From 29eb341e85fcfa42351ce066b1abaf9975645eb4 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Wed, 7 Jun 2023 22:43:42 +0100
Subject: [PATCH 1/9] feat: Create number container system algorithm

---
 other/number_container_system.py | 128 +++++++++++++++++++++++++++++++
 1 file changed, 128 insertions(+)
 create mode 100644 other/number_container_system.py

diff --git a/other/number_container_system.py b/other/number_container_system.py
new file mode 100644
index 000000000000..ef3c81f3dc9c
--- /dev/null
+++ b/other/number_container_system.py
@@ -0,0 +1,128 @@
+"""
+A number container system that uses binary search to 
+delete and insert values into arrays with O(n logn) 
+write times and O(1) read times.
+
+This container system holds integers at indexes.
+
+Further explained in this leetcode problem
+> https://leetcode.com/problems/minimum-cost-tree-from-leaf-values
+"""
+
+
+class NumberContainer:
+    def __init__(self):
+        # Holds number as the key and returns list of indexes where the number is
+        # The list of indexes is a sorted array in ascending order
+        self.numbermap: dict[int, list[int]] = {}
+        # Simply holds each index and it's number
+        self.indexmap: dict[int, int] = {}
+
+    def binary_search_delete(self, array: list[int], item: int) -> list[int]:
+        """
+        Removes the item from the array and returns
+        the new array.
+
+        >>> NumberContainer().binary_search_delete([1,2,3], 2)
+        [1, 3]
+        >>> NumberContainer().binary_search_delete([], 0)
+        Traceback (most recent call last):
+            ...
+        ValueError: The item is not in the array, and therefore cannot be deleted
+        """
+        low = 0
+        high = len(array) - 1
+
+        while low <= high:
+            mid = (low + high) // 2
+            if array[mid] == item:
+                array.pop(mid)
+                return array
+            elif array[mid] < item:
+                low = mid + 1
+            else:
+                high = mid - 1
+        raise ValueError("The item is not in the array, and therefore cannot be deleted")
+
+    def binary_search_insert(self, array: list[int], index: int) -> list[int]:
+        """
+        Inserts the index into the sorted array
+        at the correct position
+        
+        >>> NumberContainer().binary_search_insert([1,2,3], 2)
+        [1, 2, 2, 3]
+        >>> NumberContainer().binary_search_insert([0,1,3], 2)
+        [0, 1, 2, 3]
+        """
+        low = 0
+        high = len(array) - 1
+
+        while low <= high:
+            mid = (low + high) // 2
+            if array[mid] == index:
+                # If the item already exists in the array, insert it after the existing item
+                array.insert(mid + 1, index)
+                return array
+            elif array[mid] < index:
+                low = mid + 1
+            else:
+                high = mid - 1
+
+        # If the item doesn't exist in the array, insert it at the appropriate position
+        array.insert(low, index)
+        return array
+
+    def change(self, index: int, number: int) -> None:
+        """
+        Changes (sets) the index as number
+
+        >>> cont = NumberContainer()
+        >>> cont.change(0, 10)
+        >>> cont.change(0, 20)
+        >>> cont.change(-1, 20)
+        """
+        # Remove previous index
+        if index in self.indexmap:
+            n = self.indexmap[index]
+            if len(self.numbermap[n]) == 1:
+                del self.numbermap[n]
+            else:
+                self.numbermap[n] = self.binary_search_delete(self.numbermap[n], index)
+
+        # Set new index
+        self.indexmap[index] = number
+
+        # Number not seen before or empty so insert number value
+        if not number in self.numbermap:
+            self.numbermap[number] = [index]
+
+        # Here we need to perform a binary search insertion in order to insert
+        # The item in the correct place
+        else:
+            self.numbermap[number] = self.binary_search_insert(
+                self.numbermap[number], index
+            )
+
+    def find(self, number: int) -> int:
+        """
+        Returns the smallest index where the number is.
+
+        >>> cont = NumberContainer()
+        >>> cont.find(10)
+        -1
+        >>> cont.change(0, 10)
+        >>> cont.find(10)
+        0
+        >>> cont.change(0, 20)
+        >>> cont.find(10)
+        -1
+        >>> cont.find(20)
+        0
+        """
+        # Simply return the 0th index (smallest) of the indexes found (or -1)
+        return self.numbermap.get(number, [-1])[0]
+    
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From 1eb503983720fb701ca1908d4cc8077d10ae8efd Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Wed, 7 Jun 2023 21:44:19 +0000
Subject: [PATCH 2/9] updating DIRECTORY.md

