangle to be generated.
It reduces the operations done to generate a row by half
by eliminating redundant calculations.
:param num_rows: Integer specifying the number of rows in the Pascal's triangle
:return: 2-D List (matrix) representing the Pascal's triangle
Return the Pascal's triangle of given rows
>>> generate_pascal_triangle_optimized(3)
[[1], [1, 1], [1, 2, 1]]
>>> generate_pascal_triangle_optimized(1)
[[1]]
>>> generate_pascal_triangle_optimized(0)
[]
>>> generate_pascal_triangle_optimized(-5)
Traceback (most recent call last):
...
ValueError: The input value of 'num_rows' should be greater than or equal to 0
>>> generate_pascal_triangle_optimized(7.89)
Traceback (most recent call last):
...
TypeError: The input value of 'num_rows' should be 'int'
"""
if not isinstance(num_rows, int):
raise TypeError("The input value of 'num_rows' should be 'int'")
if num_rows == 0:
return []
elif num_rows < 0:
raise ValueError(
"The input value of 'num_rows' should be greater than or equal to 0"
)
result: list[list[int]] = [[1]]
for row_index in range(1, num_rows):
temp_row = [0] + result[-1] + [0]
row_length = row_index + 1
# Calculate the number of distinct elements in a row
distinct_elements = sum(divmod(row_length, 2))
row_first_half = [
temp_row[i - 1] + temp_row[i] for i in range(1, distinct_elements + 1)
]
row_second_half = row_first_half[: (row_index + 1) // 2]
row_second_half.reverse()
row = row_first_half + row_second_half
result.append(row)
return result
def benchmark() -> None:
"""
Benchmark multiple functions, with three different length int values.
"""
from collections.abc import Callable
from timeit import timeit
def benchmark_a_function(func: Callable, value: int) -> None:
call = f"{func.__name__}({value})"
timing = timeit(f"__main__.{call}", setup="import __main__")
# print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
print(f"{call:38} -- {timing:.4f} seconds")
for value in range(15): # (1, 7, 14):
for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
benchmark_a_function(func, value)
print()
if __name__ == "__main__":
import doctest
doctest.testmod()
benchmark()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/median_matrix.py | matrix/median_matrix.py | """
https://en.wikipedia.org/wiki/Median
"""
def median(matrix: list[list[int]]) -> int:
"""
Calculate the median of a sorted matrix.
Args:
matrix: A 2D matrix of integers.
Returns:
The median value of the matrix.
Examples:
>>> matrix = [[1, 3, 5], [2, 6, 9], [3, 6, 9]]
>>> median(matrix)
5
>>> matrix = [[1, 2, 3], [4, 5, 6]]
>>> median(matrix)
3
"""
# Flatten the matrix into a sorted 1D list
linear = sorted(num for row in matrix for num in row)
# Calculate the middle index
mid = (len(linear) - 1) // 2
# Return the median
return linear[mid]
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/cramers_rule_2x2.py | matrix/cramers_rule_2x2.py | # https://www.chilimath.com/lessons/advanced-algebra/cramers-rule-with-two-variables
# https://en.wikipedia.org/wiki/Cramer%27s_rule
def cramers_rule_2x2(equation1: list[int], equation2: list[int]) -> tuple[float, float]:
"""
Solves the system of linear equation in 2 variables.
:param: equation1: list of 3 numbers
:param: equation2: list of 3 numbers
:return: String of result
input format : [a1, b1, d1], [a2, b2, d2]
determinant = [[a1, b1], [a2, b2]]
determinant_x = [[d1, b1], [d2, b2]]
determinant_y = [[a1, d1], [a2, d2]]
>>> cramers_rule_2x2([2, 3, 0], [5, 1, 0])
(0.0, 0.0)
>>> cramers_rule_2x2([0, 4, 50], [2, 0, 26])
(13.0, 12.5)
>>> cramers_rule_2x2([11, 2, 30], [1, 0, 4])
(4.0, -7.0)
>>> cramers_rule_2x2([4, 7, 1], [1, 2, 0])
(2.0, -1.0)
>>> cramers_rule_2x2([1, 2, 3], [2, 4, 6])
Traceback (most recent call last):
...
ValueError: Infinite solutions. (Consistent system)
>>> cramers_rule_2x2([1, 2, 3], [2, 4, 7])
Traceback (most recent call last):
...
ValueError: No solution. (Inconsistent system)
>>> cramers_rule_2x2([1, 2, 3], [11, 22])
Traceback (most recent call last):
...
ValueError: Please enter a valid equation.
>>> cramers_rule_2x2([0, 1, 6], [0, 0, 3])
Traceback (most recent call last):
...
ValueError: No solution. (Inconsistent system)
>>> cramers_rule_2x2([0, 0, 6], [0, 0, 3])
Traceback (most recent call last):
...
ValueError: Both a & b of two equations can't be zero.
>>> cramers_rule_2x2([1, 2, 3], [1, 2, 3])
Traceback (most recent call last):
...
ValueError: Infinite solutions. (Consistent system)
>>> cramers_rule_2x2([0, 4, 50], [0, 3, 99])
Traceback (most recent call last):
...
ValueError: No solution. (Inconsistent system)
"""
# Check if the input is valid
if not len(equation1) == len(equation2) == 3:
raise ValueError("Please enter a valid equation.")
if equation1[0] == equation1[1] == equation2[0] == equation2[1] == 0:
raise ValueError("Both a & b of two equations can't be zero.")
# Extract the coefficients
a1, b1, c1 = equation1
a2, b2, c2 = equation2
# Calculate the determinants of the matrices
determinant = a1 * b2 - a2 * b1
determinant_x = c1 * b2 - c2 * b1
determinant_y = a1 * c2 - a2 * c1
# Check if the system of linear equations has a solution (using Cramer's rule)
if determinant == 0:
if determinant_x == determinant_y == 0:
raise ValueError("Infinite solutions. (Consistent system)")
else:
raise ValueError("No solution. (Inconsistent system)")
elif determinant_x == determinant_y == 0:
# Trivial solution (Inconsistent system)
return (0.0, 0.0)
else:
x = determinant_x / determinant
y = determinant_y / determinant
# Non-Trivial Solution (Consistent system)
return (x, y)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/count_paths.py | matrix/count_paths.py | """
Given a grid, where you start from the top left position [0, 0],
you want to find how many paths you can take to get to the bottom right position.
start here -> 0 0 0 0
1 1 0 0
0 0 0 1
0 1 0 0 <- finish here
how many 'distinct' paths can you take to get to the finish?
Using a recursive depth-first search algorithm below, you are able to
find the number of distinct unique paths (count).
'*' will demonstrate a path
In the example above, there are two distinct paths:
1. 2.
* * * 0 * * * *
1 1 * 0 1 1 * *
0 0 * 1 0 0 * 1
0 1 * * 0 1 * *
"""
def depth_first_search(grid: list[list[int]], row: int, col: int, visit: set) -> int:
"""
Recursive Backtracking Depth First Search Algorithm
Starting from top left of a matrix, count the number of
paths that can reach the bottom right of a matrix.
1 represents a block (inaccessible)
0 represents a valid space (accessible)
0 0 0 0
1 1 0 0
0 0 0 1
0 1 0 0
>>> grid = [[0, 0, 0, 0], [1, 1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0]]
>>> depth_first_search(grid, 0, 0, set())
2
0 0 0 0 0
0 1 1 1 0
0 1 1 1 0
0 0 0 0 0
>>> grid = [[0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]
>>> depth_first_search(grid, 0, 0, set())
2
"""
row_length, col_length = len(grid), len(grid[0])
if (
min(row, col) < 0
or row == row_length
or col == col_length
or (row, col) in visit
or grid[row][col] == 1
):
return 0
if row == row_length - 1 and col == col_length - 1:
return 1
visit.add((row, col))
count = 0
count += depth_first_search(grid, row + 1, col, visit)
count += depth_first_search(grid, row - 1, col, visit)
count += depth_first_search(grid, row, col + 1, visit)
count += depth_first_search(grid, row, col - 1, visit)
visit.remove((row, col))
return count
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/matrix_operation.py | matrix/matrix_operation.py | """
Functions for 2D matrix operations
"""
from __future__ import annotations
from typing import Any
def add(*matrix_s: list[list[int]]) -> list[list[int]]:
"""
>>> add([[1,2],[3,4]],[[2,3],[4,5]])
[[3, 5], [7, 9]]
>>> add([[1.2,2.4],[3,4]],[[2,3],[4,5]])
[[3.2, 5.4], [7, 9]]
>>> add([[1, 2], [4, 5]], [[3, 7], [3, 4]], [[3, 5], [5, 7]])
[[7, 14], [12, 16]]
>>> add([3], [4, 5])
Traceback (most recent call last):
...
TypeError: Expected a matrix, got int/list instead
"""
if all(_check_not_integer(m) for m in matrix_s):
for i in matrix_s[1:]:
_verify_matrix_sizes(matrix_s[0], i)
return [[sum(t) for t in zip(*m)] for m in zip(*matrix_s)]
raise TypeError("Expected a matrix, got int/list instead")
def subtract(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
"""
>>> subtract([[1,2],[3,4]],[[2,3],[4,5]])
[[-1, -1], [-1, -1]]
>>> subtract([[1,2.5],[3,4]],[[2,3],[4,5.5]])
[[-1, -0.5], [-1, -1.5]]
>>> subtract([3], [4, 5])
Traceback (most recent call last):
...
TypeError: Expected a matrix, got int/list instead
"""
if (
_check_not_integer(matrix_a)
and _check_not_integer(matrix_b)
and _verify_matrix_sizes(matrix_a, matrix_b)
):
return [[i - j for i, j in zip(*m)] for m in zip(matrix_a, matrix_b)]
raise TypeError("Expected a matrix, got int/list instead")
def scalar_multiply(matrix: list[list[int]], n: float) -> list[list[float]]:
"""
>>> scalar_multiply([[1,2],[3,4]],5)
[[5, 10], [15, 20]]
>>> scalar_multiply([[1.4,2.3],[3,4]],5)
[[7.0, 11.5], [15, 20]]
"""
return [[x * n for x in row] for row in matrix]
def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
"""
>>> multiply([[1,2],[3,4]],[[5,5],[7,5]])
[[19, 15], [43, 35]]
>>> multiply([[1,2.5],[3,4.5]],[[5,5],[7,5]])
[[22.5, 17.5], [46.5, 37.5]]
>>> multiply([[1, 2, 3]], [[2], [3], [4]])
[[20]]
"""
if _check_not_integer(matrix_a) and _check_not_integer(matrix_b):
rows, cols = _verify_matrix_sizes(matrix_a, matrix_b)
if cols[0] != rows[1]:
msg = (
"Cannot multiply matrix of dimensions "
f"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
)
raise ValueError(msg)
return [
[sum(m * n for m, n in zip(i, j)) for j in zip(*matrix_b)] for i in matrix_a
]
def identity(n: int) -> list[list[int]]:
"""
:param n: dimension for nxn matrix
:type n: int
:return: Identity matrix of shape [n, n]
>>> identity(3)
[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
"""
n = int(n)
return [[int(row == column) for column in range(n)] for row in range(n)]
def transpose(
matrix: list[list[int]], return_map: bool = True
) -> list[list[int]] | map[list[int]]:
"""
>>> transpose([[1,2],[3,4]]) # doctest: +ELLIPSIS
<map object at ...
>>> transpose([[1,2],[3,4]], return_map=False)
[[1, 3], [2, 4]]
>>> transpose([1, [2, 3]])
Traceback (most recent call last):
...
TypeError: Expected a matrix, got int/list instead
"""
if _check_not_integer(matrix):
if return_map:
return map(list, zip(*matrix))
else:
return list(map(list, zip(*matrix)))
raise TypeError("Expected a matrix, got int/list instead")
def minor(matrix: list[list[int]], row: int, column: int) -> list[list[int]]:
"""
>>> minor([[1, 2], [3, 4]], 1, 1)
[[1]]
"""
minor = matrix[:row] + matrix[row + 1 :]
return [row[:column] + row[column + 1 :] for row in minor]
def determinant(matrix: list[list[int]]) -> Any:
"""
>>> determinant([[1, 2], [3, 4]])
-2
>>> determinant([[1.5, 2.5], [3, 4]])
-1.5
"""
if len(matrix) == 1:
return matrix[0][0]
return sum(
x * determinant(minor(matrix, 0, i)) * (-1) ** i
for i, x in enumerate(matrix[0])
)
def inverse(matrix: list[list[int]]) -> list[list[float]] | None:
"""
>>> inverse([[1, 2], [3, 4]])
[[-2.0, 1.0], [1.5, -0.5]]
>>> inverse([[1, 1], [1, 1]])
"""
# https://stackoverflow.com/questions/20047519/python-doctests-test-for-none
det = determinant(matrix)
if det == 0:
return None
matrix_minor = [
[determinant(minor(matrix, i, j)) for j in range(len(matrix))]
for i in range(len(matrix))
]
cofactors = [
[x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row])]
for row in range(len(matrix))
]
adjugate = list(transpose(cofactors))
return scalar_multiply(adjugate, 1 / det)
def _check_not_integer(matrix: list[list[int]]) -> bool:
return not isinstance(matrix, int) and not isinstance(matrix[0], int)
def _shape(matrix: list[list[int]]) -> tuple[int, int]:
return len(matrix), len(matrix[0])
def _verify_matrix_sizes(
matrix_a: list[list[int]], matrix_b: list[list[int]]
) -> tuple[tuple[int, int], tuple[int, int]]:
shape = _shape(matrix_a) + _shape(matrix_b)
if shape[0] != shape[3] or shape[1] != shape[2]:
msg = (
"operands could not be broadcast together with shape "
f"({shape[0], shape[1]}), ({shape[2], shape[3]})"
)
raise ValueError(msg)
return (shape[0], shape[2]), (shape[1], shape[3])
def main() -> None:
matrix_a = [[12, 10], [3, 9]]
matrix_b = [[3, 4], [7, 4]]
matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
print(f"Add Operation, {add(matrix_a, matrix_b) = } \n")
print(f"Multiply Operation, {multiply(matrix_a, matrix_b) = } \n")
print(f"Identity: {identity(5)}\n")
print(f"Minor of {matrix_c} = {minor(matrix_c, 1, 2)} \n")
print(f"Determinant of {matrix_b} = {determinant(matrix_b)} \n")
print(f"Inverse of {matrix_d} = {inverse(matrix_d)}\n")
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/spiral_print.py | matrix/spiral_print.py | """
This program print the matrix in spiral form.
This problem has been solved through recursive way.
Matrix must satisfy below conditions
i) matrix should be only one or two dimensional
ii) number of column of all rows should be equal
"""
def check_matrix(matrix: list[list[int]]) -> bool:
# must be
matrix = [list(row) for row in matrix]
if matrix and isinstance(matrix, list):
if isinstance(matrix[0], list):
prev_len = 0
for row in matrix:
if prev_len == 0:
prev_len = len(row)
result = True
else:
result = prev_len == len(row)
else:
result = True
else:
result = False
return result
def spiral_print_clockwise(a: list[list[int]]) -> None:
"""
>>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
1
2
3
4
8
12
11
10
9
5
6
7
"""
if check_matrix(a) and len(a) > 0:
a = [list(row) for row in a]
mat_row = len(a)
if isinstance(a[0], list):
mat_col = len(a[0])
else:
for dat in a:
print(dat)
return
# horizotal printing increasing
for i in range(mat_col):
print(a[0][i])
# vertical printing down
for i in range(1, mat_row):
print(a[i][mat_col - 1])
# horizotal printing decreasing
if mat_row > 1:
for i in range(mat_col - 2, -1, -1):
print(a[mat_row - 1][i])
# vertical printing up
for i in range(mat_row - 2, 0, -1):
print(a[i][0])
remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
if len(remain_mat) > 0:
spiral_print_clockwise(remain_mat)
else:
return
else:
print("Not a valid matrix")
return
# Other Easy to understand Approach
def spiral_traversal(matrix: list[list]) -> list[int]:
"""
>>> spiral_traversal([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
[1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7]
Example:
matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
Algorithm:
Step 1. first pop the 0 index list. (which is [1,2,3,4] and concatenate the
output of [step 2])
Step 2. Now perform matrix's Transpose operation (Change rows to column
and vice versa) and reverse the resultant matrix.
Step 3. Pass the output of [2nd step], to same recursive function till
base case hits.
Dry Run:
Stage 1.
[1, 2, 3, 4] + spiral_traversal([
[8, 12], [7, 11], [6, 10], [5, 9]]
])
Stage 2.
[1, 2, 3, 4, 8, 12] + spiral_traversal([
[11, 10, 9], [7, 6, 5]
])
Stage 3.
[1, 2, 3, 4, 8, 12, 11, 10, 9] + spiral_traversal([
[5], [6], [7]
])
Stage 4.
[1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([
[5], [6], [7]
])
Stage 5.
[1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([[6, 7]])
Stage 6.
