Merge branch 'main' into main

.all-contributorsrc

@@ -1311,6 +1311,15 @@
  "content",
  "code"
  ]
+ },
+ {
+ "login": "jiangfz1997",
+ "name": "Fangzhou_Jiang",
+ "avatar_url": "https://avatars.githubusercontent.com/u/63608649?v=4",
+ "profile": "https://github.com/jiangfz1997",
+ "contributions": [
+ "content"
+ ]
  }
  ],
  "contributorsPerLine": 6,

Algorithms/Backtracking/README.md

@@ -4,17 +4,18 @@ Backtracking is an algorithmic-technique for solving problems recursively by try
 
 
 ## Some Popular Backtracking Algorithms
-
+* [Sudoku](Sudoku/readme.md)
+* [M Coloring](M%20Colouring%20Problem/readme.md)
+* [Sum of Subset](Subset%20Sum/README.md)
+* [Knight's Tour](The%20Knight’s%20tour%20problem/README.md)
+* [Word Boggle](Word%20Boggle/README.md)
 * [Rat in a Maze](Rat%20in%20a%20Maze/README.md)
-* [The Knight’s tour problem](The%20Knight’s%20tour%20problem/README.md)
 * [N Queen Problem](N%20Queen%20Problem/README.md)
-* [M Coloring Problem](m%20colouring/README.md)
-* [Sudoku](Sudoku/readme.md)
 * [Cryptarithmetic Puzzles](Cryptarithmetic%20Puzzles/README.md)
-* [Subset Sum Algorithm](Subset%20Sum/README.md)
-* [Tug of War](Tug%20of%20War/README.md)
-* [Word Boggle](Word%20Boggle/README.md)
-* [Permutation of a Given String](Permutation%20Of%20a%20Given%20String/README.md)
-* [Generating IP address](Generate%20IP%20Adresses/README.md)
+* [All Possible Paths](Find%20All%20Possible%20Path/README.md)
+* [Generate IP Addresses](Generate%20IP%20Adresses/README.md)
 * [Remove Invalid Parentheses](Remove%20Invalid%20Parentheses/README.md)
 * [Longest Possible Route in a Matrix with Hurdles](Longest%20Possible%20Route%20in%20a%20Matrix%20with%20Hurdles/README.md)
+* [Permutation of a Given String](Permutation%20Of%20a%20Given%20String/README.md)
+* [Magnet Puzzle](Magnet%20Puzzle/README.md)
+* [Tug of War](Tug%20of%20War/README.md)

Algorithms/Backtracking/Word Boggle/README.md

@@ -1,4 +1,4 @@
-## Largest number in K swaps
+## Word Boggle
 
 Given a dictionary of distinct words and an M x N board where every cell has one character. Find all possible words from the dictionary that can be formed by a sequence of adjacent characters on the board. We can move to any of 8 adjacent characters
 

Algorithms/Branch and Bound/README.md

@@ -10,14 +10,14 @@ The general idea of Branch and Bound algorithm is a BFS-like search for the opti
 
 - 0/1 knapsack problem
 - Job Assignment Problem
-- Travelling Salesman Problem
-- Nearest Neighbour search
+- Traveling Salesman Problem
+- Nearest Neighbor search
 - N-Queens Problem
 
 
 ## Popular Dynamic Programming Algorithms
 * [0/1 knapsack problem](Knapsack%20Problem/README.md)
 * [Job Assignment Problem](Job%20Assignment%20Problem/README.md)
-* [Travelling Salesman Problem](Not-Added)
-* [Nearest Neighbour search](Not-Added)
-* [N-Queens](Not-Added)
+* [Traveling Salesman Problem](../Traveling%20Salesman%20Problem/readme.md)
+* Nearest Neighbor search
+* [N-Queens](../Backtracking/N%20Queen%20Problem/README.md)

Algorithms/Dynamic Programming/README.md

@@ -22,14 +22,21 @@ Dynamic Programming algorithm is designed using the following four steps −
 