---
 DIRECTORY.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 231b0e2f1d2f..6dac4a9a5783 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -419,8 +419,9 @@
   * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py)
   * [G Topological Sort](graphs/g_topological_sort.py)
   * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py)
+  * [Graph Adjacency List](graphs/graph_adjacency_list.py)
+  * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py)
   * [Graph List](graphs/graph_list.py)
-  * [Graph Matrix](graphs/graph_matrix.py)
   * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py)
   * [Greedy Best First](graphs/greedy_best_first.py)
   * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py)
@@ -479,6 +480,7 @@
     * [Lib](linear_algebra/src/lib.py)
     * [Polynom For Points](linear_algebra/src/polynom_for_points.py)
     * [Power Iteration](linear_algebra/src/power_iteration.py)
+    * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py)
     * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py)
     * [Schur Complement](linear_algebra/src/schur_complement.py)
     * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py)
@@ -651,6 +653,7 @@
   * [Sigmoid Linear Unit](maths/sigmoid_linear_unit.py)
   * [Signum](maths/signum.py)
   * [Simpson Rule](maths/simpson_rule.py)
+  * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py)
   * [Sin](maths/sin.py)
   * [Sock Merchant](maths/sock_merchant.py)
   * [Softmax](maths/softmax.py)
@@ -726,6 +729,7 @@
   * [Maximum Subarray](other/maximum_subarray.py)
   * [Maximum Subsequence](other/maximum_subsequence.py)
   * [Nested Brackets](other/nested_brackets.py)
+  * [Number Container System](other/number_container_system.py)
   * [Password](other/password.py)
   * [Quine](other/quine.py)
   * [Scoring Algorithm](other/scoring_algorithm.py)

From 4743acadb1cd443afd8a5ad667d09c87b7ac9eaa Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Wed, 7 Jun 2023 22:45:40 +0100
Subject: [PATCH 3/9] chore: Fix failing tests

---
 other/number_container_system.py | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index ef3c81f3dc9c..805896c5d8c8 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -1,6 +1,6 @@
 """
-A number container system that uses binary search to 
-delete and insert values into arrays with O(n logn) 
+A number container system that uses binary search to
+delete and insert values into arrays with O(n logn)
 write times and O(1) read times.
 
 This container system holds integers at indexes.
@@ -11,7 +11,7 @@
 
 
 class NumberContainer:
-    def __init__(self):
+    def __init__(self) -> None:
         # Holds number as the key and returns list of indexes where the number is
         # The list of indexes is a sorted array in ascending order
         self.numbermap: dict[int, list[int]] = {}
@@ -42,13 +42,15 @@ def binary_search_delete(self, array: list[int], item: int) -> list[int]:
                 low = mid + 1
             else:
                 high = mid - 1
-        raise ValueError("The item is not in the array, and therefore cannot be deleted")
+        raise ValueError(
+            "The item is not in the array, and therefore cannot be deleted"
+        )
 
     def binary_search_insert(self, array: list[int], index: int) -> list[int]:
         """
         Inserts the index into the sorted array
         at the correct position
-        
+
         >>> NumberContainer().binary_search_insert([1,2,3], 2)
         [1, 2, 2, 3]
         >>> NumberContainer().binary_search_insert([0,1,3], 2)
@@ -60,7 +62,8 @@ def binary_search_insert(self, array: list[int], index: int) -> list[int]:
         while low <= high:
             mid = (low + high) // 2
             if array[mid] == index:
-                # If the item already exists in the array, insert it after the existing item
+                # If the item already exists in the array,
+                # insert it after the existing item
                 array.insert(mid + 1, index)
                 return array
             elif array[mid] < index:
@@ -93,7 +96,7 @@ def change(self, index: int, number: int) -> None:
         self.indexmap[index] = number
 
         # Number not seen before or empty so insert number value
-        if not number in self.numbermap:
+        if number not in self.numbermap:
             self.numbermap[number] = [index]
 