[1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] + spiral_traversal([])
"""
if matrix:
return list(matrix.pop(0)) + spiral_traversal(
[list(row) for row in zip(*matrix)][::-1]
)
else:
return []
# driver code
if __name__ == "__main__":
import doctest
doctest.testmod()
a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
spiral_print_clockwise(a)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/searching_in_sorted_matrix.py | matrix/searching_in_sorted_matrix.py | from __future__ import annotations
def search_in_a_sorted_matrix(mat: list[list[int]], m: int, n: int, key: float) -> None:
"""
>>> search_in_a_sorted_matrix(
... [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]], 3, 3, 5)
Key 5 found at row- 1 column- 2
>>> search_in_a_sorted_matrix(
... [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]], 3, 3, 21)
Key 21 not found
>>> search_in_a_sorted_matrix(
... [[2.1, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]], 3, 3, 2.1)
Key 2.1 found at row- 1 column- 1
>>> search_in_a_sorted_matrix(
... [[2.1, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]], 3, 3, 2.2)
Key 2.2 not found
"""
i, j = m - 1, 0
while i >= 0 and j < n:
if key == mat[i][j]:
print(f"Key {key} found at row- {i + 1} column- {j + 1}")
return
if key < mat[i][j]:
i -= 1
else:
j += 1
print(f"Key {key} not found")
def main() -> None:
mat = [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]]
x = int(input("Enter the element to be searched:"))
print(mat)
search_in_a_sorted_matrix(mat, len(mat), len(mat[0]), x)
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/matrix_multiplication_recursion.py | matrix/matrix_multiplication_recursion.py | # @Author : ojas-wani
# @File : matrix_multiplication_recursion.py
# @Date : 10/06/2023
"""
Perform matrix multiplication using a recursive algorithm.
https://en.wikipedia.org/wiki/Matrix_multiplication
"""
# type Matrix = list[list[int]] # psf/black currenttly fails on this line
Matrix = list[list[int]]
matrix_1_to_4 = [
[1, 2],
[3, 4],
]
matrix_5_to_8 = [
[5, 6],
[7, 8],
]
matrix_5_to_9_high = [
[5, 6],
[7, 8],
[9],
]
matrix_5_to_9_wide = [
[5, 6],
[7, 8, 9],
]
matrix_count_up = [
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
]
matrix_unordered = [
[5, 8, 1, 2],
[6, 7, 3, 0],
[4, 5, 9, 1],
[2, 6, 10, 14],
]
matrices = (
matrix_1_to_4,
matrix_5_to_8,
matrix_5_to_9_high,
matrix_5_to_9_wide,
matrix_count_up,
matrix_unordered,
)
def is_square(matrix: Matrix) -> bool:
"""
>>> is_square([])
True
>>> is_square(matrix_1_to_4)
True
>>> is_square(matrix_5_to_9_high)
False
"""
len_matrix = len(matrix)
return all(len(row) == len_matrix for row in matrix)
def matrix_multiply(matrix_a: Matrix, matrix_b: Matrix) -> Matrix:
"""
>>> matrix_multiply(matrix_1_to_4, matrix_5_to_8)
[[19, 22], [43, 50]]
"""
return [
[sum(a * b for a, b in zip(row, col)) for col in zip(*matrix_b)]
for row in matrix_a
]
def matrix_multiply_recursive(matrix_a: Matrix, matrix_b: Matrix) -> Matrix:
"""
:param matrix_a: A square Matrix.
:param matrix_b: Another square Matrix with the same dimensions as matrix_a.
:return: Result of matrix_a * matrix_b.
:raises ValueError: If the matrices cannot be multiplied.
>>> matrix_multiply_recursive([], [])
[]
>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_8)
[[19, 22], [43, 50]]
>>> matrix_multiply_recursive(matrix_count_up, matrix_unordered)
[[37, 61, 74, 61], [105, 165, 166, 129], [173, 269, 258, 197], [241, 373, 350, 265]]
>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_wide)
Traceback (most recent call last):
...
ValueError: Invalid matrix dimensions
>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_high)
Traceback (most recent call last):
...
ValueError: Invalid matrix dimensions
>>> matrix_multiply_recursive(matrix_1_to_4, matrix_count_up)
Traceback (most recent call last):
...
ValueError: Invalid matrix dimensions
"""
if not matrix_a or not matrix_b:
return []
if not all(
(len(matrix_a) == len(matrix_b), is_square(matrix_a), is_square(matrix_b))
):
raise ValueError("Invalid matrix dimensions")
# Initialize the result matrix with zeros
result = [[0] * len(matrix_b[0]) for _ in range(len(matrix_a))]
# Recursive multiplication of matrices
def multiply(
i_loop: int,
j_loop: int,
k_loop: int,
matrix_a: Matrix,
matrix_b: Matrix,
result: Matrix,
) -> None:
"""
:param matrix_a: A square Matrix.
:param matrix_b: Another square Matrix with the same dimensions as matrix_a.
:param result: Result matrix
:param i: Index used for iteration during multiplication.
:param j: Index used for iteration during multiplication.
:param k: Index used for iteration during multiplication.
>>> 0 > 1 # Doctests in inner functions are never run
True
"""
if i_loop >= len(matrix_a):
return
if j_loop >= len(matrix_b[0]):
return multiply(i_loop + 1, 0, 0, matrix_a, matrix_b, result)
if k_loop >= len(matrix_b):
return multiply(i_loop, j_loop + 1, 0, matrix_a, matrix_b, result)
result[i_loop][j_loop] += matrix_a[i_loop][k_loop] * matrix_b[k_loop][j_loop]
return multiply(i_loop, j_loop, k_loop + 1, matrix_a, matrix_b, result)
# Perform the recursive matrix multiplication
multiply(0, 0, 0, matrix_a, matrix_b, result)
return result
if __name__ == "__main__":
from doctest import testmod
failure_count, test_count = testmod()
if not failure_count:
matrix_a = matrices[0]
for matrix_b in matrices[1:]:
print("Multiplying:")
for row in matrix_a:
print(row)
print("By:")
for row in matrix_b:
print(row)
print("Result:")
try:
result = matrix_multiply_recursive(matrix_a, matrix_b)
for row in result:
print(row)
assert result == matrix_multiply(matrix_a, matrix_b)
except ValueError as e:
print(f"{e!r}")
print()
matrix_a = matrix_b
print("Benchmark:")
from functools import partial
from timeit import timeit
mytimeit = partial(timeit, globals=globals(), number=100_000)
for func in ("matrix_multiply", "matrix_multiply_recursive"):
print(f"{func:>25}(): {mytimeit(f'{func}(matrix_count_up, matrix_unordered)')}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/rotate_matrix.py | matrix/rotate_matrix.py | """
In this problem, we want to rotate the matrix elements by 90, 180, 270
(counterclockwise)
Discussion in stackoverflow:
https://stackoverflow.com/questions/42519/how-do-you-rotate-a-two-dimensional-array
"""
from __future__ import annotations
def make_matrix(row_size: int = 4) -> list[list[int]]:
"""
>>> make_matrix()
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
>>> make_matrix(1)
[[1]]
>>> make_matrix(-2)
[[1, 2], [3, 4]]
>>> make_matrix(3)
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
>>> make_matrix() == make_matrix(4)
True
"""
row_size = abs(row_size) or 4
return [[1 + x + y * row_size for x in range(row_size)] for y in range(row_size)]
def rotate_90(matrix: list[list[int]]) -> list[list[int]]:
"""
>>> rotate_90(make_matrix())
[[4, 8, 12, 16], [3, 7, 11, 15], [2, 6, 10, 14], [1, 5, 9, 13]]
>>> rotate_90(make_matrix()) == transpose(reverse_column(make_matrix()))
True
"""
return reverse_row(transpose(matrix))
# OR.. transpose(reverse_column(matrix))
def rotate_180(matrix: list[list[int]]) -> list[list[int]]:
"""
>>> rotate_180(make_matrix())
[[16, 15, 14, 13], [12, 11, 10, 9], [8, 7, 6, 5], [4, 3, 2, 1]]
>>> rotate_180(make_matrix()) == reverse_column(reverse_row(make_matrix()))
True
"""
return reverse_row(reverse_column(matrix))
# OR.. reverse_column(reverse_row(matrix))
def rotate_270(matrix: list[list[int]]) -> list[list[int]]:
"""
>>> rotate_270(make_matrix())
[[13, 9, 5, 1], [14, 10, 6, 2], [15, 11, 7, 3], [16, 12, 8, 4]]
>>> rotate_270(make_matrix()) == transpose(reverse_row(make_matrix()))
True
"""
return reverse_column(transpose(matrix))
# OR.. transpose(reverse_row(matrix))
def transpose(matrix: list[list[int]]) -> list[list[int]]:
matrix[:] = [list(x) for x in zip(*matrix)]
return matrix
def reverse_row(matrix: list[list[int]]) -> list[list[int]]:
matrix[:] = matrix[::-1]
return matrix
def reverse_column(matrix: list[list[int]]) -> list[list[int]]:
matrix[:] = [x[::-1] for x in matrix]
return matrix
def print_matrix(matrix: list[list[int]]) -> None:
for i in matrix:
print(*i)
if __name__ == "__main__":
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 90 counterclockwise:\n")
print_matrix(rotate_90(matrix))
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 180:\n")
print_matrix(rotate_180(matrix))
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 270 counterclockwise:\n")
print_matrix(rotate_270(matrix))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/validate_sudoku_board.py | matrix/validate_sudoku_board.py | """
LeetCode 36. Valid Sudoku
https://leetcode.com/problems/valid-sudoku/
https://en.wikipedia.org/wiki/Sudoku
Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be
validated according to the following rules:
- Each row must contain the digits 1-9 without repetition.
- Each column must contain the digits 1-9 without repetition.
- Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9
without repetition.
Note:
A Sudoku board (partially filled) could be valid but is not necessarily
solvable.
Only the filled cells need to be validated according to the mentioned rules.
"""
from collections import defaultdict
NUM_SQUARES = 9
EMPTY_CELL = "."
def is_valid_sudoku_board(sudoku_board: list[list[str]]) -> bool:
"""
This function validates (but does not solve) a sudoku board.
The board may be valid but unsolvable.
>>> is_valid_sudoku_board([
... ["5","3",".",".","7",".",".",".","."]
... ,["6",".",".","1","9","5",".",".","."]
... ,[".","9","8",".",".",".",".","6","."]
... ,["8",".",".",".","6",".",".",".","3"]
... ,["4",".",".","8",".","3",".",".","1"]
... ,["7",".",".",".","2",".",".",".","6"]
... ,[".","6",".",".",".",".","2","8","."]
... ,[".",".",".","4","1","9",".",".","5"]
... ,[".",".",".",".","8",".",".","7","9"]
... ])
True
>>> is_valid_sudoku_board([
... ["8","3",".",".","7",".",".",".","."]
... ,["6",".",".","1","9","5",".",".","."]
... ,[".","9","8",".",".",".",".","6","."]
... ,["8",".",".",".","6",".",".",".","3"]
... ,["4",".",".","8",".","3",".",".","1"]
... ,["7",".",".",".","2",".",".",".","6"]
... ,[".","6",".",".",".",".","2","8","."]
... ,[".",".",".","4","1","9",".",".","5"]
... ,[".",".",".",".","8",".",".","7","9"]
... ])
False
>>> is_valid_sudoku_board([
... ["1","2","3","4","5","6","7","8","9"]
... ,["4","5","6","7","8","9","1","2","3"]
... ,["7","8","9","1","2","3","4","5","6"]
... ,[".",".",".",".",".",".",".",".","."]
... ,[".",".",".",".",".",".",".",".","."]
... ,[".",".",".",".",".",".",".",".","."]
... ,[".",".",".",".",".",".",".",".","."]
... ,[".",".",".",".",".",".",".",".","."]
... ,[".",".",".",".",".",".",".",".","."]
... ])
True
>>> is_valid_sudoku_board([
... ["1","2","3",".",".",".",".",".","."]
... ,["4","5","6",".",".",".",".",".","."]
... ,["7","8","9",".",".",".",".",".","."]
... ,[".",".",".","4","5","6",".",".","."]
... ,[".",".",".","7","8","9",".",".","."]
... ,[".",".",".","1","2","3",".",".","."]
... ,[".",".",".",".",".",".","7","8","9"]
... ,[".",".",".",".",".",".","1","2","3"]
... ,[".",".",".",".",".",".","4","5","6"]
... ])
True
>>> is_valid_sudoku_board([
... ["1","2","3",".",".",".","5","6","4"]
... ,["4","5","6",".",".",".","8","9","7"]
... ,["7","8","9",".",".",".","2","3","1"]
... ,[".",".",".","4","5","6",".",".","."]
... ,[".",".",".","7","8","9",".",".","."]
... ,[".",".",".","1","2","3",".",".","."]
... ,["3","1","2",".",".",".","7","8","9"]
... ,["6","4","5",".",".",".","1","2","3"]
... ,["9","7","8",".",".",".","4","5","6"]
... ])
True
>>> is_valid_sudoku_board([
... ["1","2","3","4","5","6","7","8","9"]
... ,["2",".",".",".",".",".",".",".","8"]
... ,["3",".",".",".",".",".",".",".","7"]
... ,["4",".",".",".",".",".",".",".","6"]
... ,["5",".",".",".",".",".",".",".","5"]
... ,["6",".",".",".",".",".",".",".","4"]
... ,["7",".",".",".",".",".",".",".","3"]
... ,["8",".",".",".",".",".",".",".","2"]
... ,["9","8","7","6","5","4","3","2","1"]
... ])
False
>>> is_valid_sudoku_board([
... ["1","2","3","8","9","7","5","6","4"]
... ,["4","5","6","2","3","1","8","9","7"]
... ,["7","8","9","5","6","4","2","3","1"]
... ,["2","3","1","4","5","6","9","7","8"]
... ,["5","6","4","7","8","9","3","1","2"]
... ,["8","9","7","1","2","3","6","4","5"]
... ,["3","1","2","6","4","5","7","8","9"]
... ,["6","4","5","9","7","8","1","2","3"]
... ,["9","7","8","3","1","2","4","5","6"]
... ])
True
>>> is_valid_sudoku_board([["1", "2", "3", "4", "5", "6", "7", "8", "9"]])
Traceback (most recent call last):
...
ValueError: Sudoku boards must be 9x9 squares.
>>> is_valid_sudoku_board(
... [["1"], ["2"], ["3"], ["4"], ["5"], ["6"], ["7"], ["8"], ["9"]]
... )
Traceback (most recent call last):
...
ValueError: Sudoku boards must be 9x9 squares.
"""
if len(sudoku_board) != NUM_SQUARES or (
any(len(row) != NUM_SQUARES for row in sudoku_board)
):
error_message = f"Sudoku boards must be {NUM_SQUARES}x{NUM_SQUARES} squares."
raise ValueError(error_message)
row_values: defaultdict[int, set[str]] = defaultdict(set)
col_values: defaultdict[int, set[str]] = defaultdict(set)
box_values: defaultdict[tuple[int, int], set[str]] = defaultdict(set)
for row in range(NUM_SQUARES):
for col in range(NUM_SQUARES):
value = sudoku_board[row][col]
if value == EMPTY_CELL:
continue
box = (row // 3, col // 3)
if (
value in row_values[row]
or value in col_values[col]
or value in box_values[box]
):
return False
row_values[row].add(value)
col_values[col].add(value)
box_values[box].add(value)
return True
if __name__ == "__main__":
from doctest import testmod
from timeit import timeit
testmod()
print(timeit("is_valid_sudoku_board(valid_board)", globals=globals()))
print(timeit("is_valid_sudoku_board(invalid_board)", globals=globals()))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/matrix_equalization.py | matrix/matrix_equalization.py | from sys import maxsize
def array_equalization(vector: list[int], step_size: int) -> int:
"""
This algorithm equalizes all elements of the input vector
to a common value, by making the minimal number of
"updates" under the constraint of a step size (step_size).
>>> array_equalization([1, 1, 6, 2, 4, 6, 5, 1, 7, 2, 2, 1, 7, 2, 2], 4)
4
>>> array_equalization([22, 81, 88, 71, 22, 81, 632, 81, 81, 22, 92], 2)
5
>>> array_equalization([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 5)
0
>>> array_equalization([22, 22, 22, 33, 33, 33], 2)
2
>>> array_equalization([1, 2, 3], 0)
Traceback (most recent call last):
ValueError: Step size must be positive and non-zero.
>>> array_equalization([1, 2, 3], -1)
Traceback (most recent call last):
ValueError: Step size must be positive and non-zero.
>>> array_equalization([1, 2, 3], 0.5)
Traceback (most recent call last):
ValueError: Step size must be an integer.
>>> array_equalization([1, 2, 3], maxsize)
1
"""
if step_size <= 0:
raise ValueError("Step size must be positive and non-zero.")
if not isinstance(step_size, int):
raise ValueError("Step size must be an integer.")
unique_elements = set(vector)
min_updates = maxsize
for element in unique_elements:
elem_index = 0
updates = 0
while elem_index < len(vector):
if vector[elem_index] != element:
updates += 1
elem_index += step_size
else:
elem_index += 1
min_updates = min(min_updates, updates)
return min_updates
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/matrix_class.py | matrix/matrix_class.py | # An OOP approach to representing and manipulating matrices
from __future__ import annotations
class Matrix:
"""
Matrix object generated from a 2D array where each element is an array representing
a row.
Rows can contain type int or float.
Common operations and information available.
>>> rows = [
... [1, 2, 3],
... [4, 5, 6],
... [7, 8, 9]
... ]
>>> matrix = Matrix(rows)
>>> print(matrix)
[[1. 2. 3.]
[4. 5. 6.]
[7. 8. 9.]]
Matrix rows and columns are available as 2D arrays
>>> matrix.rows
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
>>> matrix.columns()
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]
Order is returned as a tuple
>>> matrix.order
(3, 3)
Squareness and invertability are represented as bool
>>> matrix.is_square
True
>>> matrix.is_invertable()
False
Identity, Minors, Cofactors and Adjugate are returned as Matrices. Inverse can be
a Matrix or Nonetype
>>> print(matrix.identity())
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
>>> print(matrix.minors())
[[-3. -6. -3.]
[-6. -12. -6.]
[-3. -6. -3.]]
>>> print(matrix.cofactors())
[[-3. 6. -3.]
[6. -12. 6.]
[-3. 6. -3.]]