 ### Popular Dynamic Programming Algorithms
 * [Fibonacci Sequence](Fibonacci%20Sequence/README.md)
+* [Nth Fibonacci](Nth%20Fibonnaci/README.md)
+* [Nth Catalan Number/Sequence](Nth%20Catalan%20Number/README.md)
 * [Longest Common Subsequence](Longest%20Common%20Subsequence/README.md)
 * [Longest Increasing Subsequence](Longest%20Increasing%20Subsequence/README.md)
+* [Longest Common Substring](Longest%20Common%20Substring/readme.md)
+* [Longest Palindromic Substring](Longest%20Palindromic%20Substring/README.md)
 * [Knapsack Problem](Knapsack%20Problem/README.md)
 * [Edit Distance](Edit%20Distance/README.md)
-* [Coin Change](Coin%20Change/README.md)
+* Coin Change
 * [Matrix Chain Multiplication](Matrix%20Chain%20Multiplication/README.md)
+* [Balanced Tree Count](Count%20Balanced%20Binary%20Trees%20of%20Height%20h/readme.md)
+* [Counting Hops](Count%20Number%20Of%20Hops/README.md)
 * [Floyd Warshall Algorithm](Floyd%20Warshall%20Algorithm/readme.md)
-* [Subset Sum Problem](Subset%20Sum%20Problem/readme.md)
+* [Gold Mine Problem](Gold%20Mine%20Problem/README.md)
+* [Least Common Multiple (LCM)](LCM/LCM.md)
 * [Painting Fence Algorithm](Painting%20Fence%20Algorithm/readme.md)
-* [Coin Change](Coin%20Change/readme.md)
-* [Longest Common Substring](Longest%20Common%20Substring/readme.md)
+* [Staircase](Staircase/README.md)
+* [Subset Sum Problem](Subset%20Sum%20Problem/readme.md)

Algorithms/Graphs/readme.md

@@ -3,7 +3,7 @@ A Graph is a non-linear data structure consisting of vertices and edges. The ver
 
 
 ## Components of a Graph
-- **[Vertices](#verticies)** - A vertex is a node of the graph. It can be denoted by any symbol such as V, U, X, Y, etc. A vertex may also be referred to as a node or a point.
+- **[Vertices](#vertices)** - A vertex is a node of the graph. It can be denoted by any symbol such as V, U, X, Y, etc. A vertex may also be referred to as a node or a point.
 - **[Edges](#edges)** - An edge is a connection between two nodes. It can be denoted by any symbol such as E, F, G, H, etc. An edge may also be referred to as a link or a line.
 - **[Weight](#weight)** - A weight is a value associated with an edge. It can be denoted by any symbol such as W, X, Y, Z, etc. A weight may also be referred to as a cost.
 
@@ -102,18 +102,22 @@ Pic Will be added
 ## Graph Topics
 1. [Graph Traversal](Traversal%20Algorithms/readme.md)
  - [Breadth First Search](Traversal%20Algorithms/BreadthFirstSearch/readme.md)
- - [Depth First Search](Traversal%20Algorithms/DepthFirstSearch/readme.md)]
-2. [Cycle Detection](Cycle%20Detection/readme.md)
- - [Undirected Graph](Cycle%20Detection/Undirected%20Graph/readme.md)
+ - [A* Search](Traversal%20Algorithms/AstarSearch/readme.md)
+ - [Depth First Search](Traversal%20Algorithms/DepthFirstSearch/readme.md)
+2. [Topological Sorts](Topological%20Sort/readme.md)
+3. [Cycle Detection](Cycle%20Detection/readme.md)
+ - Undirected Graph
  - [DFS](Cycle%20Detection/Undirected%20Graph/DFS/readme.md)
  - [BFS](Cycle%20Detection/Undirected%20Graph/BFS/readme.md)
  - [Directed Graph](Cycle%20Detection/Directed%20Graph/readme.md)
- - [DFS](notadded)
- - [BFS](notadded)
-3. [Shortest Path](Shortest%20Path/readme.md)
+4. [Shortest Path](Shortest%20Path/readme.md)
  - [Dijkstra's Algorithm](Traversal%20Algorithms/Dijkstra'sAlgorithm/readme.md)
  - [Bellman Ford Algorithm](Shortest%20Path/BellmanFordAlgorithm/readme.md)
+ - [Bellman-Ford Algorithm](Bellman-Ford%20Algorithm/readme.md)
  - [Floyd Warshall Algorithm](Shortest%20Path/FloydWarshallAlgorithm/readme.md)
-4. [Spanning Tree Algorithm](Spanning%20Tree%20Algorithm/readme.md)
- - [KruskalsAlgorithm](Spanning%20Tree%20Algorithm\KruskalsAlgorithm/readme.md)
- - [PrimsAlgorithm](Spanning%20Tree%20Algorithm\PrimsAlgorithm/readme.md)] 
+5. [Spanning Tree Algorithm](Spanning%20Tree%20Algorithm/readme.md)
+ - [KruskalsAlgorithm](Spanning%20Tree%20Algorithm/KruskalsAlgorithm/readme.md)
+ - [PrimsAlgorithm](Spanning%20Tree%20Algorithm/PrimsAlgorithm/readme.md)
+ - [Disjoint Set Union / Union find](DSU/readme.md)
+6. Strongly Connected Components
+ - [Kosaraju's Algorithm](Kosaraju%20Algorithm/readme.md)