         # Here we need to perform a binary search insertion in order to insert
@@ -121,7 +124,8 @@ def find(self, number: int) -> int:
         """
         # Simply return the 0th index (smallest) of the indexes found (or -1)
         return self.numbermap.get(number, [-1])[0]
-    
+
+
 if __name__ == "__main__":
     import doctest
 

From 82e1a0bbba3b3b48f3674f05c0a43a7ef65450d9 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 09:48:50 +0100
Subject: [PATCH 4/9] Update other/number_container_system.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 other/number_container_system.py | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index 805896c5d8c8..31c56164e185 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -1,7 +1,6 @@
 """
-A number container system that uses binary search to
-delete and insert values into arrays with O(n logn)
-write times and O(1) read times.
+A number container system that uses binary search to delete and insert values into
+arrays with O(n logn) write times and O(1) read times.
 
 This container system holds integers at indexes.
 

From c95797b4aaac72cd9e51dd403527f1c69e237dcc Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 09:49:04 +0100
Subject: [PATCH 5/9] Update other/number_container_system.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 other/number_container_system.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index 31c56164e185..3c9c6184afa9 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -11,8 +11,8 @@
 
 class NumberContainer:
     def __init__(self) -> None:
-        # Holds number as the key and returns list of indexes where the number is
-        # The list of indexes is a sorted array in ascending order
+        # numbermap keys are the number and its values are lists of indexes sorted
+        # in ascending order
         self.numbermap: dict[int, list[int]] = {}
         # Simply holds each index and it's number
         self.indexmap: dict[int, int] = {}

From 9bf70fec275dd229309839ae6c600daf1aaaaa01 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 09:49:10 +0100
Subject: [PATCH 6/9] Update other/number_container_system.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 other/number_container_system.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index 3c9c6184afa9..b3ae13e0d8b7 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -14,7 +14,7 @@ def __init__(self) -> None:
         # numbermap keys are the number and its values are lists of indexes sorted
         # in ascending order
         self.numbermap: dict[int, list[int]] = {}
-        # Simply holds each index and it's number
+        # indexmap keys are an index and it's values are the number at that index
         self.indexmap: dict[int, int] = {}
 
     def binary_search_delete(self, array: list[int], item: int) -> list[int]:

From 232215349108eb2038db8632010f028bcd4e0c46 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 11:13:46 +0100
Subject: [PATCH 7/9] chore: Add more tests

---
 other/number_container_system.py | 57 ++++++++++++++++++++++++++++----
 1 file changed, 51 insertions(+), 6 deletions(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index b3ae13e0d8b7..b9db6ffb4e45 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -19,16 +19,45 @@ def __init__(self) -> None:
 
     def binary_search_delete(self, array: list[int], item: int) -> list[int]:
         """
-        Removes the item from the array and returns
+        Removes the item from the sorted array and returns
         the new array.
 
         >>> NumberContainer().binary_search_delete([1,2,3], 2)
         [1, 3]
-        >>> NumberContainer().binary_search_delete([], 0)
+        >>> NumberContainer().binary_search_delete([0, 0, 0], 0)
+        [0, 0]
+        >>> NumberContainer().binary_search_delete([-1, -1, -1], -1)
+        [-1, -1]
+        >>> NumberContainer().binary_search_delete([-1, 0], 0)
+        [-1]
+        >>> NumberContainer().binary_search_delete([-1, 0], -1)
+        [0]
+        >>> NumberContainer().binary_search_delete(range(7), 3)
+        [0, 1, 2, 4, 5, 6]
+        >>> NumberContainer().binary_search_delete([1.1, 2.2, 3.3], 2.2)
+        [1.1, 3.3]
+        >>> NumberContainer().binary_search_delete("abcde", "c")
+        ['a', 'b', 'd', 'e']
+        >>> NumberContainer().binary_search_delete([0, -1, 2, 4], 0)
         Traceback (most recent call last):
             ...
-        ValueError: The item is not in the array, and therefore cannot be deleted
+        ValueError: Either the item is not in the array or the array was unsorted
+        >>> NumberContainer().binary_search_delete([2, 0, 4, -1, 11], -1)
+        Traceback (most recent call last):
+            ...
+        ValueError: Either the item is not in the array or the array was unsorted
+        >>> NumberContainer().binary_search_delete(125, 1)
+        Traceback (most recent call last):
+            ...
+        TypeError: binary_search_delete() only accepts either a list, range or str
         """
+        if isinstance(array, (range, str)):
+            array = list(array)
+        elif not isinstance(array, list):
+            raise TypeError(
+                "binary_search_delete() only accepts either a list, range or str"
+            )
+
         low = 0
         high = len(array) - 1
 