>>> # won't be apparent due to the nature of the cofactor matrix
>>> print(matrix.adjugate())
[[-3. 6. -3.]
[6. -12. 6.]
[-3. 6. -3.]]
>>> matrix.inverse()
Traceback (most recent call last):
...
TypeError: Only matrices with a non-zero determinant have an inverse
Determinant is an int, float, or Nonetype
>>> matrix.determinant()
0
Negation, scalar multiplication, addition, subtraction, multiplication and
exponentiation are available and all return a Matrix
>>> print(-matrix)
[[-1. -2. -3.]
[-4. -5. -6.]
[-7. -8. -9.]]
>>> matrix2 = matrix * 3
>>> print(matrix2)
[[3. 6. 9.]
[12. 15. 18.]
[21. 24. 27.]]
>>> print(matrix + matrix2)
[[4. 8. 12.]
[16. 20. 24.]
[28. 32. 36.]]
>>> print(matrix - matrix2)
[[-2. -4. -6.]
[-8. -10. -12.]
[-14. -16. -18.]]
>>> print(matrix ** 3)
[[468. 576. 684.]
[1062. 1305. 1548.]
[1656. 2034. 2412.]]
Matrices can also be modified
>>> matrix.add_row([10, 11, 12])
>>> print(matrix)
[[1. 2. 3.]
[4. 5. 6.]
[7. 8. 9.]
[10. 11. 12.]]
>>> matrix2.add_column([8, 16, 32])
>>> print(matrix2)
[[3. 6. 9. 8.]
[12. 15. 18. 16.]
[21. 24. 27. 32.]]
>>> print(matrix * matrix2)
[[90. 108. 126. 136.]
[198. 243. 288. 304.]
[306. 378. 450. 472.]
[414. 513. 612. 640.]]
"""
def __init__(self, rows: list[list[int]]):
error = TypeError(
"Matrices must be formed from a list of zero or more lists containing at "
"least one and the same number of values, each of which must be of type "
"int or float."
)
if len(rows) != 0:
cols = len(rows[0])
if cols == 0:
raise error
for row in rows:
if len(row) != cols:
raise error
for value in row:
if not isinstance(value, (int, float)):
raise error
self.rows = rows
else:
self.rows = []
# MATRIX INFORMATION
def columns(self) -> list[list[int]]:
return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]
@property
def num_rows(self) -> int:
return len(self.rows)
@property
def num_columns(self) -> int:
return len(self.rows[0])
@property
def order(self) -> tuple[int, int]:
return self.num_rows, self.num_columns
@property
def is_square(self) -> bool:
return self.order[0] == self.order[1]
def identity(self) -> Matrix:
values = [
[0 if column_num != row_num else 1 for column_num in range(self.num_rows)]
for row_num in range(self.num_rows)
]
return Matrix(values)
def determinant(self) -> int:
if not self.is_square:
return 0
if self.order == (0, 0):
return 1
if self.order == (1, 1):
return int(self.rows[0][0])
if self.order == (2, 2):
return int(
(self.rows[0][0] * self.rows[1][1])
- (self.rows[0][1] * self.rows[1][0])
)
else:
return sum(
self.rows[0][column] * self.cofactors().rows[0][column]
for column in range(self.num_columns)
)
def is_invertable(self) -> bool:
return bool(self.determinant())
def get_minor(self, row: int, column: int) -> int:
values = [
[
self.rows[other_row][other_column]
for other_column in range(self.num_columns)
if other_column != column
]
for other_row in range(self.num_rows)
if other_row != row
]
return Matrix(values).determinant()
def get_cofactor(self, row: int, column: int) -> int:
if (row + column) % 2 == 0:
return self.get_minor(row, column)
return -1 * self.get_minor(row, column)
def minors(self) -> Matrix:
return Matrix(
[
[self.get_minor(row, column) for column in range(self.num_columns)]
for row in range(self.num_rows)
]
)
def cofactors(self) -> Matrix:
return Matrix(
[
[
self.minors().rows[row][column]
if (row + column) % 2 == 0
else self.minors().rows[row][column] * -1
for column in range(self.minors().num_columns)
]
for row in range(self.minors().num_rows)
]
)
def adjugate(self) -> Matrix:
values = [
[self.cofactors().rows[column][row] for column in range(self.num_columns)]
for row in range(self.num_rows)
]
return Matrix(values)
def inverse(self) -> Matrix:
determinant = self.determinant()
if not determinant:
raise TypeError("Only matrices with a non-zero determinant have an inverse")
return self.adjugate() * (1 / determinant)
def __repr__(self) -> str:
return str(self.rows)
def __str__(self) -> str:
if self.num_rows == 0:
return "[]"
if self.num_rows == 1:
return "[[" + ". ".join(str(self.rows[0])) + "]]"
return (
"["
+ "\n ".join(
[
"[" + ". ".join([str(value) for value in row]) + ".]"
for row in self.rows
]
)
+ "]"
)
# MATRIX MANIPULATION
def add_row(self, row: list[int], position: int | None = None) -> None:
type_error = TypeError("Row must be a list containing all ints and/or floats")
if not isinstance(row, list):
raise type_error
for value in row:
if not isinstance(value, (int, float)):
raise type_error
if len(row) != self.num_columns:
raise ValueError(
"Row must be equal in length to the other rows in the matrix"
)
if position is None:
self.rows.append(row)
else:
self.rows = [*self.rows[0:position], row, *self.rows[position:]]
def add_column(self, column: list[int], position: int | None = None) -> None:
type_error = TypeError(
"Column must be a list containing all ints and/or floats"
)
if not isinstance(column, list):
raise type_error
for value in column:
if not isinstance(value, (int, float)):
raise type_error
if len(column) != self.num_rows:
raise ValueError(
"Column must be equal in length to the other columns in the matrix"
)
if position is None:
self.rows = [self.rows[i] + [column[i]] for i in range(self.num_rows)]
else:
self.rows = [
[*self.rows[i][0:position], column[i], *self.rows[i][position:]]
for i in range(self.num_rows)
]
# MATRIX OPERATIONS
def __eq__(self, other: object) -> bool:
if not isinstance(other, Matrix):
return NotImplemented
return self.rows == other.rows
def __ne__(self, other: object) -> bool:
return not self == other
def __neg__(self) -> Matrix:
return self * -1
def __add__(self, other: Matrix) -> Matrix:
if self.order != other.order:
raise ValueError("Addition requires matrices of the same order")
return Matrix(
[
[self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns)]
for i in range(self.num_rows)
]
)
def __sub__(self, other: Matrix) -> Matrix:
if self.order != other.order:
raise ValueError("Subtraction requires matrices of the same order")
return Matrix(
[
[self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns)]
for i in range(self.num_rows)
]
)
def __mul__(self, other: Matrix | float) -> Matrix:
if isinstance(other, (int, float)):
return Matrix(
[[int(element * other) for element in row] for row in self.rows]
)
elif isinstance(other, Matrix):
if self.num_columns != other.num_rows:
raise ValueError(
"The number of columns in the first matrix must "
"be equal to the number of rows in the second"
)
return Matrix(
[
[Matrix.dot_product(row, column) for column in other.columns()]
for row in self.rows
]
)
else:
raise TypeError(
"A Matrix can only be multiplied by an int, float, or another matrix"
)
def __pow__(self, other: int) -> Matrix:
if not isinstance(other, int):
raise TypeError("A Matrix can only be raised to the power of an int")
if not self.is_square:
raise ValueError("Only square matrices can be raised to a power")
if other == 0:
return self.identity()
if other < 0:
if self.is_invertable():
return self.inverse() ** (-other)
raise ValueError(
"Only invertable matrices can be raised to a negative power"
)
result = self
for _ in range(other - 1):
result *= self
return result
@classmethod
def dot_product(cls, row: list[int], column: list[int]) -> int:
return sum(row[i] * column[i] for i in range(len(row)))
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/__init__.py | matrix/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/count_negative_numbers_in_sorted_matrix.py | matrix/count_negative_numbers_in_sorted_matrix.py | """
Given an matrix of numbers in which all rows and all columns are sorted in decreasing
order, return the number of negative numbers in grid.
Reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
"""
def generate_large_matrix() -> list[list[int]]:
"""
>>> generate_large_matrix() # doctest: +ELLIPSIS
[[1000, ..., -999], [999, ..., -1001], ..., [2, ..., -1998]]
"""
return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
grid = generate_large_matrix()
test_grids = (
[[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
[[3, 2], [1, 0]],
[[7, 7, 6]],
[[7, 7, 6], [-1, -2, -3]],
grid,
)
def validate_grid(grid: list[list[int]]) -> None:
"""
Validate that the rows and columns of the grid is sorted in decreasing order.
>>> for grid in test_grids:
... validate_grid(grid)
"""
assert all(row == sorted(row, reverse=True) for row in grid)
assert all(list(col) == sorted(col, reverse=True) for col in zip(*grid))
def find_negative_index(array: list[int]) -> int:
"""
Find the smallest negative index
>>> find_negative_index([0,0,0,0])
4
>>> find_negative_index([4,3,2,-1])
3
>>> find_negative_index([1,0,-1,-10])
2
>>> find_negative_index([0,0,0,-1])
3
>>> find_negative_index([11,8,7,-3,-5,-9])
3
>>> find_negative_index([-1,-1,-2,-3])
0
>>> find_negative_index([5,1,0])
3
>>> find_negative_index([-5,-5,-5])
0
>>> find_negative_index([0])
1
>>> find_negative_index([])
0
"""
left = 0
right = len(array) - 1
# Edge cases such as no values or all numbers are negative.
if not array or array[0] < 0:
return 0
while right + 1 > left:
mid = (left + right) // 2
num = array[mid]
# Num must be negative and the index must be greater than or equal to 0.
if num < 0 and array[mid - 1] >= 0:
return mid
if num >= 0:
left = mid + 1
else:
right = mid - 1
# No negative numbers so return the last index of the array + 1 which is the length.
return len(array)
def count_negatives_binary_search(grid: list[list[int]]) -> int:
"""
An O(m logn) solution that uses binary search in order to find the boundary between
positive and negative numbers
>>> [count_negatives_binary_search(grid) for grid in test_grids]
[8, 0, 0, 3, 1498500]
"""
total = 0
bound = len(grid[0])
for i in range(len(grid)):
bound = find_negative_index(grid[i][:bound])
total += bound
return (len(grid) * len(grid[0])) - total
def count_negatives_brute_force(grid: list[list[int]]) -> int:
"""
This solution is O(n^2) because it iterates through every column and row.
>>> [count_negatives_brute_force(grid) for grid in test_grids]
[8, 0, 0, 3, 1498500]
"""
return len([number for row in grid for number in row if number < 0])
def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
"""
Similar to the brute force solution above but uses break in order to reduce the
number of iterations.
>>> [count_negatives_brute_force_with_break(grid) for grid in test_grids]
[8, 0, 0, 3, 1498500]
"""
total = 0
for row in grid:
for i, number in enumerate(row):
if number < 0:
total += len(row) - i
break
return total
def benchmark() -> None:
"""Benchmark our functions next to each other"""
from timeit import timeit
print("Running benchmarks")
setup = (
"from __main__ import count_negatives_binary_search, "
"count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
)
for func in (
"count_negatives_binary_search", # took 0.7727 seconds
"count_negatives_brute_force_with_break", # took 4.6505 seconds
"count_negatives_brute_force", # took 12.8160 seconds
):
time = timeit(f"{func}(grid=grid)", setup=setup, number=500)
print(f"{func}() took {time:0.4f} seconds")
if __name__ == "__main__":
import doctest
doctest.testmod()
benchmark()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/nth_fibonacci_using_matrix_exponentiation.py | matrix/nth_fibonacci_using_matrix_exponentiation.py | """
Implementation of finding nth fibonacci number using matrix exponentiation.
Time Complexity is about O(log(n)*8), where 8 is the complexity of matrix
multiplication of size 2 by 2.
And on the other hand complexity of bruteforce solution is O(n).
As we know
f[n] = f[n-1] + f[n-1]
Converting to matrix,
[f(n),f(n-1)] = [[1,1],[1,0]] * [f(n-1),f(n-2)]
-> [f(n),f(n-1)] = [[1,1],[1,0]]^2 * [f(n-2),f(n-3)]
...
...
-> [f(n),f(n-1)] = [[1,1],[1,0]]^(n-1) * [f(1),f(0)]
So we just need the n times multiplication of the matrix [1,1],[1,0]].
We can decrease the n times multiplication by following the divide and conquer approach.
"""
def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
matrix_c = []
n = len(matrix_a)
for i in range(n):
list_1 = []
for j in range(n):
val = 0
for k in range(n):
val = val + matrix_a[i][k] * matrix_b[k][j]
list_1.append(val)
matrix_c.append(list_1)
return matrix_c
def identity(n: int) -> list[list[int]]:
return [[int(row == column) for column in range(n)] for row in range(n)]
def nth_fibonacci_matrix(n: int) -> int:
"""
>>> nth_fibonacci_matrix(100)
354224848179261915075
>>> nth_fibonacci_matrix(-100)
-100
"""
if n <= 1:
return n
res_matrix = identity(2)
fibonacci_matrix = [[1, 1], [1, 0]]
n = n - 1
while n > 0:
if n % 2 == 1:
res_matrix = multiply(res_matrix, fibonacci_matrix)
fibonacci_matrix = multiply(fibonacci_matrix, fibonacci_matrix)
n = int(n / 2)
return res_matrix[0][0]
def nth_fibonacci_bruteforce(n: int) -> int:
"""
>>> nth_fibonacci_bruteforce(100)
354224848179261915075
>>> nth_fibonacci_bruteforce(-100)
-100
"""
if n <= 1:
return n
fib0 = 0
fib1 = 1
for _ in range(2, n + 1):
fib0, fib1 = fib1, fib0 + fib1
return fib1
def main() -> None:
for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
n = int("".join(c for c in ordinal if c in "0123456789")) # 1000th --> 1000
print(
f"{ordinal} fibonacci number using matrix exponentiation is "
f"{nth_fibonacci_matrix(n)} and using bruteforce is "
f"{nth_fibonacci_bruteforce(n)}\n"
)
# from timeit import timeit
# print(timeit("nth_fibonacci_matrix(1000000)",
# "from main import nth_fibonacci_matrix", number=5))
# print(timeit("nth_fibonacci_bruteforce(1000000)",
# "from main import nth_fibonacci_bruteforce", number=5))
# 2.3342058970001744
# 57.256506615000035
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/matrix_based_game.py | matrix/matrix_based_game.py | """
Matrix-Based Game Script
=========================
This script implements a matrix-based game where players interact with a grid of
elements. The primary goals are to:
- Identify connected elements of the same type from a selected position.
- Remove those elements, adjust the matrix by simulating gravity, and reorganize empty
columns.
- Calculate and display the score based on the number of elements removed in each move.
Functions:
-----------
1. `find_repeat`: Finds all connected elements of the same type.
2. `increment_score`: Calculates the score for a given move.
3. `move_x`: Simulates gravity in a column.
4. `move_y`: Reorganizes the matrix by shifting columns leftward when a column becomes
empty.
5. `play`: Executes a single move, updating the matrix and returning the score.
Input Format:
--------------
1. Matrix size (`lines`): Integer specifying the size of the matrix (N x N).
2. Matrix content (`matrix`): Rows of the matrix, each consisting of characters.
3. Number of moves (`movs`): Integer indicating the number of moves.
4. List of moves (`movements`): A comma-separated string of coordinates for each move.
(0,0) position starts from first left column to last right, and below row to up row
Example Input:
---------------
4
RRBG
RBBG
YYGG
XYGG
2
0 1,1 1
Example (0,0) = X
Output:
--------
The script outputs the total score after processing all moves.
Usage:
-------
Run the script and provide the required inputs as prompted.
"""
def validate_matrix_size(size: int) -> None:
"""
>>> validate_matrix_size(-1)
Traceback (most recent call last):
...
ValueError: Matrix size must be a positive integer.
"""
if not isinstance(size, int) or size <= 0:
raise ValueError("Matrix size must be a positive integer.")
def validate_matrix_content(matrix: list[str], size: int) -> None:
"""
Validates that the number of elements in the matrix matches the given size.
>>> validate_matrix_content(['aaaa', 'aaaa', 'aaaa', 'aaaa'], 3)
Traceback (most recent call last):
...
ValueError: The matrix dont match with size.
>>> validate_matrix_content(['aa%', 'aaa', 'aaa'], 3)
Traceback (most recent call last):
...
ValueError: Matrix rows can only contain letters and numbers.
>>> validate_matrix_content(['aaa', 'aaa', 'aaaa'], 3)
Traceback (most recent call last):
...
ValueError: Each row in the matrix must have exactly 3 characters.
"""
print(matrix)
if len(matrix) != size:
raise ValueError("The matrix dont match with size.")
for row in matrix:
if len(row) != size:
msg = f"Each row in the matrix must have exactly {size} characters."
raise ValueError(msg)
if not all(char.isalnum() for char in row):
raise ValueError("Matrix rows can only contain letters and numbers.")
def validate_moves(moves: list[tuple[int, int]], size: int) -> None:
"""
>>> validate_moves([(1, 2), (-1, 0)], 3)
Traceback (most recent call last):
...
ValueError: Move is out of bounds for a matrix.
"""
for move in moves:
x, y = move
if not (0 <= x < size and 0 <= y < size):
raise ValueError("Move is out of bounds for a matrix.")
def parse_moves(input_str: str) -> list[tuple[int, int]]:
"""
>>> parse_moves("0 1, 1 1")
[(0, 1), (1, 1)]
>>> parse_moves("0 1, 1 1, 2")
Traceback (most recent call last):
...
ValueError: Each move must have exactly two numbers.
