From fdbd6f1582971f42b3d11d7b9ceadc1b624d97da Mon Sep 17 00:00:00 2001
From: Isaiah Iroko <isaiahiroko@gmail.com>
Date: Tue, 6 Sep 2022 08:58:20 +0100
Subject: [PATCH 1/2] update ts complexity

---
 README.md                     |   6 ++
 docs/time-space-complexity.md | 106 ++++++++++++++++++++++++++++++++++
 2 files changed, 112 insertions(+)
 create mode 100644 docs/time-space-complexity.md

diff --git a/README.md b/README.md
index b00841f..244899b 100644
--- a/README.md
+++ b/README.md
@@ -34,6 +34,12 @@ A collection of exercises to help improve your understanding of algorithms and d
 * [Brute Force](./doc/brute-force.md)
 * [Divide and Conquer](./doc/divide-and-conquer.md)
   
+## Concepts
+
+* [Time & Space Complexity](./doc/time-space-complexity.md)
+* [Brute Force](./doc/brute-force.md)
+* [Divide and Conquer](./doc/divide-and-conquer.md)
+  
 ## Contributing
 
 * _This project is work in progress_ If you would like to contribute, please do get in touch.
diff --git a/docs/time-space-complexity.md b/docs/time-space-complexity.md
new file mode 100644
index 0000000..21d179e
--- /dev/null
+++ b/docs/time-space-complexity.md
@@ -0,0 +1,106 @@
+# Algo
+
+## Docs
+
+## Time & Space Complexity
+
+1. Rate of increase of time/space wrt to input size of a function
+
+2. Types
+- Big O
+- Little O
+- Big Ω
+- Little Ω
+- Big Θ 
+
+3. Big O
+- O(1) => Constant
+- O(log n) => Logarithmic
+- O(n) => Linear
+- O(n log n) => Logarithmic linear
+- O(n^2) => Quadratic
+- O(n^m) => Polynomial
+- O(m^n) => Exponential
+- O(n!) => Factorial
+
+3. General Maths Operations
+- Addition is O(1) e.g 2 + 1
+- Subtraction is O(1) e.g 2 - 1
+- Multiplication is O(1) e.g 2 * 1
+- Division is O(1) e.g 2/1
+
+4. Bitwise Operations
+- AnD (&) is O(n)
+- OR (|) is O(n)
+- nOT (~) is O(n)
+- XOR (&) is O(n)
+- SHIFT LEFT (<<) is O(n)
+- SHIFT RIGHT (>>) is O(n)
+
+- Addition
+```
+Sample: 0011 & 0101
+
+Table:
+a   b   carry(&)   sum(XOR)
+0   0   0           0
+0   1   0           1
+1   0   0           1
+1   1   1           0
+
+Pseudo Code:
+a, b = 0011, 0101
+
+while b !=0 {
+    a = a^b //a XOR b
+    b = (a & b) << 1 //a AnD b, then SHIFT LEFT
+}
+
+return a
+```
+
+- Subtraction
+```
+Sample: 0011 & 0101
+
+Table:
+a   b   borrow(~a & b)   diff(XOR)
+0   0   0               0
+0   1   0               1
+1   0   0               1
+1   1   1               0
+
+Pseudo Code:
+a, b = 0011, 0101
+
+while b !=0 {
+    a = a^b //a XOR b
+    b = (~a & b) << 1 //~a AnD b, then SHIFT LEFT
+}
+
+return a
+```
+
+5. Array Operations
+- Access ith element O(1)
+- Transverse O(n)
+- Update ith element O(i)
+- Insert O(n)
+- Delete O(n)
+
+5. Sorting Operations
+- Bubble sort O(n^2)
+- Selection sort O(n^2)
+- Insertions sort O(n^2)
+- Heap sort O(n log n)
+- Quick sort O(n^2)
+- Merge sort O(n log n)
+
+6. Search Operations
+- Binary search O(log n)
+- Linear search O(n)
+- Hash Map search O(n)
+
+Reference
+- https://www.amazon.com/Time-Complexity-Analysis-Coding-Interviews-ebook/dp/B09FF18MFH
+

From aa839bd06d1ecbd71f749c2677f6581dc00c57ba Mon Sep 17 00:00:00 2001
From: Isaiah Iroko <isaiahiroko@gmail.com>
Date: Wed, 21 Sep 2022 10:42:25 +0100
Subject: [PATCH 2/2] add structure