@@ -42,19 +71,34 @@ def binary_search_delete(self, array: list[int], item: int) -> list[int]:
             else:
                 high = mid - 1
         raise ValueError(
-            "The item is not in the array, and therefore cannot be deleted"
+            "Either the item is not in the array or the array was unsorted"
         )
 
     def binary_search_insert(self, array: list[int], index: int) -> list[int]:
         """
         Inserts the index into the sorted array
-        at the correct position
+        at the correct position.
 
         >>> NumberContainer().binary_search_insert([1,2,3], 2)
         [1, 2, 2, 3]
         >>> NumberContainer().binary_search_insert([0,1,3], 2)
         [0, 1, 2, 3]
+        >>> NumberContainer().binary_search_insert([-5, -3, 0, 0, 11, 103], 51)
+        [-5, -3, 0, 0, 11, 51, 103]
+        >>> NumberContainer().binary_search_insert([-5, -3, 0, 0, 11, 100, 103], 101)
+        [-5, -3, 0, 0, 11, 100, 101, 103]
+        >>> NumberContainer().binary_search_insert(range(10), 4)
+        [0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9]
+        >>> NumberContainer().binary_search_insert("abd", "c")
+        ['a', 'b', 'c', 'd']
         """
+        if isinstance(array, (range, str)):
+            array = list(array)
+        elif not isinstance(array, list):
+            raise TypeError(
+                "binary_search_insert() only accepts either a list, range or str"
+            )
+
         low = 0
         high = len(array) - 1
 
@@ -81,7 +125,8 @@ def change(self, index: int, number: int) -> None:
         >>> cont = NumberContainer()
         >>> cont.change(0, 10)
         >>> cont.change(0, 20)
-        >>> cont.change(-1, 20)
+        >>> cont.change(-13, 20)
+        >>> cont.change(-100030, 20032903290)
         """
         # Remove previous index
         if index in self.indexmap:

From c6c021aeff4f397c765873e3e7fa26033c67a45e Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 11:16:30 +0100
Subject: [PATCH 8/9] chore: Create binary_search_insert failing test

---
 other/number_container_system.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index b9db6ffb4e45..39e5d2b81224 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -91,6 +91,10 @@ def binary_search_insert(self, array: list[int], index: int) -> list[int]:
         [0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9]
         >>> NumberContainer().binary_search_insert("abd", "c")
         ['a', 'b', 'c', 'd']
+        >>> NumberContainer().binary_search_insert(131, 23)
+        Traceback (most recent call last):
+            ...
+        TypeError: binary_search_insert() only accepts either a list, range or str
         """
         if isinstance(array, (range, str)):
             array = list(array)

From f9801ac4528b6609dcd41eecd23497e9a2c8ea9f Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 11:20:18 +0100
Subject: [PATCH 9/9] type: Update typehints to accept str, list and range

---
 other/number_container_system.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/other/number_container_system.py b/other/number_container_system.py
index 39e5d2b81224..f547bc8a229e 100644
--- a/other/number_container_system.py
+++ b/other/number_container_system.py
@@ -17,7 +17,7 @@ def __init__(self) -> None:
         # indexmap keys are an index and it's values are the number at that index
         self.indexmap: dict[int, int] = {}
 
-    def binary_search_delete(self, array: list[int], item: int) -> list[int]:
+    def binary_search_delete(self, array: list | str | range, item: int) -> list[int]:
         """
         Removes the item from the sorted array and returns
         the new array.
@@ -74,7 +74,7 @@ def binary_search_delete(self, array: list[int], item: int) -> list[int]:
             "Either the item is not in the array or the array was unsorted"
         )
 
-    def binary_search_insert(self, array: list[int], index: int) -> list[int]:
+    def binary_search_insert(self, array: list | str | range, index: int) -> list[int]:
         """
         Inserts the index into the sorted array
         at the correct position.