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Add graham scan algorithm (#4205)
* Add graham scan algorithm
* Fix argument name p with point
* Add tests in inner function
* updating DIRECTORY.md
* Fix graham scan for isort --profile=black
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
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@ -30,6 +30,8 @@
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* [Binary Count Trailing Zeros](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_count_trailing_zeros.py)
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* [Binary Or Operator](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_or_operator.py)
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* [Binary Xor Operator](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_xor_operator.py)
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* [Count Number Of One Bits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/count_number_of_one_bits.py)
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* [Reverse Bits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/reverse_bits.py)
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* [Single Bit Manipulation Operations](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/single_bit_manipulation_operations.py)
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## Blockchain
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@ -122,6 +124,7 @@
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* [Fenwick Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/fenwick_tree.py)
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* [Lazy Segment Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/lazy_segment_tree.py)
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* [Lowest Common Ancestor](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/lowest_common_ancestor.py)
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* [Merge Two Binary Trees](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/merge_two_binary_trees.py)
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* [Non Recursive Segment Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/non_recursive_segment_tree.py)
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* [Number Of Possible Binary Trees](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/number_of_possible_binary_trees.py)
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* [Red Black Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/red_black_tree.py)
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@ -274,6 +277,7 @@
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## Graphics
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* [Bezier Curve](https://github.com/TheAlgorithms/Python/blob/master/graphics/bezier_curve.py)
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* [Koch Snowflake](https://github.com/TheAlgorithms/Python/blob/master/graphics/koch_snowflake.py)
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* [Vector3 For 2D Rendering](https://github.com/TheAlgorithms/Python/blob/master/graphics/vector3_for_2d_rendering.py)
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## Graphs
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@ -520,6 +524,7 @@
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* [Frequency Finder](https://github.com/TheAlgorithms/Python/blob/master/other/frequency_finder.py)
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* [Game Of Life](https://github.com/TheAlgorithms/Python/blob/master/other/game_of_life.py)
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* [Gauss Easter](https://github.com/TheAlgorithms/Python/blob/master/other/gauss_easter.py)
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* [Graham Scan](https://github.com/TheAlgorithms/Python/blob/master/other/graham_scan.py)
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* [Greedy](https://github.com/TheAlgorithms/Python/blob/master/other/greedy.py)
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* [Integeration By Simpson Approx](https://github.com/TheAlgorithms/Python/blob/master/other/integeration_by_simpson_approx.py)
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* [Largest Subarray Sum](https://github.com/TheAlgorithms/Python/blob/master/other/largest_subarray_sum.py)
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@ -840,6 +845,7 @@
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* [Merge Insertion Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_insertion_sort.py)
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* [Merge Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_sort.py)
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* [Natural Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/natural_sort.py)
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* [Odd Even Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_sort.py)
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* [Odd Even Transposition Parallel](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_parallel.py)
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* [Odd Even Transposition Single Threaded](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_single_threaded.py)
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* [Pancake Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/pancake_sort.py)
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@ -856,6 +862,7 @@
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* [Recursive Quick Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/recursive_quick_sort.py)
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* [Selection Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/selection_sort.py)
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* [Shell Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/shell_sort.py)
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* [Slowsort](https://github.com/TheAlgorithms/Python/blob/master/sorts/slowsort.py)
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* [Stooge Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/stooge_sort.py)
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* [Strand Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/strand_sort.py)
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* [Tim Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/tim_sort.py)
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171
other/graham_scan.py
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171
other/graham_scan.py
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"""
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This is a pure Python implementation of the merge-insertion sort algorithm
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Source: https://en.wikipedia.org/wiki/Graham_scan
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For doctests run following command:
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python3 -m doctest -v graham_scan.py
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"""
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from __future__ import annotations
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from collections import deque
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from enum import Enum
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from math import atan2, degrees
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from sys import maxsize
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def graham_scan(points: list[list[int, int]]) -> list[list[int, int]]:
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"""Pure implementation of graham scan algorithm in Python
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:param points: The unique points on coordinates.
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:return: The points on convex hell.