>>> parse_moves("0 1, 1 1, 2 4 5 6")
Traceback (most recent call last):
...
ValueError: Each move must have exactly two numbers.
"""
moves = []
for pair in input_str.split(","):
parts = pair.strip().split()
if len(parts) != 2:
raise ValueError("Each move must have exactly two numbers.")
x, y = map(int, parts)
moves.append((x, y))
return moves
def find_repeat(
matrix_g: list[list[str]], row: int, column: int, size: int
) -> set[tuple[int, int]]:
"""
Finds all connected elements of the same type from a given position.
>>> find_repeat([['A', 'B', 'A'], ['A', 'B', 'A'], ['A', 'A', 'A']], 0, 0, 3)
{(1, 2), (2, 1), (0, 0), (2, 0), (0, 2), (2, 2), (1, 0)}
>>> find_repeat([['-', '-', '-'], ['-', '-', '-'], ['-', '-', '-']], 1, 1, 3)
set()
"""
column = size - 1 - column
visited = set()
repeated = set()
if (color := matrix_g[column][row]) != "-":
def dfs(row_n: int, column_n: int) -> None:
if row_n < 0 or row_n >= size or column_n < 0 or column_n >= size:
return
if (row_n, column_n) in visited:
return
visited.add((row_n, column_n))
if matrix_g[row_n][column_n] == color:
repeated.add((row_n, column_n))
dfs(row_n - 1, column_n)
dfs(row_n + 1, column_n)
dfs(row_n, column_n - 1)
dfs(row_n, column_n + 1)
dfs(column, row)
return repeated
def increment_score(count: int) -> int:
"""
Calculates the score for a move based on the number of elements removed.
>>> increment_score(3)
6
>>> increment_score(0)
0
"""
return int(count * (count + 1) / 2)
def move_x(matrix_g: list[list[str]], column: int, size: int) -> list[list[str]]:
"""
Simulates gravity in a specific column.
>>> move_x([['-', 'A'], ['-', '-'], ['-', 'C']], 1, 2)
[['-', '-'], ['-', 'A'], ['-', 'C']]
"""
new_list = []
for row in range(size):
if matrix_g[row][column] != "-":
new_list.append(matrix_g[row][column])
else:
new_list.insert(0, matrix_g[row][column])
for row in range(size):
matrix_g[row][column] = new_list[row]
return matrix_g
def move_y(matrix_g: list[list[str]], size: int) -> list[list[str]]:
"""
Shifts all columns leftward when an entire column becomes empty.
>>> move_y([['-', 'A'], ['-', '-'], ['-', 'C']], 2)
[['A', '-'], ['-', '-'], ['-', 'C']]
"""
empty_columns = []
for column in range(size - 1, -1, -1):
if all(matrix_g[row][column] == "-" for row in range(size)):
empty_columns.append(column)
for column in empty_columns:
for col in range(column + 1, size):
for row in range(size):
matrix_g[row][col - 1] = matrix_g[row][col]
for row in range(size):
matrix_g[row][-1] = "-"
return matrix_g
def play(
matrix_g: list[list[str]], pos_x: int, pos_y: int, size: int
) -> tuple[list[list[str]], int]:
"""
Processes a single move, updating the matrix and calculating the score.
>>> play([['R', 'G'], ['R', 'G']], 0, 0, 2)
([['G', '-'], ['G', '-']], 3)
"""
same_colors = find_repeat(matrix_g, pos_x, pos_y, size)
if len(same_colors) != 0:
for pos in same_colors:
matrix_g[pos[0]][pos[1]] = "-"
for column in range(size):
matrix_g = move_x(matrix_g, column, size)
matrix_g = move_y(matrix_g, size)
return (matrix_g, increment_score(len(same_colors)))
def process_game(size: int, matrix: list[str], moves: list[tuple[int, int]]) -> int:
"""Processes the game logic for the given matrix and moves.
Args:
size (int): Size of the game board.
matrix (List[str]): Initial game matrix.
moves (List[Tuple[int, int]]): List of moves as (x, y) coordinates.
Returns:
int: The total score obtained.
>>> process_game(3, ['aaa', 'bbb', 'ccc'], [(0, 0)])
6
"""
game_matrix = [list(row) for row in matrix]
total_score = 0
for move in moves:
pos_x, pos_y = move
game_matrix, score = play(game_matrix, pos_x, pos_y, size)
total_score += score
return total_score
if __name__ == "__main__":
import doctest
doctest.testmod(verbose=True)
try:
size = int(input("Enter the size of the matrix: "))
validate_matrix_size(size)
print(f"Enter the {size} rows of the matrix:")
matrix = [input(f"Row {i + 1}: ") for i in range(size)]
validate_matrix_content(matrix, size)
moves_input = input("Enter the moves (e.g., '0 0, 1 1'): ")
moves = parse_moves(moves_input)
validate_moves(moves, size)
score = process_game(size, matrix, moves)
print(f"Total score: {score}")
except ValueError as e:
print(f"{e}")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/binary_search_matrix.py | matrix/binary_search_matrix.py | def binary_search(array: list, lower_bound: int, upper_bound: int, value: int) -> int:
"""
This function carries out Binary search on a 1d array and
return -1 if it do not exist
array: A 1d sorted array
value : the value meant to be searched
>>> matrix = [1, 4, 7, 11, 15]
>>> binary_search(matrix, 0, len(matrix) - 1, 1)
0
>>> binary_search(matrix, 0, len(matrix) - 1, 23)
-1
"""
r = int((lower_bound + upper_bound) // 2)
if array[r] == value:
return r
if lower_bound >= upper_bound:
return -1
if array[r] < value:
return binary_search(array, r + 1, upper_bound, value)
else:
return binary_search(array, lower_bound, r - 1, value)
def mat_bin_search(value: int, matrix: list) -> list:
"""
This function loops over a 2d matrix and calls binarySearch on
the selected 1d array and returns [-1, -1] is it do not exist
value : value meant to be searched
matrix = a sorted 2d matrix
>>> matrix = [[1, 4, 7, 11, 15],
... [2, 5, 8, 12, 19],
... [3, 6, 9, 16, 22],
... [10, 13, 14, 17, 24],
... [18, 21, 23, 26, 30]]
>>> target = 1
>>> mat_bin_search(target, matrix)
[0, 0]
>>> target = 34
>>> mat_bin_search(target, matrix)
[-1, -1]
"""
index = 0
if matrix[index][0] == value:
return [index, 0]
while index < len(matrix) and matrix[index][0] < value:
r = binary_search(matrix[index], 0, len(matrix[index]) - 1, value)
if r != -1:
return [index, r]
index += 1
return [-1, -1]
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/inverse_of_matrix.py | matrix/inverse_of_matrix.py | from __future__ import annotations
from decimal import Decimal
from numpy import array
def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
"""
A matrix multiplied with its inverse gives the identity matrix.
This function finds the inverse of a 2x2 and 3x3 matrix.
If the determinant of a matrix is 0, its inverse does not exist.
Sources for fixing inaccurate float arithmetic:
https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python
https://docs.python.org/3/library/decimal.html
Doctests for 2x2
>>> inverse_of_matrix([[2, 5], [2, 0]])
[[0.0, 0.5], [0.2, -0.2]]
>>> inverse_of_matrix([[2.5, 5], [1, 2]])
Traceback (most recent call last):
...
ValueError: This matrix has no inverse.
>>> inverse_of_matrix([[12, -16], [-9, 0]])
[[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]]
>>> inverse_of_matrix([[12, 3], [16, 8]])
[[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]]
>>> inverse_of_matrix([[10, 5], [3, 2.5]])
[[0.25, -0.5], [-0.3, 1.0]]
Doctests for 3x3
>>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]])
[[2.0, 5.0, -4.0], [1.0, 1.0, -1.0], [-5.0, -12.0, 10.0]]
>>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]])
Traceback (most recent call last):
...
ValueError: This matrix has no inverse.
>>> inverse_of_matrix([[],[]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.
>>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.
>>> inverse_of_matrix([[1, 2, 1], [0,3, 4]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.
>>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]])
Traceback (most recent call last):
...
ValueError: This matrix has no inverse.
>>> inverse_of_matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
"""
d = Decimal
# Check if the provided matrix has 2 rows and 2 columns
# since this implementation only works for 2x2 matrices
if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
# Calculate the determinant of the matrix
determinant = float(
d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1])
)
if determinant == 0:
raise ValueError("This matrix has no inverse.")
# Creates a copy of the matrix with swapped positions of the elements
swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
# Calculate the inverse of the matrix
return [
[(float(d(n)) / determinant) or 0.0 for n in row] for row in swapped_matrix
]
elif (
len(matrix) == 3
and len(matrix[0]) == 3
and len(matrix[1]) == 3
and len(matrix[2]) == 3
):
# Calculate the determinant of the matrix using Sarrus rule
determinant = float(
(
(d(matrix[0][0]) * d(matrix[1][1]) * d(matrix[2][2]))
+ (d(matrix[0][1]) * d(matrix[1][2]) * d(matrix[2][0]))
+ (d(matrix[0][2]) * d(matrix[1][0]) * d(matrix[2][1]))
)
- (
(d(matrix[0][2]) * d(matrix[1][1]) * d(matrix[2][0]))
+ (d(matrix[0][1]) * d(matrix[1][0]) * d(matrix[2][2]))
+ (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
)
)
if determinant == 0:
raise ValueError("This matrix has no inverse.")
# Creating cofactor matrix
cofactor_matrix = [
[d(0.0), d(0.0), d(0.0)],
[d(0.0), d(0.0), d(0.0)],
[d(0.0), d(0.0), d(0.0)],
]
cofactor_matrix[0][0] = (d(matrix[1][1]) * d(matrix[2][2])) - (
d(matrix[1][2]) * d(matrix[2][1])
)
cofactor_matrix[0][1] = -(
(d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
)
cofactor_matrix[0][2] = (d(matrix[1][0]) * d(matrix[2][1])) - (
d(matrix[1][1]) * d(matrix[2][0])
)
cofactor_matrix[1][0] = -(
(d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
)
cofactor_matrix[1][1] = (d(matrix[0][0]) * d(matrix[2][2])) - (
d(matrix[0][2]) * d(matrix[2][0])
)
cofactor_matrix[1][2] = -(
(d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
)
cofactor_matrix[2][0] = (d(matrix[0][1]) * d(matrix[1][2])) - (
d(matrix[0][2]) * d(matrix[1][1])
)
cofactor_matrix[2][1] = -(
(d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
)
cofactor_matrix[2][2] = (d(matrix[0][0]) * d(matrix[1][1])) - (
d(matrix[0][1]) * d(matrix[1][0])
)
# Transpose the cofactor matrix (Adjoint matrix)
adjoint_matrix = array(cofactor_matrix)
for i in range(3):
for j in range(3):
adjoint_matrix[i][j] = cofactor_matrix[j][i]
# Inverse of the matrix using the formula (1/determinant) * adjoint matrix
inverse_matrix = array(cofactor_matrix)
for i in range(3):
for j in range(3):
inverse_matrix[i][j] /= d(determinant)
# Calculate the inverse of the matrix
return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix]
raise ValueError("Please provide a matrix of size 2x2 or 3x3.")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/count_islands_in_matrix.py | matrix/count_islands_in_matrix.py | # An island in matrix is a group of linked areas, all having the same value.
# This code counts number of islands in a given matrix, with including diagonal
# connections.
class Matrix: # Public class to implement a graph
def __init__(self, row: int, col: int, graph: list[list[bool]]) -> None:
self.ROW = row
self.COL = col
self.graph = graph
def is_safe(self, i: int, j: int, visited: list[list[bool]]) -> bool:
return (
0 <= i < self.ROW
and 0 <= j < self.COL
and not visited[i][j]
and self.graph[i][j]
)
def diffs(self, i: int, j: int, visited: list[list[bool]]) -> None:
# Checking all 8 elements surrounding nth element
row_nbr = [-1, -1, -1, 0, 0, 1, 1, 1] # Coordinate order
col_nbr = [-1, 0, 1, -1, 1, -1, 0, 1]
visited[i][j] = True # Make those cells visited
for k in range(8):
if self.is_safe(i + row_nbr[k], j + col_nbr[k], visited):
self.diffs(i + row_nbr[k], j + col_nbr[k], visited)
def count_islands(self) -> int: # And finally, count all islands.
visited = [[False for j in range(self.COL)] for i in range(self.ROW)]
count = 0
for i in range(self.ROW):
for j in range(self.COL):
if visited[i][j] is False and self.graph[i][j] == 1:
self.diffs(i, j, visited)
count += 1
return count
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/tests/__init__.py | matrix/tests/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/matrix/tests/test_matrix_operation.py | matrix/tests/test_matrix_operation.py | """
Testing here assumes that numpy and linalg is ALWAYS correct!!!!
If running from PyCharm you can place the following line in "Additional Arguments" for
the pytest run configuration
-vv -m mat_ops -p no:cacheprovider
"""
import logging
# standard libraries
import sys
import numpy as np
import pytest
# Custom/local libraries
from matrix import matrix_operation as matop
mat_a = [[12, 10], [3, 9]]
mat_b = [[3, 4], [7, 4]]
mat_c = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
mat_d = [[3, 0, -2], [2, 0, 2], [0, 1, 1]]
mat_e = [[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]]
mat_f = [1]
mat_h = [2]
logger = logging.getLogger()
logger.level = logging.DEBUG
stream_handler = logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)
@pytest.mark.mat_ops
@pytest.mark.parametrize(
("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]
)
def test_addition(mat1, mat2):
if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2):
logger.info(f"\n\t{test_addition.__name__} returned integer")
with pytest.raises(TypeError):
matop.add(mat1, mat2)
elif (np.array(mat1)).shape == (np.array(mat2)).shape:
logger.info(f"\n\t{test_addition.__name__} with same matrix dims")
act = (np.array(mat1) + np.array(mat2)).tolist()
theo = matop.add(mat1, mat2)
assert theo == act
else:
logger.info(f"\n\t{test_addition.__name__} with different matrix dims")
with pytest.raises(ValueError):
matop.add(mat1, mat2)
@pytest.mark.mat_ops
@pytest.mark.parametrize(
("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]
)
def test_subtraction(mat1, mat2):
if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2):
logger.info(f"\n\t{test_subtraction.__name__} returned integer")
with pytest.raises(TypeError):
matop.subtract(mat1, mat2)
elif (np.array(mat1)).shape == (np.array(mat2)).shape:
logger.info(f"\n\t{test_subtraction.__name__} with same matrix dims")
act = (np.array(mat1) - np.array(mat2)).tolist()
theo = matop.subtract(mat1, mat2)
assert theo == act
else:
logger.info(f"\n\t{test_subtraction.__name__} with different matrix dims")
with pytest.raises(ValueError):
assert matop.subtract(mat1, mat2)
@pytest.mark.mat_ops
@pytest.mark.parametrize(
("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]
)
def test_multiplication(mat1, mat2):
if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2):
logger.info(f"\n\t{test_multiplication.__name__} returned integer")
with pytest.raises(TypeError):
matop.add(mat1, mat2)
elif (np.array(mat1)).shape == (np.array(mat2)).shape:
logger.info(f"\n\t{test_multiplication.__name__} meets dim requirements")
act = (np.matmul(mat1, mat2)).tolist()
theo = matop.multiply(mat1, mat2)
assert theo == act
else:
logger.info(
f"\n\t{test_multiplication.__name__} does not meet dim requirements"
)
with pytest.raises(ValueError):
assert matop.subtract(mat1, mat2)
@pytest.mark.mat_ops
def test_scalar_multiply():
act = (3.5 * np.array(mat_a)).tolist()
theo = matop.scalar_multiply(mat_a, 3.5)
assert theo == act
@pytest.mark.mat_ops
def test_identity():
act = (np.identity(5)).tolist()
theo = matop.identity(5)
assert theo == act
@pytest.mark.mat_ops
@pytest.mark.parametrize("mat", [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f])
def test_transpose(mat):
if (np.array(mat)).shape < (2, 2):
logger.info(f"\n\t{test_transpose.__name__} returned integer")
with pytest.raises(TypeError):
matop.transpose(mat)
else:
act = (np.transpose(mat)).tolist()
theo = matop.transpose(mat, return_map=False)
assert theo == act
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/graphics/digital_differential_analyzer_line.py | graphics/digital_differential_analyzer_line.py | import matplotlib.pyplot as plt
def digital_differential_analyzer_line(
p1: tuple[int, int], p2: tuple[int, int]
) -> list[tuple[int, int]]:
"""
Draws a line between two points using the DDA algorithm.
Args:
- p1: Coordinates of the starting point.
- p2: Coordinates of the ending point.
Returns:
- List of coordinate points that form the line.
>>> digital_differential_analyzer_line((1, 1), (4, 4))
[(2, 2), (3, 3), (4, 4)]
"""
x1, y1 = p1
x2, y2 = p2
dx = x2 - x1
dy = y2 - y1
steps = max(abs(dx), abs(dy))
x_increment = dx / float(steps)
y_increment = dy / float(steps)
coordinates = []
x: float = x1
y: float = y1
for _ in range(steps):
x += x_increment
y += y_increment
coordinates.append((round(x), round(y)))
return coordinates
if __name__ == "__main__":
import doctest
doctest.testmod()
x1 = int(input("Enter the x-coordinate of the starting point: "))
y1 = int(input("Enter the y-coordinate of the starting point: "))
x2 = int(input("Enter the x-coordinate of the ending point: "))
y2 = int(input("Enter the y-coordinate of the ending point: "))
coordinates = digital_differential_analyzer_line((x1, y1), (x2, y2))
x_points, y_points = zip(*coordinates)
plt.plot(x_points, y_points, marker="o")
plt.title("Digital Differential Analyzer Line Drawing Algorithm")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.grid()
plt.show()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/graphics/butterfly_pattern.py | graphics/butterfly_pattern.py | def butterfly_pattern(n: int) -> str:
"""
Creates a butterfly pattern of size n and returns it as a string.