Algorithms/Greedy Algorithm/readme.md

@@ -2,11 +2,11 @@
 Greedy algorithms are a simple, intuitive class of algorithms that can be used to find the optimal solution to some optimization problems. They are called greedy because at each step they make the choice that seems best at that moment. This means that greedy algorithms do not guarantee to return the globally optimal solution, but instead make locally optimal choices in the hope of finding a global optimum. Greedy algorithms are used for optimization problems. An optimization problem can be solved using Greedy if the problem has the following property: at every step, we can make a choice that looks best at the moment, and we get the optimal solution to the complete problem.
 
 ## Popular Greedy Algorithms
-* [Activity Selection](Not-added)
+* Activity Selection
 * [Huffman Coding](Huffman%20Coding%20Algorithm/readme.md)
 * [Prim's Algorithm](Prim%27s%20Algorithm/readme.md)
 * [Kruskal's Algorithm](Krushkal%27s%20Algorithm/readme.md)
 * [Dijkstra's Algorithm](Dijkstra%27s%20Algorithm/readme.md)
-* [Job Sequencing](not-added)
-* [Fractional Knapsack](not-added)
-* [Huffman Decoding](not-added)
+* Job Sequencing
+* Fractional Knapsack
+* [Ford-Fulkerson Algorithm](Ford-Fulkerson/readme.md)

Algorithms/Searching/readme.md

@@ -3,6 +3,9 @@ A search algorithm is the step-by-step procedure used to locate specific data am
 
 
 * [Sequential / Linear Search](./SequentialSearch/readme.md)
+* [Linear Search](./LinearSearch/readme.md)
 * [Binary Search](./BinarySearch/readme.md)
 * [Hashing](./Hashing/readme.md)
-
+* Jump Search
+* Interpolation Search
+* Exponential Search

Algorithms/Sliding Window Algorithm/readme.md

@@ -19,7 +19,7 @@ Sliding window can be used on fixed-length windows or variable-length windows.
  Eg. Find the largest subarray in a given array with sum equal to k.
 
 
-You will understand more cleary when we will solve the questions by both the methods.
+You will understand more clearly when we will solve the questions by both the methods.
 
 
 ### Popular Sliding Window Algorithms

Algorithms/Sorting/readme.md

@@ -8,6 +8,7 @@ the study of algorithms. There are several reasons:
 Sometimes an application inherently needs to sort information. For example,
 in order to prepare customer statements, banks need to sort checks by check
 number.
+
 Algorithms often use sorting as a key subroutine. For example, a program that
 renders graphical objects which are layered on top of each other might have
 to sort the objects according to an “above” relation so that it can draw these
@@ -18,16 +19,15 @@ ploy a rich set of techniques. In fact, many important techniques used through-
 out algorithm design appear in the body of sorting algorithms that have been
 developed over the years. In this way, sorting is also a problem of historical
 interest.
+
 We can prove a nontrivial lower bound for sorting (as we shall do in Chapter 8).
 Our best upper bounds match the lower bound asymptotically, and so we know
 that our sorting algorithms are asymptotically optimal. Moreover, we can use
 the lower bound for sorting to prove lower bounds for certain other problems.
-Many engineering issues come to the fore when implementing sorting algo-
-rithms. The fastest sorting program for a particular situation may depend on
+Many engineering issues come to the fore when implementing sorting algorithms. The fastest sorting program for a particular situation may depend on
 many factors, such as prior knowledge about the keys and satellite data, the
 memory hierarchy (caches and virtual memory) of the host computer, and the
-software environment. Many of these issues are best dealt with at the algorith-
-mic level, rather than by “tweaking” the code.
+software environment. Many of these issues are best dealt with at the algorithmic level, rather than by “tweaking” the code.
 
 ### Popular Sorting Algorithms
 - [Bubble Sort](BubbleSort/readme.md)
@@ -41,4 +41,3 @@ mic level, rather than by “tweaking” the code.
 - [Shell Sort](ShellSort/readme.md)
 - [Count Sort](CountSort/readme.md)
 - [Tim Sort](TimSort/readme.md)
-