---
 README.md                      |    2 +-
 docs/array.md                  |    5 +
 docs/binary-search-tree.md     |    5 +
 docs/binary-tree.md            |    5 +
 docs/brute-force.md            |    5 +
 docs/divide-and-conquer.md     |    5 +
 docs/graph.md                  |    5 +
 docs/hash-table.md             |    5 +
 docs/heap.md                   |    5 +
 docs/linked-list.md            |   68 ++
 docs/maths.md                  |   15 +
 docs/matrix.md                 |    0
 docs/queue.md                  |    5 +
 docs/revalidate user images.ep | 2096 ++++++++++++++++++++++++++++++++
 docs/sliding-window.md         |    5 +
 docs/stack.md                  |    5 +
 docs/string.md                 |    6 +
 docs/time-space-complexity.md  |    9 +-
 docs/tree.md                   |    5 +
 docs/trie.md                   |    5 +
 20 files changed, 2257 insertions(+), 4 deletions(-)
 create mode 100644 docs/maths.md
 create mode 100644 docs/matrix.md
 create mode 100644 docs/revalidate user images.ep
 create mode 100644 docs/tree.md

diff --git a/README.md b/README.md
index 244899b..88d90d0 100644
--- a/README.md
+++ b/README.md
@@ -20,7 +20,7 @@ A collection of exercises to help improve your understanding of algorithms and d
 *  [Graph](./doc/graph.md) - Graph is a data structure that is used to represent a network of nodes. Each node is connected to a set of other nodes, which are called its neighbors. Graphs are used to represent networks of computers, social networks, and other networks.
 * [Trie](./doc/trie.md) - Trie is a data structure that is used to store strings. It is similar to a binary search tree, except that it is optimized for string searches.
 * [Hash table](./doc/hash-table.md) - Hash table is a data structure that is used to store data. It is similar to an 
-
+* [Matrix](./doc/matrix.md) - 
 