>>> print(butterfly_pattern(3))
* *
** **
*****
** **
* *
>>> print(butterfly_pattern(5))
* *
** **
*** ***
**** ****
*********
**** ****
*** ***
** **
* *
"""
result = []
# Upper part
for i in range(1, n):
left_stars = "*" * i
spaces = " " * (2 * (n - i) - 1)
right_stars = "*" * i
result.append(left_stars + spaces + right_stars)
# Middle part
result.append("*" * (2 * n - 1))
# Lower part
for i in range(n - 1, 0, -1):
left_stars = "*" * i
spaces = " " * (2 * (n - i) - 1)
right_stars = "*" * i
result.append(left_stars + spaces + right_stars)
return "\n".join(result)
if __name__ == "__main__":
n = int(input("Enter the size of the butterfly pattern: "))
print(butterfly_pattern(n))
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/graphics/__init__.py | graphics/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/graphics/vector3_for_2d_rendering.py | graphics/vector3_for_2d_rendering.py | """
render 3d points for 2d surfaces.
"""
from __future__ import annotations
import math
__version__ = "2020.9.26"
__author__ = "xcodz-dot, cclaus, dhruvmanila"
def convert_to_2d(
x: float, y: float, z: float, scale: float, distance: float
) -> tuple[float, float]:
"""
Converts 3d point to a 2d drawable point
>>> convert_to_2d(1.0, 2.0, 3.0, 10.0, 10.0)
(7.6923076923076925, 15.384615384615385)
>>> convert_to_2d(1, 2, 3, 10, 10)
(7.6923076923076925, 15.384615384615385)
>>> convert_to_2d("1", 2, 3, 10, 10) # '1' is str
Traceback (most recent call last):
...
TypeError: Input values must either be float or int: ['1', 2, 3, 10, 10]
"""
if not all(isinstance(val, (float, int)) for val in locals().values()):
msg = f"Input values must either be float or int: {list(locals().values())}"
raise TypeError(msg)
projected_x = ((x * distance) / (z + distance)) * scale
projected_y = ((y * distance) / (z + distance)) * scale
return projected_x, projected_y
def rotate(
x: float, y: float, z: float, axis: str, angle: float
) -> tuple[float, float, float]:
"""
rotate a point around a certain axis with a certain angle
angle can be any integer between 1, 360 and axis can be any one of
'x', 'y', 'z'
>>> rotate(1.0, 2.0, 3.0, 'y', 90.0)
(3.130524675073759, 2.0, 0.4470070007889556)
>>> rotate(1, 2, 3, "z", 180)
(0.999736015495891, -2.0001319704760485, 3)
>>> rotate('1', 2, 3, "z", 90.0) # '1' is str
Traceback (most recent call last):
...
TypeError: Input values except axis must either be float or int: ['1', 2, 3, 90.0]
>>> rotate(1, 2, 3, "n", 90) # 'n' is not a valid axis
Traceback (most recent call last):
...
ValueError: not a valid axis, choose one of 'x', 'y', 'z'
>>> rotate(1, 2, 3, "x", -90)
(1, -2.5049096187183877, -2.5933429780983657)
>>> rotate(1, 2, 3, "x", 450) # 450 wrap around to 90
(1, 3.5776792428178217, -0.44744970165427644)
"""
if not isinstance(axis, str):
raise TypeError("Axis must be a str")
input_variables = locals()
del input_variables["axis"]
if not all(isinstance(val, (float, int)) for val in input_variables.values()):
msg = (
"Input values except axis must either be float or int: "
f"{list(input_variables.values())}"
)
raise TypeError(msg)
angle = (angle % 360) / 450 * 180 / math.pi
if axis == "z":
new_x = x * math.cos(angle) - y * math.sin(angle)
new_y = y * math.cos(angle) + x * math.sin(angle)
new_z = z
elif axis == "x":
new_y = y * math.cos(angle) - z * math.sin(angle)
new_z = z * math.cos(angle) + y * math.sin(angle)
new_x = x
elif axis == "y":
new_x = x * math.cos(angle) - z * math.sin(angle)
new_z = z * math.cos(angle) + x * math.sin(angle)
new_y = y
else:
raise ValueError("not a valid axis, choose one of 'x', 'y', 'z'")
return new_x, new_y, new_z
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{convert_to_2d(1.0, 2.0, 3.0, 10.0, 10.0) = }")
print(f"{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/graphics/bezier_curve.py | graphics/bezier_curve.py | # https://en.wikipedia.org/wiki/B%C3%A9zier_curve
# https://www.tutorialspoint.com/computer_graphics/computer_graphics_curves.htm
from __future__ import annotations
from scipy.special import comb
class BezierCurve:
"""
Bezier curve is a weighted sum of a set of control points.
Generate Bezier curves from a given set of control points.
This implementation works only for 2d coordinates in the xy plane.
"""
def __init__(self, list_of_points: list[tuple[float, float]]):
"""
list_of_points: Control points in the xy plane on which to interpolate. These
points control the behavior (shape) of the Bezier curve.
"""
self.list_of_points = list_of_points
# Degree determines the flexibility of the curve.
# Degree = 1 will produce a straight line.
self.degree = len(list_of_points) - 1
def basis_function(self, t: float) -> list[float]:
"""
The basis function determines the weight of each control point at time t.
t: time value between 0 and 1 inclusive at which to evaluate the basis of
the curve.
returns the x, y values of basis function at time t
>>> curve = BezierCurve([(1,1), (1,2)])
>>> [float(x) for x in curve.basis_function(0)]
[1.0, 0.0]
>>> [float(x) for x in curve.basis_function(1)]
[0.0, 1.0]
"""
assert 0 <= t <= 1, "Time t must be between 0 and 1."
output_values: list[float] = []
for i in range(len(self.list_of_points)):
# basis function for each i
output_values.append(
comb(self.degree, i) * ((1 - t) ** (self.degree - i)) * (t**i)
)
# the basis must sum up to 1 for it to produce a valid Bezier curve.
assert round(sum(output_values), 5) == 1
return output_values
def bezier_curve_function(self, t: float) -> tuple[float, float]:
"""
The function to produce the values of the Bezier curve at time t.
t: the value of time t at which to evaluate the Bezier function
Returns the x, y coordinates of the Bezier curve at time t.
The first point in the curve is when t = 0.
The last point in the curve is when t = 1.
>>> curve = BezierCurve([(1,1), (1,2)])
>>> tuple(float(x) for x in curve.bezier_curve_function(0))
(1.0, 1.0)
>>> tuple(float(x) for x in curve.bezier_curve_function(1))
(1.0, 2.0)
"""
assert 0 <= t <= 1, "Time t must be between 0 and 1."
basis_function = self.basis_function(t)
x = 0.0
y = 0.0
for i in range(len(self.list_of_points)):
# For all points, sum up the product of i-th basis function and i-th point.
x += basis_function[i] * self.list_of_points[i][0]
y += basis_function[i] * self.list_of_points[i][1]
return (x, y)
def plot_curve(self, step_size: float = 0.01):
"""
Plots the Bezier curve using matplotlib plotting capabilities.
step_size: defines the step(s) at which to evaluate the Bezier curve.
The smaller the step size, the finer the curve produced.
"""
from matplotlib import pyplot as plt
to_plot_x: list[float] = [] # x coordinates of points to plot
to_plot_y: list[float] = [] # y coordinates of points to plot
t = 0.0
while t <= 1:
value = self.bezier_curve_function(t)
to_plot_x.append(value[0])
to_plot_y.append(value[1])
t += step_size
x = [i[0] for i in self.list_of_points]
y = [i[1] for i in self.list_of_points]
plt.plot(
to_plot_x,
to_plot_y,
color="blue",
label="Curve of Degree " + str(self.degree),
)
plt.scatter(x, y, color="red", label="Control Points")
plt.legend()
plt.show()
if __name__ == "__main__":
import doctest
doctest.testmod()
BezierCurve([(1, 2), (3, 5)]).plot_curve() # degree 1
BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve() # degree 2
BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve() # degree 3
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/geometry/__init__.py | geometry/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/geometry/geometry.py | geometry/geometry.py | from __future__ import annotations
import math
from dataclasses import dataclass, field
from types import NoneType
from typing import Self
# Building block classes
@dataclass
class Angle:
"""
An Angle in degrees (unit of measurement)
>>> Angle()
Angle(degrees=90)
>>> Angle(45.5)
Angle(degrees=45.5)
>>> Angle(-1)
Traceback (most recent call last):
...
TypeError: degrees must be a numeric value between 0 and 360.
>>> Angle(361)
Traceback (most recent call last):
...
TypeError: degrees must be a numeric value between 0 and 360.
"""
degrees: float = 90
def __post_init__(self) -> None:
if not isinstance(self.degrees, (int, float)) or not 0 <= self.degrees <= 360:
raise TypeError("degrees must be a numeric value between 0 and 360.")
@dataclass
class Side:
"""
A side of a two dimensional Shape such as Polygon, etc.
adjacent_sides: a list of sides which are adjacent to the current side
angle: the angle in degrees between each adjacent side
length: the length of the current side in meters
>>> Side(5)
Side(length=5, angle=Angle(degrees=90), next_side=None)
>>> Side(5, Angle(45.6))
Side(length=5, angle=Angle(degrees=45.6), next_side=None)
>>> Side(5, Angle(45.6), Side(1, Angle(2))) # doctest: +ELLIPSIS
Side(length=5, angle=Angle(degrees=45.6), next_side=Side(length=1, angle=Angle(d...
>>> Side(-1)
Traceback (most recent call last):
...
TypeError: length must be a positive numeric value.
>>> Side(5, None)
Traceback (most recent call last):
...
TypeError: angle must be an Angle object.
>>> Side(5, Angle(90), "Invalid next_side")
Traceback (most recent call last):
...
TypeError: next_side must be a Side or None.
"""
length: float
angle: Angle = field(default_factory=Angle)
next_side: Side | None = None
def __post_init__(self) -> None:
if not isinstance(self.length, (int, float)) or self.length <= 0:
raise TypeError("length must be a positive numeric value.")
if not isinstance(self.angle, Angle):
raise TypeError("angle must be an Angle object.")
if not isinstance(self.next_side, (Side, NoneType)):
raise TypeError("next_side must be a Side or None.")
@dataclass
class Ellipse:
"""
A geometric Ellipse on a 2D surface
>>> Ellipse(5, 10)
Ellipse(major_radius=5, minor_radius=10)
>>> Ellipse(5, 10) is Ellipse(5, 10)
False
>>> Ellipse(5, 10) == Ellipse(5, 10)
True
"""
major_radius: float
minor_radius: float
@property
def area(self) -> float:
"""
>>> Ellipse(5, 10).area
157.07963267948966
"""
return math.pi * self.major_radius * self.minor_radius
@property
def perimeter(self) -> float:
"""
>>> Ellipse(5, 10).perimeter
47.12388980384689
"""
return math.pi * (self.major_radius + self.minor_radius)
class Circle(Ellipse):
"""
A geometric Circle on a 2D surface
>>> Circle(5)
Circle(radius=5)
>>> Circle(5) is Circle(5)
False
>>> Circle(5) == Circle(5)
True
>>> Circle(5).area
78.53981633974483
>>> Circle(5).perimeter
31.41592653589793
"""
def __init__(self, radius: float) -> None:
super().__init__(radius, radius)
self.radius = radius
def __repr__(self) -> str:
return f"Circle(radius={self.radius})"
@property
def diameter(self) -> float:
"""
>>> Circle(5).diameter
10
"""
return self.radius * 2
def max_parts(self, num_cuts: float) -> float:
"""
Return the maximum number of parts that circle can be divided into if cut
'num_cuts' times.
>>> circle = Circle(5)
>>> circle.max_parts(0)
1.0
>>> circle.max_parts(7)
29.0
>>> circle.max_parts(54)
1486.0
>>> circle.max_parts(22.5)
265.375
>>> circle.max_parts(-222)
Traceback (most recent call last):
...
TypeError: num_cuts must be a positive numeric value.
>>> circle.max_parts("-222")
Traceback (most recent call last):
...
TypeError: num_cuts must be a positive numeric value.
"""
if not isinstance(num_cuts, (int, float)) or num_cuts < 0:
raise TypeError("num_cuts must be a positive numeric value.")
return (num_cuts + 2 + num_cuts**2) * 0.5
@dataclass
class Polygon:
"""
An abstract class which represents Polygon on a 2D surface.
>>> Polygon()
Polygon(sides=[])
>>> polygon = Polygon()
>>> polygon.add_side(Side(5)).get_side(0)
Side(length=5, angle=Angle(degrees=90), next_side=None)
>>> polygon.get_side(1)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> polygon.set_side(0, Side(10)).get_side(0)
Side(length=10, angle=Angle(degrees=90), next_side=None)
>>> polygon.set_side(1, Side(10))
Traceback (most recent call last):
...
IndexError: list assignment index out of range
"""
sides: list[Side] = field(default_factory=list)
def add_side(self, side: Side) -> Self:
"""
>>> Polygon().add_side(Side(5))
Polygon(sides=[Side(length=5, angle=Angle(degrees=90), next_side=None)])
"""
self.sides.append(side)
return self
def get_side(self, index: int) -> Side:
"""
>>> Polygon().get_side(0)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> Polygon().add_side(Side(5)).get_side(-1)
Side(length=5, angle=Angle(degrees=90), next_side=None)
"""
return self.sides[index]
def set_side(self, index: int, side: Side) -> Self:
"""
>>> Polygon().set_side(0, Side(5))
Traceback (most recent call last):
...
IndexError: list assignment index out of range
>>> Polygon().add_side(Side(5)).set_side(0, Side(10))
Polygon(sides=[Side(length=10, angle=Angle(degrees=90), next_side=None)])
"""
self.sides[index] = side
return self
class Rectangle(Polygon):
"""
A geometric rectangle on a 2D surface.
>>> rectangle_one = Rectangle(5, 10)
>>> rectangle_one.perimeter()
30
>>> rectangle_one.area()
50
>>> Rectangle(-5, 10)
Traceback (most recent call last):
...
TypeError: length must be a positive numeric value.
"""
def __init__(self, short_side_length: float, long_side_length: float) -> None:
super().__init__()
self.short_side_length = short_side_length
self.long_side_length = long_side_length
self.post_init()
def post_init(self) -> None:
"""
>>> Rectangle(5, 10) # doctest: +NORMALIZE_WHITESPACE
Rectangle(sides=[Side(length=5, angle=Angle(degrees=90), next_side=None),
Side(length=10, angle=Angle(degrees=90), next_side=None)])
"""
self.short_side = Side(self.short_side_length)
self.long_side = Side(self.long_side_length)
super().add_side(self.short_side)
super().add_side(self.long_side)
def perimeter(self) -> float:
return (self.short_side.length + self.long_side.length) * 2
def area(self) -> float:
return self.short_side.length * self.long_side.length
@dataclass
class Square(Rectangle):
"""
a structure which represents a
geometrical square on a 2D surface
>>> square_one = Square(5)
>>> square_one.perimeter()
20
>>> square_one.area()
25
"""
def __init__(self, side_length: float) -> None:
super().__init__(side_length, side_length)
def perimeter(self) -> float:
return super().perimeter()
def area(self) -> float:
return super().area()
if __name__ == "__main__":
__import__("doctest").testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/rgb_hsv_conversion.py | conversions/rgb_hsv_conversion.py | """
The RGB color model is an additive color model in which red, green, and blue light
are added together in various ways to reproduce a broad array of colors. The name
of the model comes from the initials of the three additive primary colors, red,
green, and blue. Meanwhile, the HSV representation models how colors appear under
light. In it, colors are represented using three components: hue, saturation and
(brightness-)value. This file provides functions for converting colors from one
representation to the other.
(description adapted from https://en.wikipedia.org/wiki/RGB_color_model and
https://en.wikipedia.org/wiki/HSL_and_HSV).
"""
def hsv_to_rgb(hue: float, saturation: float, value: float) -> list[int]:
"""
Conversion from the HSV-representation to the RGB-representation.
Expected RGB-values taken from
https://www.rapidtables.com/convert/color/hsv-to-rgb.html
>>> hsv_to_rgb(0, 0, 0)
[0, 0, 0]
>>> hsv_to_rgb(0, 0, 1)
[255, 255, 255]
>>> hsv_to_rgb(0, 1, 1)
[255, 0, 0]
>>> hsv_to_rgb(60, 1, 1)
[255, 255, 0]
>>> hsv_to_rgb(120, 1, 1)
[0, 255, 0]
>>> hsv_to_rgb(240, 1, 1)
[0, 0, 255]
>>> hsv_to_rgb(300, 1, 1)
[255, 0, 255]
>>> hsv_to_rgb(180, 0.5, 0.5)
[64, 128, 128]
>>> hsv_to_rgb(234, 0.14, 0.88)
[193, 196, 224]
>>> hsv_to_rgb(330, 0.75, 0.5)
[128, 32, 80]
"""
if hue < 0 or hue > 360:
raise Exception("hue should be between 0 and 360")
if saturation < 0 or saturation > 1:
raise Exception("saturation should be between 0 and 1")
if value < 0 or value > 1:
raise Exception("value should be between 0 and 1")
chroma = value * saturation
hue_section = hue / 60
second_largest_component = chroma * (1 - abs(hue_section % 2 - 1))
match_value = value - chroma
if hue_section >= 0 and hue_section <= 1:
red = round(255 * (chroma + match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (match_value))
elif hue_section > 1 and hue_section <= 2:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (match_value))
elif hue_section > 2 and hue_section <= 3:
red = round(255 * (match_value))
green = round(255 * (chroma + match_value))
blue = round(255 * (second_largest_component + match_value))
elif hue_section > 3 and hue_section <= 4:
red = round(255 * (match_value))
green = round(255 * (second_largest_component + match_value))
blue = round(255 * (chroma + match_value))
elif hue_section > 4 and hue_section <= 5:
red = round(255 * (second_largest_component + match_value))
green = round(255 * (match_value))
blue = round(255 * (chroma + match_value))
else:
red = round(255 * (chroma + match_value))
green = round(255 * (match_value))
blue = round(255 * (second_largest_component + match_value))
return [red, green, blue]
def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]:
"""
Conversion from the RGB-representation to the HSV-representation.