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Examples:
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>>> graham_scan([(9, 6), (3, 1), (0, 0), (5, 5), (5, 2), (7, 0), (3, 3), (1, 4)])
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[(0, 0), (7, 0), (9, 6), (5, 5), (1, 4)]
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>>> graham_scan([(0, 0), (1, 0), (1, 1), (0, 1)])
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[(0, 0), (1, 0), (1, 1), (0, 1)]
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>>> graham_scan([(0, 0), (1, 1), (2, 2), (3, 3), (-1, 2)])
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[(0, 0), (1, 1), (2, 2), (3, 3), (-1, 2)]
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>>> graham_scan([(-100, 20), (99, 3), (1, 10000001), (5133186, -25), (-66, -4)])
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[(5133186, -25), (1, 10000001), (-100, 20), (-66, -4)]
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"""
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if len(points) <= 2:
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# There is no convex hull
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raise ValueError("graham_scan: argument must contain more than 3 points.")
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if len(points) == 3:
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return points
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# find the lowest and the most left point
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minidx = 0
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miny, minx = maxsize, maxsize
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for i, point in enumerate(points):
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x = point[0]
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y = point[1]
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if y < miny:
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miny = y
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minx = x
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minidx = i
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if y == miny:
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if x < minx:
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minx = x
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minidx = i
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# remove the lowest and the most left point from points for preparing for sort
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points.pop(minidx)
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def angle_comparer(point: list[int, int], minx: int, miny: int) -> float:
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"""Return the angle toward to point from (minx, miny)
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:param point: The target point
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minx: The starting point's x
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miny: The starting point's y
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:return: the angle
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Examples:
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>>> angle_comparer([1,1], 0, 0)
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45.0
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>>> angle_comparer([100,1], 10, 10)
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-5.710593137499642
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>>> angle_comparer([5,5], 2, 3)
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33.690067525979785
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"""
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# sort the points accorgind to the angle from the lowest and the most left point
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x = point[0]
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y = point[1]
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angle = degrees(atan2(y - miny, x - minx))
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return angle
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sorted_points = sorted(points, key=lambda point: angle_comparer(point, minx, miny))
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# This insert actually costs complexity,
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# and you should insteadly add (minx, miny) into stack later.
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# I'm using insert just for easy understanding.
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sorted_points.insert(0, (minx, miny))
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# traversal from the lowest and the most left point in anti-clockwise direction
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# if direction gets right, the previous point is not the convex hull.
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class Direction(Enum):
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left = 1
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straight = 2
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right = 3
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def check_direction(
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starting: list[int, int], via: list[int, int], target: list[int, int]
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) -> Direction:
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"""Return the direction toward to the line from via to target from starting
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:param starting: The starting point
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via: The via point
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target: The target point
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:return: the Direction
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Examples:
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>>> check_direction([1,1], [2,2], [3,3])
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Direction.straight
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>>> check_direction([60,1], [-50,199], [30,2])
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Direction.left
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>>> check_direction([0,0], [5,5], [10,0])
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Direction.right
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"""
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x0, y0 = starting
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x1, y1 = via
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x2, y2 = target
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via_angle = degrees(atan2(y1 - y0, x1 - x0))
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if via_angle < 0:
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via_angle += 360
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target_angle = degrees(atan2(y2 - y0, x2 - x0))
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if target_angle < 0:
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target_angle += 360
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# t-
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# \ \
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# \ v
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# \|
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# s
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# via_angle is always lower than target_angle, if direction is left.
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# If they are same, it means they are on a same line of convex hull.
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if target_angle > via_angle:
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return Direction.left
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if target_angle == via_angle:
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return Direction.straight
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if target_angle < via_angle:
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return Direction.right
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stack = deque()
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stack.append(sorted_points[0])
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stack.append(sorted_points[1])
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stack.append(sorted_points[2])
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# In any ways, the first 3 points line are towards left.
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# Because we sort them the angle from minx, miny.
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current_direction = Direction.left
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for i in range(3, len(sorted_points)):
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while True:
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starting = stack[-2]
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via = stack[-1]
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target = sorted_points[i]
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next_direction = check_direction(starting, via, target)
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if next_direction == Direction.left:
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current_direction = Direction.left
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break
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if next_direction == Direction.straight:
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if current_direction == Direction.left:
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# We keep current_direction as left.
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# Because if the straight line keeps as straight,
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# we want to know if this straight line is towards left.
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break
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elif current_direction == Direction.right:
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# If the straight line is towards right,
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# every previous points on those straigh line is not convex hull.
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stack.pop()
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if next_direction == Direction.right:
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stack.pop()
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stack.append(sorted_points[i])
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return list(stack)
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