 ## Exercises
 
diff --git a/docs/array.md b/docs/array.md
index e69de29..ad20672 100644
--- a/docs/array.md
+++ b/docs/array.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Array
diff --git a/docs/binary-search-tree.md b/docs/binary-search-tree.md
index e69de29..a665698 100644
--- a/docs/binary-search-tree.md
+++ b/docs/binary-search-tree.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Binary Search Tree
diff --git a/docs/binary-tree.md b/docs/binary-tree.md
index e69de29..901c4e9 100644
--- a/docs/binary-tree.md
+++ b/docs/binary-tree.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Binary Tree
diff --git a/docs/brute-force.md b/docs/brute-force.md
index e69de29..da0e802 100644
--- a/docs/brute-force.md
+++ b/docs/brute-force.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Brute Force
diff --git a/docs/divide-and-conquer.md b/docs/divide-and-conquer.md
index e69de29..43b2f52 100644
--- a/docs/divide-and-conquer.md
+++ b/docs/divide-and-conquer.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Divide & Conquer
diff --git a/docs/graph.md b/docs/graph.md
index e69de29..38c0351 100644
--- a/docs/graph.md
+++ b/docs/graph.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Graph
diff --git a/docs/hash-table.md b/docs/hash-table.md
index e69de29..cd403bb 100644
--- a/docs/hash-table.md
+++ b/docs/hash-table.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Hash Table
diff --git a/docs/heap.md b/docs/heap.md
index e69de29..8a59db3 100644
--- a/docs/heap.md
+++ b/docs/heap.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Heap
diff --git a/docs/linked-list.md b/docs/linked-list.md
index e69de29..9375b35 100644
--- a/docs/linked-list.md
+++ b/docs/linked-list.md
@@ -0,0 +1,68 @@
+# Algo
+
+## Docs
+
+## Linked List
+
+### Introduction
+1. A linked list is a linear collection of data elements, in which linear order is not given by their physical placement in memory. Each pointing to the next node by means of a pointer. It is a data structure consisting of a group of nodes which together represent a sequence.
+
+2. A LinkedList is a data structure consisting of nodes in memory, and every field stores a pointer to the following field, forming a connection to nodes of the list. The data fields aren’t in the exact memory location. But using pointers, they get to connect and reference each other just like arrays.
+
+3. LinkedList is more efficient and preferable to arrays because they can store heterogeneous data, are dynamically sized, insertion is faster, and they are memory-efficient than arrays. 
+
+4. Linked lists are also the backbone of more complex data structures such as stacks and queues. The idea of linking each node with pointers also carries over to other data structures such as trees and graphs.
+
+4. Go has built in `list` and `container` types:
+- `container` The container package contains the implementation of several data structures and their algorithms in Go.
+- `container/list` The list package, on the other hand, includes an implementation of the LinkedList data structure you can use in your Go programs. 
+
+1. Types
+```go
+type Node struct {
+	prev *Node // for only doubly and circular types
+	next *Node
+	val  any
+}
+
+type Container struct {
+	head *Node
+	tail *Node // for only circular types
+}
+```
+
+2. Behaviours
+- Insert
+```go
+```
+
+- Display
+```go
+```
+
+- Reverse
+```go
+```
+
+- First
+```go
+```
+
+- Last
+```go
+```
+
+- Next
+```go
+```
+
+- Length
+```go
+```
+
+
+2. Types
+- Singly
+- Doubly
+- Circular
+- Singly
diff --git a/docs/maths.md b/docs/maths.md
new file mode 100644
index 0000000..7a83e7d
--- /dev/null
+++ b/docs/maths.md
@@ -0,0 +1,15 @@
+# Algo
+
+## Docs
+
+## Maths Crash Course
+
+### Logarithmic
+
+### Permutations and factorial
+
+### Sets
+
+### Sequence & Series
+
+### Modular arithmetic
diff --git a/docs/matrix.md b/docs/matrix.md
new file mode 100644
index 0000000..e69de29
diff --git a/docs/queue.md b/docs/queue.md
index e69de29..aa92c90 100644
--- a/docs/queue.md
+++ b/docs/queue.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Queue
diff --git a/docs/revalidate user images.ep b/docs/revalidate user images.ep
new file mode 100644
index 0000000..97905d0
--- /dev/null
+++ b/docs/revalidate user images.ep	
@@ -0,0 +1,2096 @@
+POST [kabani-simulate]/onboard/re-validate/image
+
+BODY
+{
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+        "3ff66770-f254-44f6-93bf-47be9e1c2e38",
+        "d822b0b1-6418-4254-88f6-e43e3fae8a61",
+        "a41eaee7-03b2-4d0b-a20f-55016f097005",
+        "eac6940c-963d-4a04-97da-933fdfe1c5aa",
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+        "4d0d0f34-c9a0-4d88-8d09-43c7c5a63619",
+        "17e986b5-3558-475c-bac3-b5e60bf6c7e0",
+        "e9f86423-116c-41fe-978b-555fb513cae0",
+        "d18ce1d4-5e3c-4449-b48e-da6a1db4ffc6",
+        "ff370128-41ac-41f4-b614-774383925c28",
+        "1a583100-7ced-4614-820d-ea71442a36bd",
+        "d3ef220f-195d-4c86-9cf1-c1b49e7f3c97",
+        "d2eba71b-6478-44f8-8fc8-90311b0e01cc",
+        "67ec00da-e858-4dd8-b546-80166f152d68",
+        "83f1b75f-769f-4b92-85e6-b6e2a56edf8c",
+        "63ee52d3-e79d-4e6c-a5de-0300818b8271",
+        "1194f581-7444-42c2-bb2d-82b927948422",
+        "067d58a6-07b3-4b24-abe1-7f3512fce54f",
+        "6ae4cb26-868e-4d00-b916-5f6bef0129a2",
+        "09e9fe6b-b084-4840-947d-039fd1644ca7",
+        "e0834f77-ee1b-4d0e-89d1-ea99a34651b8",
+        "7c105a0b-0597-48a1-9947-bec97b9eae0b"
+    ]
+}
diff --git a/docs/sliding-window.md b/docs/sliding-window.md
index e69de29..46ac2be 100644
--- a/docs/sliding-window.md
+++ b/docs/sliding-window.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Sliding Windor
diff --git a/docs/stack.md b/docs/stack.md
index e69de29..f5989d3 100644
--- a/docs/stack.md
+++ b/docs/stack.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Stack
diff --git a/docs/string.md b/docs/string.md
index 6725801..f3bc196 100644
--- a/docs/string.md
+++ b/docs/string.md
@@ -1 +1,7 @@
+# Algo
+
+## Docs
+
+## String
+
 String is a sequence of characters, and it is immutable.
\ No newline at end of file
diff --git a/docs/time-space-complexity.md b/docs/time-space-complexity.md
index 21d179e..1f8baf3 100644
--- a/docs/time-space-complexity.md
+++ b/docs/time-space-complexity.md
@@ -88,7 +88,7 @@ return a
 - Insert O(n)
 - Delete O(n)
 
-5. Sorting Operations
+6. Sorting Operations
 - Bubble sort O(n^2)
 - Selection sort O(n^2)
 - Insertions sort O(n^2)
@@ -96,11 +96,14 @@ return a
 - Quick sort O(n^2)
 - Merge sort O(n log n)
 
-6. Search Operations
+7. Search Operations
 - Binary search O(log n)
 - Linear search O(n)
 - Hash Map search O(n)
 
-Reference
+8. Notes
+- Do not consider constants. For instance, O(2n)and O(5n) can be loosely said to belong to the family of functions O(n)
+
+9. Reference
 - https://www.amazon.com/Time-Complexity-Analysis-Coding-Interviews-ebook/dp/B09FF18MFH
 
diff --git a/docs/tree.md b/docs/tree.md
new file mode 100644
index 0000000..7429306
--- /dev/null
+++ b/docs/tree.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Tree
diff --git a/docs/trie.md b/docs/trie.md
index e69de29..655f45b 100644
--- a/docs/trie.md
+++ b/docs/trie.md
@@ -0,0 +1,5 @@
+# Algo
+
+## Docs
+
+## Trie