The tested values are the reverse values from the hsv_to_rgb-doctests.
Function "approximately_equal_hsv" is needed because of small deviations due to
rounding for the RGB-values.
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 0), [0, 0, 0])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 255), [0, 0, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 0), [0, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 255, 0), [60, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 255, 0), [120, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(0, 0, 255), [240, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(255, 0, 255), [300, 1, 1])
True
>>> approximately_equal_hsv(rgb_to_hsv(64, 128, 128), [180, 0.5, 0.5])
True
>>> approximately_equal_hsv(rgb_to_hsv(193, 196, 224), [234, 0.14, 0.88])
True
>>> approximately_equal_hsv(rgb_to_hsv(128, 32, 80), [330, 0.75, 0.5])
True
"""
if red < 0 or red > 255:
raise Exception("red should be between 0 and 255")
if green < 0 or green > 255:
raise Exception("green should be between 0 and 255")
if blue < 0 or blue > 255:
raise Exception("blue should be between 0 and 255")
float_red = red / 255
float_green = green / 255
float_blue = blue / 255
value = max(float_red, float_green, float_blue)
chroma = value - min(float_red, float_green, float_blue)
saturation = 0 if value == 0 else chroma / value
if chroma == 0:
hue = 0.0
elif value == float_red:
hue = 60 * (0 + (float_green - float_blue) / chroma)
elif value == float_green:
hue = 60 * (2 + (float_blue - float_red) / chroma)
else:
hue = 60 * (4 + (float_red - float_green) / chroma)
hue = (hue + 360) % 360
return [hue, saturation, value]
def approximately_equal_hsv(hsv_1: list[float], hsv_2: list[float]) -> bool:
"""
Utility-function to check that two hsv-colors are approximately equal
>>> approximately_equal_hsv([0, 0, 0], [0, 0, 0])
True
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.500001, 0.30001])
True
>>> approximately_equal_hsv([0, 0, 0], [1, 0, 0])
False
>>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.6, 0.30001])
False
"""
check_hue = abs(hsv_1[0] - hsv_2[0]) < 0.2
check_saturation = abs(hsv_1[1] - hsv_2[1]) < 0.002
check_value = abs(hsv_1[2] - hsv_2[2]) < 0.002
return check_hue and check_saturation and check_value
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/binary_to_octal.py | conversions/binary_to_octal.py | """
The function below will convert any binary string to the octal equivalent.
>>> bin_to_octal("1111")
'17'
>>> bin_to_octal("101010101010011")
'52523'
>>> bin_to_octal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> bin_to_octal("a-1")
Traceback (most recent call last):
...
ValueError: Non-binary value was passed to the function
"""
def bin_to_octal(bin_string: str) -> str:
if not all(char in "01" for char in bin_string):
raise ValueError("Non-binary value was passed to the function")
if not bin_string:
raise ValueError("Empty string was passed to the function")
oct_string = ""
while len(bin_string) % 3 != 0:
bin_string = "0" + bin_string
bin_string_in_3_list = [
bin_string[index : index + 3]
for index in range(len(bin_string))
if index % 3 == 0
]
for bin_group in bin_string_in_3_list:
oct_val = 0
for index, val in enumerate(bin_group):
oct_val += int(2 ** (2 - index) * int(val))
oct_string += str(oct_val)
return oct_string
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/hex_to_bin.py | conversions/hex_to_bin.py | def hex_to_bin(hex_num: str) -> int:
"""
Convert a hexadecimal value to its binary equivalent
#https://stackoverflow.com/questions/1425493/convert-hex-to-binary
Here, we have used the bitwise right shift operator: >>
Shifts the bits of the number to the right and fills 0 on voids left as a result.
Similar effect as of dividing the number with some power of two.
Example:
a = 10
a >> 1 = 5
>>> hex_to_bin("AC")
10101100
>>> hex_to_bin("9A4")
100110100100
>>> hex_to_bin(" 12f ")
100101111
>>> hex_to_bin("FfFf")
1111111111111111
>>> hex_to_bin("-fFfF")
-1111111111111111
>>> hex_to_bin("F-f")
Traceback (most recent call last):
...
ValueError: Invalid value was passed to the function
>>> hex_to_bin("")
Traceback (most recent call last):
...
ValueError: No value was passed to the function
"""
hex_num = hex_num.strip()
if not hex_num:
raise ValueError("No value was passed to the function")
is_negative = hex_num[0] == "-"
if is_negative:
hex_num = hex_num[1:]
try:
int_num = int(hex_num, 16)
except ValueError:
raise ValueError("Invalid value was passed to the function")
bin_str = ""
while int_num > 0:
bin_str = str(int_num % 2) + bin_str
int_num >>= 1
return int(("-" + bin_str) if is_negative else bin_str)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/ipv4_conversion.py | conversions/ipv4_conversion.py | # https://www.geeksforgeeks.org/convert-ip-address-to-integer-and-vice-versa/
def ipv4_to_decimal(ipv4_address: str) -> int:
"""
Convert an IPv4 address to its decimal representation.
Args:
ip_address: A string representing an IPv4 address (e.g., "192.168.0.1").
Returns:
int: The decimal representation of the IP address.
>>> ipv4_to_decimal("192.168.0.1")
3232235521
>>> ipv4_to_decimal("10.0.0.255")
167772415
>>> ipv4_to_decimal("10.0.255")
Traceback (most recent call last):
...
ValueError: Invalid IPv4 address format
>>> ipv4_to_decimal("10.0.0.256")
Traceback (most recent call last):
...
ValueError: Invalid IPv4 octet 256
"""
octets = [int(octet) for octet in ipv4_address.split(".")]
if len(octets) != 4:
raise ValueError("Invalid IPv4 address format")
decimal_ipv4 = 0
for octet in octets:
if not 0 <= octet <= 255:
raise ValueError(f"Invalid IPv4 octet {octet}") # noqa: EM102
decimal_ipv4 = (decimal_ipv4 << 8) + int(octet)
return decimal_ipv4
def alt_ipv4_to_decimal(ipv4_address: str) -> int:
"""
>>> alt_ipv4_to_decimal("192.168.0.1")
3232235521
>>> alt_ipv4_to_decimal("10.0.0.255")
167772415
"""
return int("0x" + "".join(f"{int(i):02x}" for i in ipv4_address.split(".")), 16)
def decimal_to_ipv4(decimal_ipv4: int) -> str:
"""
Convert a decimal representation of an IP address to its IPv4 format.
Args:
decimal_ipv4: An integer representing the decimal IP address.
Returns:
The IPv4 representation of the decimal IP address.
>>> decimal_to_ipv4(3232235521)
'192.168.0.1'
>>> decimal_to_ipv4(167772415)
'10.0.0.255'
>>> decimal_to_ipv4(-1)
Traceback (most recent call last):
...
ValueError: Invalid decimal IPv4 address
"""
if not (0 <= decimal_ipv4 <= 4294967295):
raise ValueError("Invalid decimal IPv4 address")
ip_parts = []
for _ in range(4):
ip_parts.append(str(decimal_ipv4 & 255))
decimal_ipv4 >>= 8
return ".".join(reversed(ip_parts))
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/excel_title_to_column.py | conversions/excel_title_to_column.py | def excel_title_to_column(column_title: str) -> int:
"""
Given a string column_title that represents
the column title in an Excel sheet, return
its corresponding column number.
>>> excel_title_to_column("A")
1
>>> excel_title_to_column("B")
2
>>> excel_title_to_column("AB")
28
>>> excel_title_to_column("Z")
26
"""
assert column_title.isupper()
answer = 0
index = len(column_title) - 1
power = 0
while index >= 0:
value = (ord(column_title[index]) - 64) * pow(26, power)
answer += value
power += 1
index -= 1
return answer
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/molecular_chemistry.py | conversions/molecular_chemistry.py | """
Functions useful for doing molecular chemistry:
* molarity_to_normality
* moles_to_pressure
* moles_to_volume
* pressure_and_volume_to_temperature
"""
def molarity_to_normality(nfactor: int, moles: float, volume: float) -> float:
"""
Convert molarity to normality.
Volume is taken in litres.
Wikipedia reference: https://en.wikipedia.org/wiki/Equivalent_concentration
Wikipedia reference: https://en.wikipedia.org/wiki/Molar_concentration
>>> molarity_to_normality(2, 3.1, 0.31)
20
>>> molarity_to_normality(4, 11.4, 5.7)
8
"""
return round(float(moles / volume) * nfactor)
def moles_to_pressure(volume: float, moles: float, temperature: float) -> float:
"""
Convert moles to pressure.
Ideal gas laws are used.
Temperature is taken in kelvin.
Volume is taken in litres.
Pressure has atm as SI unit.
Wikipedia reference: https://en.wikipedia.org/wiki/Gas_laws
Wikipedia reference: https://en.wikipedia.org/wiki/Pressure
Wikipedia reference: https://en.wikipedia.org/wiki/Temperature
>>> moles_to_pressure(0.82, 3, 300)
90
>>> moles_to_pressure(8.2, 5, 200)
10
"""
return round(float((moles * 0.0821 * temperature) / (volume)))
def moles_to_volume(pressure: float, moles: float, temperature: float) -> float:
"""
Convert moles to volume.
Ideal gas laws are used.
Temperature is taken in kelvin.
Volume is taken in litres.
Pressure has atm as SI unit.
Wikipedia reference: https://en.wikipedia.org/wiki/Gas_laws
Wikipedia reference: https://en.wikipedia.org/wiki/Pressure
Wikipedia reference: https://en.wikipedia.org/wiki/Temperature
>>> moles_to_volume(0.82, 3, 300)
90
>>> moles_to_volume(8.2, 5, 200)
10
"""
return round(float((moles * 0.0821 * temperature) / (pressure)))
def pressure_and_volume_to_temperature(
pressure: float, moles: float, volume: float
) -> float:
"""
Convert pressure and volume to temperature.
Ideal gas laws are used.
Temperature is taken in kelvin.
Volume is taken in litres.
Pressure has atm as SI unit.
Wikipedia reference: https://en.wikipedia.org/wiki/Gas_laws
Wikipedia reference: https://en.wikipedia.org/wiki/Pressure
Wikipedia reference: https://en.wikipedia.org/wiki/Temperature
>>> pressure_and_volume_to_temperature(0.82, 1, 2)
20
>>> pressure_and_volume_to_temperature(8.2, 5, 3)
60
"""
return round(float((pressure * volume) / (0.0821 * moles)))
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/prefix_conversions.py | conversions/prefix_conversions.py | """
Convert International System of Units (SI) and Binary prefixes
"""
from __future__ import annotations
from enum import Enum
class SIUnit(Enum):
yotta = 24
zetta = 21
exa = 18
peta = 15
tera = 12
giga = 9
mega = 6
kilo = 3
hecto = 2
deca = 1
deci = -1
centi = -2
milli = -3
micro = -6
nano = -9
pico = -12
femto = -15
atto = -18
zepto = -21
yocto = -24
class BinaryUnit(Enum):
yotta = 8
zetta = 7
exa = 6
peta = 5
tera = 4
giga = 3
mega = 2
kilo = 1
def convert_si_prefix(
known_amount: float,
known_prefix: str | SIUnit,
unknown_prefix: str | SIUnit,
) -> float:
"""
Wikipedia reference: https://en.wikipedia.org/wiki/Binary_prefix
Wikipedia reference: https://en.wikipedia.org/wiki/International_System_of_Units
>>> convert_si_prefix(1, SIUnit.giga, SIUnit.mega)
1000
>>> convert_si_prefix(1, SIUnit.mega, SIUnit.giga)
0.001
>>> convert_si_prefix(1, SIUnit.kilo, SIUnit.kilo)
1
>>> convert_si_prefix(1, 'giga', 'mega')
1000
>>> convert_si_prefix(1, 'gIGa', 'mEGa')
1000
"""
if isinstance(known_prefix, str):
known_prefix = SIUnit[known_prefix.lower()]
if isinstance(unknown_prefix, str):
unknown_prefix = SIUnit[unknown_prefix.lower()]
unknown_amount: float = known_amount * (
10 ** (known_prefix.value - unknown_prefix.value)
)
return unknown_amount
def convert_binary_prefix(
known_amount: float,
known_prefix: str | BinaryUnit,
unknown_prefix: str | BinaryUnit,
) -> float:
"""
Wikipedia reference: https://en.wikipedia.org/wiki/Metric_prefix
>>> convert_binary_prefix(1, BinaryUnit.giga, BinaryUnit.mega)
1024
>>> convert_binary_prefix(1, BinaryUnit.mega, BinaryUnit.giga)
0.0009765625
>>> convert_binary_prefix(1, BinaryUnit.kilo, BinaryUnit.kilo)
1
>>> convert_binary_prefix(1, 'giga', 'mega')
1024
>>> convert_binary_prefix(1, 'gIGa', 'mEGa')
1024
"""
if isinstance(known_prefix, str):
known_prefix = BinaryUnit[known_prefix.lower()]
if isinstance(unknown_prefix, str):
unknown_prefix = BinaryUnit[unknown_prefix.lower()]
unknown_amount: float = known_amount * (
2 ** ((known_prefix.value - unknown_prefix.value) * 10)
)
return unknown_amount
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/convert_number_to_words.py | conversions/convert_number_to_words.py | from enum import Enum
from typing import Literal
class NumberingSystem(Enum):
SHORT = (
(15, "quadrillion"),
(12, "trillion"),
(9, "billion"),
(6, "million"),
(3, "thousand"),
(2, "hundred"),
)
LONG = (
(15, "billiard"),
(9, "milliard"),
(6, "million"),
(3, "thousand"),
(2, "hundred"),
)
INDIAN = (
(14, "crore crore"),
(12, "lakh crore"),
(7, "crore"),
(5, "lakh"),
(3, "thousand"),
(2, "hundred"),
)
@classmethod
def max_value(cls, system: str) -> int:
"""
Gets the max value supported by the given number system.
>>> NumberingSystem.max_value("short") == 10**18 - 1
True
>>> NumberingSystem.max_value("long") == 10**21 - 1
True
>>> NumberingSystem.max_value("indian") == 10**19 - 1
True
"""
match system_enum := cls[system.upper()]:
case cls.SHORT:
max_exp = system_enum.value[0][0] + 3
case cls.LONG:
max_exp = system_enum.value[0][0] + 6
case cls.INDIAN:
max_exp = 19
case _:
raise ValueError("Invalid numbering system")
return 10**max_exp - 1
class NumberWords(Enum):
ONES = { # noqa: RUF012
0: "",
1: "one",
2: "two",
3: "three",
4: "four",
5: "five",
6: "six",
7: "seven",
8: "eight",
9: "nine",
}
TEENS = { # noqa: RUF012
0: "ten",
1: "eleven",
2: "twelve",
3: "thirteen",
4: "fourteen",
5: "fifteen",
6: "sixteen",
7: "seventeen",
8: "eighteen",
9: "nineteen",
}
TENS = { # noqa: RUF012
2: "twenty",
3: "thirty",
4: "forty",
5: "fifty",
6: "sixty",
7: "seventy",
8: "eighty",
9: "ninety",
}
def convert_small_number(num: int) -> str:
"""
Converts small, non-negative integers with irregular constructions in English (i.e.,
numbers under 100) into words.
>>> convert_small_number(0)
'zero'
>>> convert_small_number(5)
'five'
>>> convert_small_number(10)
'ten'
>>> convert_small_number(15)
'fifteen'
>>> convert_small_number(20)
'twenty'
>>> convert_small_number(25)
'twenty-five'
>>> convert_small_number(-1)
Traceback (most recent call last):
...
ValueError: This function only accepts non-negative integers
>>> convert_small_number(123)
Traceback (most recent call last):
...
ValueError: This function only converts numbers less than 100
"""
if num < 0:
raise ValueError("This function only accepts non-negative integers")
if num >= 100:
raise ValueError("This function only converts numbers less than 100")
tens, ones = divmod(num, 10)
if tens == 0:
return NumberWords.ONES.value[ones] or "zero"
if tens == 1:
return NumberWords.TEENS.value[ones]
return (
NumberWords.TENS.value[tens]
+ ("-" if NumberWords.ONES.value[ones] else "")
+ NumberWords.ONES.value[ones]
)
def convert_number(
num: int, system: Literal["short", "long", "indian"] = "short"
) -> str:
"""
Converts an integer to English words.
:param num: The integer to be converted
:param system: The numbering system (short, long, or Indian)
>>> convert_number(0)
'zero'
>>> convert_number(1)
'one'
>>> convert_number(100)
'one hundred'
>>> convert_number(-100)
'negative one hundred'
>>> convert_number(123_456_789_012_345) # doctest: +NORMALIZE_WHITESPACE
'one hundred twenty-three trillion four hundred fifty-six billion
seven hundred eighty-nine million twelve thousand three hundred forty-five'
>>> convert_number(123_456_789_012_345, "long") # doctest: +NORMALIZE_WHITESPACE
'one hundred twenty-three thousand four hundred fifty-six milliard
seven hundred eighty-nine million twelve thousand three hundred forty-five'
>>> convert_number(12_34_56_78_90_12_345, "indian") # doctest: +NORMALIZE_WHITESPACE
'one crore crore twenty-three lakh crore
forty-five thousand six hundred seventy-eight crore
ninety lakh twelve thousand three hundred forty-five'
>>> convert_number(10**18)
Traceback (most recent call last):
...
ValueError: Input number is too large
>>> convert_number(10**21, "long")
Traceback (most recent call last):
...
ValueError: Input number is too large
>>> convert_number(10**19, "indian")
Traceback (most recent call last):
...
ValueError: Input number is too large
"""
word_groups = []
if num < 0:
word_groups.append("negative")
num *= -1
if num > NumberingSystem.max_value(system):
raise ValueError("Input number is too large")
for power, unit in NumberingSystem[system.upper()].value:
digit_group, num = divmod(num, 10**power)
if digit_group > 0:
word_group = (
convert_number(digit_group, system)
if digit_group >= 100
else convert_small_number(digit_group)
)
word_groups.append(f"{word_group} {unit}")
if num > 0 or not word_groups: # word_groups is only empty if input num was 0
word_groups.append(convert_small_number(num))
return " ".join(word_groups)
if __name__ == "__main__":
import doctest
doctest.testmod()
print(f"{convert_number(123456789) = }")
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/roman_numerals.py | conversions/roman_numerals.py | ROMAN = [
(1000, "M"),
(900, "CM"),
(500, "D"),
(400, "CD"),
(100, "C"),
(90, "XC"),
(50, "L"),
(40, "XL"),
(10, "X"),
(9, "IX"),
(5, "V"),
(4, "IV"),
(1, "I"),
]
def roman_to_int(roman: str) -> int:
"""
LeetCode No. 13 Roman to Integer
Given a roman numeral, convert it to an integer.
Input is guaranteed to be within the range from 1 to 3999.
https://en.wikipedia.org/wiki/Roman_numerals
>>> tests = {"III": 3, "CLIV": 154, "MIX": 1009, "MMD": 2500, "MMMCMXCIX": 3999}
>>> all(roman_to_int(key) == value for key, value in tests.items())
True
"""
vals = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
total = 0
place = 0
while place < len(roman):
if (place + 1 < len(roman)) and (vals[roman[place]] < vals[roman[place + 1]]):
total += vals[roman[place + 1]] - vals[roman[place]]
place += 2
else:
total += vals[roman[place]]
place += 1
return total
def int_to_roman(number: int) -> str:
"""
Given a integer, convert it to an roman numeral.
https://en.wikipedia.org/wiki/Roman_numerals
>>> tests = {"III": 3, "CLIV": 154, "MIX": 1009, "MMD": 2500, "MMMCMXCIX": 3999}
>>> all(int_to_roman(value) == key for key, value in tests.items())
True
"""
result = []
for arabic, roman in ROMAN:
(factor, number) = divmod(number, arabic)
result.append(roman * factor)
if number == 0:
break
return "".join(result)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/temperature_conversions.py | conversions/temperature_conversions.py | """Convert between different units of temperature"""
def celsius_to_fahrenheit(celsius: float, ndigits: int = 2) -> float:
"""
Convert a given value from Celsius to Fahrenheit and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
>>> celsius_to_fahrenheit(273.354, 3)
524.037
>>> celsius_to_fahrenheit(273.354, 0)
524.0
>>> celsius_to_fahrenheit(-40.0)
-40.0
>>> celsius_to_fahrenheit(-20.0)
-4.0
>>> celsius_to_fahrenheit(0)
32.0
>>> celsius_to_fahrenheit(20)
68.0
>>> celsius_to_fahrenheit("40")
104.0
>>> celsius_to_fahrenheit("celsius")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'celsius'
"""
return round((float(celsius) * 9 / 5) + 32, ndigits)
def celsius_to_kelvin(celsius: float, ndigits: int = 2) -> float:
"""
Convert a given value from Celsius to Kelvin and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
>>> celsius_to_kelvin(273.354, 3)
546.504
>>> celsius_to_kelvin(273.354, 0)
547.0
>>> celsius_to_kelvin(0)
273.15
>>> celsius_to_kelvin(20.0)
293.15
>>> celsius_to_kelvin("40")
313.15
>>> celsius_to_kelvin("celsius")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'celsius'
"""
return round(float(celsius) + 273.15, ndigits)
def celsius_to_rankine(celsius: float, ndigits: int = 2) -> float:
"""
Convert a given value from Celsius to Rankine and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
>>> celsius_to_rankine(273.354, 3)
983.707
>>> celsius_to_rankine(273.354, 0)
984.0
>>> celsius_to_rankine(0)
491.67
>>> celsius_to_rankine(20.0)
527.67
>>> celsius_to_rankine("40")
563.67
>>> celsius_to_rankine("celsius")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'celsius'
"""
return round((float(celsius) * 9 / 5) + 491.67, ndigits)
def fahrenheit_to_celsius(fahrenheit: float, ndigits: int = 2) -> float:
"""
Convert a given value from Fahrenheit to Celsius and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
>>> fahrenheit_to_celsius(273.354, 3)
134.086
>>> fahrenheit_to_celsius(273.354, 0)
134.0
>>> fahrenheit_to_celsius(0)
-17.78
>>> fahrenheit_to_celsius(20.0)
-6.67
>>> fahrenheit_to_celsius(40.0)
4.44
>>> fahrenheit_to_celsius(60)
15.56
>>> fahrenheit_to_celsius(80)
26.67
>>> fahrenheit_to_celsius("100")
37.78
>>> fahrenheit_to_celsius("fahrenheit")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'fahrenheit'
"""
return round((float(fahrenheit) - 32) * 5 / 9, ndigits)
def fahrenheit_to_kelvin(fahrenheit: float, ndigits: int = 2) -> float:
"""
Convert a given value from Fahrenheit to Kelvin and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
>>> fahrenheit_to_kelvin(273.354, 3)
407.236
>>> fahrenheit_to_kelvin(273.354, 0)
407.0
>>> fahrenheit_to_kelvin(0)
255.37
>>> fahrenheit_to_kelvin(20.0)
266.48
>>> fahrenheit_to_kelvin(40.0)
277.59
>>> fahrenheit_to_kelvin(60)
288.71
>>> fahrenheit_to_kelvin(80)
299.82
>>> fahrenheit_to_kelvin("100")
310.93
>>> fahrenheit_to_kelvin("fahrenheit")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'fahrenheit'
"""
return round(((float(fahrenheit) - 32) * 5 / 9) + 273.15, ndigits)
def fahrenheit_to_rankine(fahrenheit: float, ndigits: int = 2) -> float:
"""
Convert a given value from Fahrenheit to Rankine and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
>>> fahrenheit_to_rankine(273.354, 3)
733.024
>>> fahrenheit_to_rankine(273.354, 0)
733.0
>>> fahrenheit_to_rankine(0)
459.67
>>> fahrenheit_to_rankine(20.0)
479.67
>>> fahrenheit_to_rankine(40.0)
499.67
>>> fahrenheit_to_rankine(60)
519.67
>>> fahrenheit_to_rankine(80)
539.67
>>> fahrenheit_to_rankine("100")
559.67
>>> fahrenheit_to_rankine("fahrenheit")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'fahrenheit'
"""
return round(float(fahrenheit) + 459.67, ndigits)
def kelvin_to_celsius(kelvin: float, ndigits: int = 2) -> float:
"""
Convert a given value from Kelvin to Celsius and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
>>> kelvin_to_celsius(273.354, 3)
0.204
>>> kelvin_to_celsius(273.354, 0)
0.0
>>> kelvin_to_celsius(273.15)
0.0
>>> kelvin_to_celsius(300)
26.85
>>> kelvin_to_celsius("315.5")
42.35
>>> kelvin_to_celsius("kelvin")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'kelvin'
"""
return round(float(kelvin) - 273.15, ndigits)
def kelvin_to_fahrenheit(kelvin: float, ndigits: int = 2) -> float:
"""
Convert a given value from Kelvin to Fahrenheit and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
>>> kelvin_to_fahrenheit(273.354, 3)
32.367
>>> kelvin_to_fahrenheit(273.354, 0)
32.0
>>> kelvin_to_fahrenheit(273.15)
32.0
>>> kelvin_to_fahrenheit(300)
80.33
>>> kelvin_to_fahrenheit("315.5")
108.23
>>> kelvin_to_fahrenheit("kelvin")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'kelvin'
"""
return round(((float(kelvin) - 273.15) * 9 / 5) + 32, ndigits)
def kelvin_to_rankine(kelvin: float, ndigits: int = 2) -> float:
"""
Convert a given value from Kelvin to Rankine and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
>>> kelvin_to_rankine(273.354, 3)
492.037
>>> kelvin_to_rankine(273.354, 0)
492.0
>>> kelvin_to_rankine(0)
0.0
>>> kelvin_to_rankine(20.0)
36.0
>>> kelvin_to_rankine("40")
72.0
>>> kelvin_to_rankine("kelvin")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'kelvin'
"""
return round((float(kelvin) * 9 / 5), ndigits)
def rankine_to_celsius(rankine: float, ndigits: int = 2) -> float:
"""
Convert a given value from Rankine to Celsius and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
Wikipedia reference: https://en.wikipedia.org/wiki/Celsius
>>> rankine_to_celsius(273.354, 3)
-121.287
>>> rankine_to_celsius(273.354, 0)
-121.0
>>> rankine_to_celsius(273.15)
-121.4
>>> rankine_to_celsius(300)
-106.48
>>> rankine_to_celsius("315.5")
-97.87
>>> rankine_to_celsius("rankine")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'rankine'
"""
return round((float(rankine) - 491.67) * 5 / 9, ndigits)
def rankine_to_fahrenheit(rankine: float, ndigits: int = 2) -> float:
"""
Convert a given value from Rankine to Fahrenheit and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
Wikipedia reference: https://en.wikipedia.org/wiki/Fahrenheit
>>> rankine_to_fahrenheit(273.15)
-186.52
>>> rankine_to_fahrenheit(300)
-159.67
>>> rankine_to_fahrenheit("315.5")
-144.17
>>> rankine_to_fahrenheit("rankine")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'rankine'
"""
return round(float(rankine) - 459.67, ndigits)
def rankine_to_kelvin(rankine: float, ndigits: int = 2) -> float:
"""
Convert a given value from Rankine to Kelvin and round it to 2 decimal places.
Wikipedia reference: https://en.wikipedia.org/wiki/Rankine_scale
Wikipedia reference: https://en.wikipedia.org/wiki/Kelvin
>>> rankine_to_kelvin(0)
0.0
>>> rankine_to_kelvin(20.0)
11.11
>>> rankine_to_kelvin("40")
22.22
>>> rankine_to_kelvin("rankine")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'rankine'
"""
return round((float(rankine) * 5 / 9), ndigits)
def reaumur_to_kelvin(reaumur: float, ndigits: int = 2) -> float:
"""
Convert a given value from reaumur to Kelvin and round it to 2 decimal places.
Reference:- http://www.csgnetwork.com/temp2conv.html
>>> reaumur_to_kelvin(0)
273.15
>>> reaumur_to_kelvin(20.0)
298.15
>>> reaumur_to_kelvin(40)
323.15
>>> reaumur_to_kelvin("reaumur")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'reaumur'
"""
return round((float(reaumur) * 1.25 + 273.15), ndigits)
def reaumur_to_fahrenheit(reaumur: float, ndigits: int = 2) -> float:
"""
Convert a given value from reaumur to fahrenheit and round it to 2 decimal places.
Reference:- http://www.csgnetwork.com/temp2conv.html
>>> reaumur_to_fahrenheit(0)
32.0
>>> reaumur_to_fahrenheit(20.0)
77.0
>>> reaumur_to_fahrenheit(40)
122.0
>>> reaumur_to_fahrenheit("reaumur")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'reaumur'
"""
return round((float(reaumur) * 2.25 + 32), ndigits)
def reaumur_to_celsius(reaumur: float, ndigits: int = 2) -> float:
"""
Convert a given value from reaumur to celsius and round it to 2 decimal places.
Reference:- http://www.csgnetwork.com/temp2conv.html
>>> reaumur_to_celsius(0)
0.0
>>> reaumur_to_celsius(20.0)
25.0
>>> reaumur_to_celsius(40)
50.0
>>> reaumur_to_celsius("reaumur")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'reaumur'
"""
return round((float(reaumur) * 1.25), ndigits)
def reaumur_to_rankine(reaumur: float, ndigits: int = 2) -> float:
"""
Convert a given value from reaumur to rankine and round it to 2 decimal places.
Reference:- http://www.csgnetwork.com/temp2conv.html
>>> reaumur_to_rankine(0)
491.67
>>> reaumur_to_rankine(20.0)
536.67
>>> reaumur_to_rankine(40)
581.67
>>> reaumur_to_rankine("reaumur")
Traceback (most recent call last):
...
ValueError: could not convert string to float: 'reaumur'
"""
return round((float(reaumur) * 2.25 + 32 + 459.67), ndigits)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/length_conversion.py | conversions/length_conversion.py | """
Conversion of length units.
Available Units:- Metre,Kilometre,Feet,Inch,Centimeter,Yard,Foot,Mile,Millimeter
USAGE :
-> Import this file into their respective project.
-> Use the function length_conversion() for conversion of length units.
-> Parameters :
-> value : The number of from units you want to convert
-> from_type : From which type you want to convert
-> to_type : To which type you want to convert
REFERENCES :
-> Wikipedia reference: https://en.wikipedia.org/wiki/Meter
-> Wikipedia reference: https://en.wikipedia.org/wiki/Kilometer
-> Wikipedia reference: https://en.wikipedia.org/wiki/Feet
-> Wikipedia reference: https://en.wikipedia.org/wiki/Inch
-> Wikipedia reference: https://en.wikipedia.org/wiki/Centimeter
-> Wikipedia reference: https://en.wikipedia.org/wiki/Yard
-> Wikipedia reference: https://en.wikipedia.org/wiki/Foot
-> Wikipedia reference: https://en.wikipedia.org/wiki/Mile
-> Wikipedia reference: https://en.wikipedia.org/wiki/Millimeter
"""
from typing import NamedTuple
class FromTo(NamedTuple):
from_factor: float
to_factor: float
TYPE_CONVERSION = {
"millimeter": "mm",
"centimeter": "cm",
"meter": "m",
"kilometer": "km",
"inch": "in",
"inche": "in", # Trailing 's' has been stripped off
"feet": "ft",
"foot": "ft",
"yard": "yd",
"mile": "mi",
}
METRIC_CONVERSION = {
"mm": FromTo(0.001, 1000),
"cm": FromTo(0.01, 100),
"m": FromTo(1, 1),
"km": FromTo(1000, 0.001),
"in": FromTo(0.0254, 39.3701),
"ft": FromTo(0.3048, 3.28084),
"yd": FromTo(0.9144, 1.09361),
"mi": FromTo(1609.34, 0.000621371),
}
def length_conversion(value: float, from_type: str, to_type: str) -> float:
"""
Conversion between length units.
>>> length_conversion(4, "METER", "FEET")
13.12336
>>> length_conversion(4, "M", "FT")
13.12336
>>> length_conversion(1, "meter", "kilometer")
0.001
>>> length_conversion(1, "kilometer", "inch")
39370.1
>>> length_conversion(3, "kilometer", "mile")
1.8641130000000001
>>> length_conversion(2, "feet", "meter")
0.6096
>>> length_conversion(4, "feet", "yard")
1.333329312
>>> length_conversion(1, "inch", "meter")
0.0254
>>> length_conversion(2, "inch", "mile")
3.15656468e-05
>>> length_conversion(2, "centimeter", "millimeter")
20.0
>>> length_conversion(2, "centimeter", "yard")
0.0218722
>>> length_conversion(4, "yard", "meter")
3.6576
>>> length_conversion(4, "yard", "kilometer")
0.0036576
>>> length_conversion(3, "foot", "meter")
0.9144000000000001
>>> length_conversion(3, "foot", "inch")
36.00001944
>>> length_conversion(4, "mile", "kilometer")
6.43736
>>> length_conversion(2, "miles", "InChEs")
126719.753468
>>> length_conversion(3, "millimeter", "centimeter")
0.3
>>> length_conversion(3, "mm", "in")
0.1181103
>>> length_conversion(4, "wrongUnit", "inch")
Traceback (most recent call last):
...
ValueError: Invalid 'from_type' value: 'wrongUnit'.
Conversion abbreviations are: mm, cm, m, km, in, ft, yd, mi
"""
new_from = from_type.lower().rstrip("s")
new_from = TYPE_CONVERSION.get(new_from, new_from)
new_to = to_type.lower().rstrip("s")
new_to = TYPE_CONVERSION.get(new_to, new_to)
if new_from not in METRIC_CONVERSION:
msg = (
f"Invalid 'from_type' value: {from_type!r}.\n"
f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
)
raise ValueError(msg)
if new_to not in METRIC_CONVERSION:
msg = (
f"Invalid 'to_type' value: {to_type!r}.\n"
f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
)
raise ValueError(msg)
return (
value
* METRIC_CONVERSION[new_from].from_factor
* METRIC_CONVERSION[new_to].to_factor
)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/speed_conversions.py | conversions/speed_conversions.py | """
Convert speed units
https://en.wikipedia.org/wiki/Kilometres_per_hour
https://en.wikipedia.org/wiki/Miles_per_hour
https://en.wikipedia.org/wiki/Knot_(unit)
https://en.wikipedia.org/wiki/Metre_per_second
"""
speed_chart: dict[str, float] = {
"km/h": 1.0,
"m/s": 3.6,
"mph": 1.609344,
"knot": 1.852,
}
speed_chart_inverse: dict[str, float] = {
"km/h": 1.0,
"m/s": 0.277777778,
"mph": 0.621371192,
"knot": 0.539956803,
}
def convert_speed(speed: float, unit_from: str, unit_to: str) -> float:
"""
Convert speed from one unit to another using the speed_chart above.
"km/h": 1.0,
"m/s": 3.6,
"mph": 1.609344,
"knot": 1.852,
>>> convert_speed(100, "km/h", "m/s")
27.778
>>> convert_speed(100, "km/h", "mph")
62.137
>>> convert_speed(100, "km/h", "knot")
53.996
>>> convert_speed(100, "m/s", "km/h")
360.0
>>> convert_speed(100, "m/s", "mph")
223.694
>>> convert_speed(100, "m/s", "knot")
194.384
>>> convert_speed(100, "mph", "km/h")
160.934
>>> convert_speed(100, "mph", "m/s")
44.704
>>> convert_speed(100, "mph", "knot")
86.898
>>> convert_speed(100, "knot", "km/h")
185.2
>>> convert_speed(100, "knot", "m/s")
51.444
>>> convert_speed(100, "knot", "mph")
115.078
"""
if unit_to not in speed_chart or unit_from not in speed_chart_inverse:
msg = (
f"Incorrect 'from_type' or 'to_type' value: {unit_from!r}, {unit_to!r}\n"
f"Valid values are: {', '.join(speed_chart_inverse)}"
)
raise ValueError(msg)
return round(speed * speed_chart[unit_from] * speed_chart_inverse[unit_to], 3)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/octal_to_decimal.py | conversions/octal_to_decimal.py | def oct_to_decimal(oct_string: str) -> int:
"""
Convert a octal value to its decimal equivalent
>>> oct_to_decimal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> oct_to_decimal("-")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("e")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("8")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("-e")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("-8")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("1")
1
>>> oct_to_decimal("-1")
-1
>>> oct_to_decimal("12")
10
>>> oct_to_decimal(" 12 ")
10
>>> oct_to_decimal("-45")
-37
>>> oct_to_decimal("-")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("0")
0
>>> oct_to_decimal("-4055")
-2093
>>> oct_to_decimal("2-0Fm")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> oct_to_decimal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> oct_to_decimal("19")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
"""
oct_string = str(oct_string).strip()
if not oct_string:
raise ValueError("Empty string was passed to the function")
is_negative = oct_string[0] == "-"
if is_negative:
oct_string = oct_string[1:]
if not oct_string.isdigit() or not all(0 <= int(char) <= 7 for char in oct_string):
raise ValueError("Non-octal value was passed to the function")
decimal_number = 0
for char in oct_string:
decimal_number = 8 * decimal_number + int(char)
if is_negative:
decimal_number = -decimal_number
return decimal_number
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/decimal_to_hexadecimal.py | conversions/decimal_to_hexadecimal.py | """Convert Base 10 (Decimal) Values to Hexadecimal Representations"""
# set decimal value for each hexadecimal digit
values = {
0: "0",
1: "1",
2: "2",
3: "3",
4: "4",
5: "5",
6: "6",
7: "7",
8: "8",
9: "9",
10: "a",
11: "b",
12: "c",
13: "d",
14: "e",
15: "f",
}
def decimal_to_hexadecimal(decimal: float) -> str:
"""
take integer decimal value, return hexadecimal representation as str beginning
with 0x
>>> decimal_to_hexadecimal(5)
'0x5'
>>> decimal_to_hexadecimal(15)
'0xf'
>>> decimal_to_hexadecimal(37)
'0x25'
>>> decimal_to_hexadecimal(255)
'0xff'
>>> decimal_to_hexadecimal(4096)
'0x1000'
>>> decimal_to_hexadecimal(999098)
'0xf3eba'
>>> # negatives work too
>>> decimal_to_hexadecimal(-256)
'-0x100'
>>> # floats are acceptable if equivalent to an int
>>> decimal_to_hexadecimal(17.0)
'0x11'
>>> # other floats will error
>>> decimal_to_hexadecimal(16.16) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
AssertionError
>>> # strings will error as well
>>> decimal_to_hexadecimal('0xfffff') # doctest: +ELLIPSIS
Traceback (most recent call last):
...
AssertionError
>>> # results are the same when compared to Python's default hex function
>>> decimal_to_hexadecimal(-256) == hex(-256)
True
"""
assert isinstance(decimal, (int, float))
assert decimal == int(decimal)
decimal = int(decimal)
hexadecimal = ""
negative = False
if decimal < 0:
negative = True
decimal *= -1
while decimal > 0:
decimal, remainder = divmod(decimal, 16)
hexadecimal = values[remainder] + hexadecimal
hexadecimal = "0x" + hexadecimal
if negative:
hexadecimal = "-" + hexadecimal
return hexadecimal
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/prefix_conversions_string.py | conversions/prefix_conversions_string.py | """
* Author: Manuel Di Lullo (https://github.com/manueldilullo)
* Description: Convert a number to use the correct SI or Binary unit prefix.
Inspired by prefix_conversion.py file in this repository by lance-pyles
URL: https://en.wikipedia.org/wiki/Metric_prefix#List_of_SI_prefixes
URL: https://en.wikipedia.org/wiki/Binary_prefix
"""
from __future__ import annotations
from enum import Enum, unique
from typing import TypeVar
# Create a generic variable that can be 'Enum', or any subclass.
T = TypeVar("T", bound="Enum")
@unique
class BinaryUnit(Enum):
yotta = 80
zetta = 70
exa = 60
peta = 50
tera = 40
giga = 30
mega = 20
kilo = 10
@unique
class SIUnit(Enum):
yotta = 24
zetta = 21
exa = 18
peta = 15
tera = 12
giga = 9
mega = 6
kilo = 3
hecto = 2
deca = 1
deci = -1
centi = -2
milli = -3
micro = -6
nano = -9
pico = -12
femto = -15
atto = -18
zepto = -21
yocto = -24
@classmethod
def get_positive(cls) -> dict:
"""
Returns a dictionary with only the elements of this enum
that has a positive value
>>> from itertools import islice
>>> positive = SIUnit.get_positive()
>>> inc = iter(positive.items())
>>> dict(islice(inc, len(positive) // 2))
{'yotta': 24, 'zetta': 21, 'exa': 18, 'peta': 15, 'tera': 12}
>>> dict(inc)
{'giga': 9, 'mega': 6, 'kilo': 3, 'hecto': 2, 'deca': 1}
"""
return {unit.name: unit.value for unit in cls if unit.value > 0}
@classmethod
def get_negative(cls) -> dict:
"""
Returns a dictionary with only the elements of this enum
that has a negative value
@example
>>> from itertools import islice
>>> negative = SIUnit.get_negative()
>>> inc = iter(negative.items())
>>> dict(islice(inc, len(negative) // 2))
{'deci': -1, 'centi': -2, 'milli': -3, 'micro': -6, 'nano': -9}
>>> dict(inc)
{'pico': -12, 'femto': -15, 'atto': -18, 'zepto': -21, 'yocto': -24}
"""
return {unit.name: unit.value for unit in cls if unit.value < 0}
def add_si_prefix(value: float) -> str:
"""
Function that converts a number to his version with SI prefix
@input value (an integer)
@example:
>>> add_si_prefix(10000)
'10.0 kilo'
"""
prefixes = SIUnit.get_positive() if value > 0 else SIUnit.get_negative()
for name_prefix, value_prefix in prefixes.items():
numerical_part = value / (10**value_prefix)
if numerical_part > 1:
return f"{numerical_part!s} {name_prefix}"
return str(value)
def add_binary_prefix(value: float) -> str:
"""
Function that converts a number to his version with Binary prefix
@input value (an integer)
@example:
>>> add_binary_prefix(65536)
'64.0 kilo'
"""
for prefix in BinaryUnit:
numerical_part = value / (2**prefix.value)
if numerical_part > 1:
return f"{numerical_part!s} {prefix.name}"
return str(value)
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/__init__.py | conversions/__init__.py | python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false | |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/astronomical_length_scale_conversion.py | conversions/astronomical_length_scale_conversion.py | """
Conversion of length units.
Available Units:
Metre, Kilometre, Megametre, Gigametre,
Terametre, Petametre, Exametre, Zettametre, Yottametre
USAGE :
-> Import this file into their respective project.
-> Use the function length_conversion() for conversion of length units.
-> Parameters :
-> value : The number of from units you want to convert
-> from_type : From which type you want to convert
-> to_type : To which type you want to convert
REFERENCES :
-> Wikipedia reference: https://en.wikipedia.org/wiki/Meter
-> Wikipedia reference: https://en.wikipedia.org/wiki/Kilometer
-> Wikipedia reference: https://en.wikipedia.org/wiki/Orders_of_magnitude_(length)
"""
UNIT_SYMBOL = {
"meter": "m",
"kilometer": "km",
"megametre": "Mm",
"gigametre": "Gm",
"terametre": "Tm",
"petametre": "Pm",
"exametre": "Em",
"zettametre": "Zm",
"yottametre": "Ym",
}
# Exponent of the factor(meter)
METRIC_CONVERSION = {
"m": 0,
"km": 3,
"Mm": 6,
"Gm": 9,
"Tm": 12,
"Pm": 15,
"Em": 18,
"Zm": 21,
"Ym": 24,
}
def length_conversion(value: float, from_type: str, to_type: str) -> float:
"""
Conversion between astronomical length units.
>>> length_conversion(1, "meter", "kilometer")
0.001
>>> length_conversion(1, "meter", "megametre")
1e-06
>>> length_conversion(1, "gigametre", "meter")
1000000000
>>> length_conversion(1, "gigametre", "terametre")
0.001
>>> length_conversion(1, "petametre", "terametre")
1000
>>> length_conversion(1, "petametre", "exametre")
0.001
>>> length_conversion(1, "terametre", "zettametre")
1e-09
>>> length_conversion(1, "yottametre", "zettametre")
1000
>>> length_conversion(4, "wrongUnit", "inch")
Traceback (most recent call last):
...
ValueError: Invalid 'from_type' value: 'wrongUnit'.
Conversion abbreviations are: m, km, Mm, Gm, Tm, Pm, Em, Zm, Ym
"""
from_sanitized = from_type.lower().strip("s")
to_sanitized = to_type.lower().strip("s")
from_sanitized = UNIT_SYMBOL.get(from_sanitized, from_sanitized)
to_sanitized = UNIT_SYMBOL.get(to_sanitized, to_sanitized)
if from_sanitized not in METRIC_CONVERSION:
msg = (
f"Invalid 'from_type' value: {from_type!r}.\n"
f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
)
raise ValueError(msg)
if to_sanitized not in METRIC_CONVERSION:
msg = (
f"Invalid 'to_type' value: {to_type!r}.\n"
f"Conversion abbreviations are: {', '.join(METRIC_CONVERSION)}"
)
raise ValueError(msg)
from_exponent = METRIC_CONVERSION[from_sanitized]
to_exponent = METRIC_CONVERSION[to_sanitized]
exponent = 1
if from_exponent > to_exponent:
exponent = from_exponent - to_exponent
else:
exponent = -(to_exponent - from_exponent)
return value * pow(10, exponent)
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/octal_to_binary.py | conversions/octal_to_binary.py | """
* Author: Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
* Description: Convert a Octal number to Binary.
References for better understanding:
https://en.wikipedia.org/wiki/Binary_number
https://en.wikipedia.org/wiki/Octal
"""
def octal_to_binary(octal_number: str) -> str:
"""
Convert an Octal number to Binary.
>>> octal_to_binary("17")
'001111'
>>> octal_to_binary("7")
'111'
>>> octal_to_binary("Av")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> octal_to_binary("@#")
Traceback (most recent call last):
...
ValueError: Non-octal value was passed to the function
>>> octal_to_binary("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
"""
if not octal_number:
raise ValueError("Empty string was passed to the function")
binary_number = ""
octal_digits = "01234567"
for digit in octal_number:
if digit not in octal_digits:
raise ValueError("Non-octal value was passed to the function")
binary_digit = ""
value = int(digit)
for _ in range(3):
binary_digit = str(value % 2) + binary_digit
value //= 2
binary_number += binary_digit
return binary_number
if __name__ == "__main__":
import doctest
doctest.testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/binary_to_decimal.py | conversions/binary_to_decimal.py | def bin_to_decimal(bin_string: str) -> int:
"""
Convert a binary value to its decimal equivalent
>>> bin_to_decimal("101")
5
>>> bin_to_decimal(" 1010 ")
10
>>> bin_to_decimal("-11101")
-29
>>> bin_to_decimal("0")
0
>>> bin_to_decimal("a")
Traceback (most recent call last):
...
ValueError: Non-binary value was passed to the function
>>> bin_to_decimal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> bin_to_decimal("39")
Traceback (most recent call last):
...
ValueError: Non-binary value was passed to the function
"""
bin_string = str(bin_string).strip()
if not bin_string:
raise ValueError("Empty string was passed to the function")
is_negative = bin_string[0] == "-"
if is_negative:
bin_string = bin_string[1:]
if not all(char in "01" for char in bin_string):
raise ValueError("Non-binary value was passed to the function")
decimal_number = 0
for char in bin_string:
decimal_number = 2 * decimal_number + int(char)
return -decimal_number if is_negative else decimal_number
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/hexadecimal_to_decimal.py | conversions/hexadecimal_to_decimal.py | hex_table = {hex(i)[2:]: i for i in range(16)} # Use [:2] to strip off the leading '0x'
def hex_to_decimal(hex_string: str) -> int:
"""
Convert a hexadecimal value to its decimal equivalent
#https://www.programiz.com/python-programming/methods/built-in/hex
>>> hex_to_decimal("a")
10
>>> hex_to_decimal("12f")
303
>>> hex_to_decimal(" 12f ")
303
>>> hex_to_decimal("FfFf")
65535
>>> hex_to_decimal("-Ff")
-255
>>> hex_to_decimal("F-f")
Traceback (most recent call last):
...
ValueError: Non-hexadecimal value was passed to the function
>>> hex_to_decimal("")
Traceback (most recent call last):
...
ValueError: Empty string was passed to the function
>>> hex_to_decimal("12m")
Traceback (most recent call last):
...
ValueError: Non-hexadecimal value was passed to the function
"""
hex_string = hex_string.strip().lower()
if not hex_string:
raise ValueError("Empty string was passed to the function")
is_negative = hex_string[0] == "-"
if is_negative:
hex_string = hex_string[1:]
if not all(char in hex_table for char in hex_string):
raise ValueError("Non-hexadecimal value was passed to the function")
decimal_number = 0
for char in hex_string:
decimal_number = 16 * decimal_number + hex_table[char]
return -decimal_number if is_negative else decimal_number
if __name__ == "__main__":
from doctest import testmod
testmod()
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
TheAlgorithms/Python | https://github.com/TheAlgorithms/Python/blob/2c15b8c54eb8130e83640fe1d911c10eb6cd70d4/conversions/decimal_to_any.py | conversions/decimal_to_any.py | """Convert a positive Decimal Number to Any Other Representation"""
from string import ascii_uppercase
ALPHABET_VALUES = {str(ord(c) - 55): c for c in ascii_uppercase}
def decimal_to_any(num: int, base: int) -> str:
"""
Convert a positive integer to another base as str.
>>> decimal_to_any(0, 2)
'0'
>>> decimal_to_any(5, 4)
'11'
>>> decimal_to_any(20, 3)
'202'
>>> decimal_to_any(58, 16)
'3A'
>>> decimal_to_any(243, 17)
'E5'
>>> decimal_to_any(34923, 36)
'QY3'
>>> decimal_to_any(10, 11)
'A'
>>> decimal_to_any(16, 16)
'10'
>>> decimal_to_any(36, 36)
'10'
>>> # negatives will error
>>> decimal_to_any(-45, 8) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
ValueError: parameter must be positive int
>>> # floats will error
>>> decimal_to_any(34.4, 6) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: int() can't convert non-string with explicit base
>>> # a float base will error
>>> decimal_to_any(5, 2.5) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
>>> # a str base will error
>>> decimal_to_any(10, '16') # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: 'str' object cannot be interpreted as an integer
>>> # a base less than 2 will error
>>> decimal_to_any(7, 0) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
ValueError: base must be >= 2
>>> # a base greater than 36 will error
>>> decimal_to_any(34, 37) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
ValueError: base must be <= 36
"""
if isinstance(num, float):
raise TypeError("int() can't convert non-string with explicit base")
if num < 0:
raise ValueError("parameter must be positive int")
if isinstance(base, str):
raise TypeError("'str' object cannot be interpreted as an integer")
if isinstance(base, float):
raise TypeError("'float' object cannot be interpreted as an integer")
if base in (0, 1):
raise ValueError("base must be >= 2")
if base > 36:
raise ValueError("base must be <= 36")
new_value = ""
mod = 0
div = 0
while div != 1:
div, mod = divmod(num, base)
if base >= 11 and 9 < mod < 36:
actual_value = ALPHABET_VALUES[str(mod)]
else:
actual_value = str(mod)
new_value += actual_value
div = num // base
num = div
if div == 0:
return str(new_value[::-1])
elif div == 1:
new_value += str(div)
return str(new_value[::-1])
return new_value[::-1]
if __name__ == "__main__":
import doctest
doctest.testmod()
for base in range(2, 37):
for num in range(1000):
assert int(decimal_to_any(num, base), base) == num, (
num,
base,
decimal_to_any(num, base),
int(decimal_to_any(num, base), base),
)
| python | MIT | 2c15b8c54eb8130e83640fe1d911c10eb6cd70d4 | 2026-01-04T14:38:15.231112Z | false |
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