Create README.md

Author: abhisheks008

Dynamic Programming/Nth Catalan Numbers/README.md

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+# Nth Catalan Numbers using Dynamic Programming
+Language used : **Python 3**
+
+## 🎯 Aim
+The aim of this script is to find out the n'th catalan numbers using Dynamic Programming.
+
+## 👉 Purpose
+The main purpose of this script is to show the implementation of Dynamic programming on finding out the n'th catalan numbers.
+
+## 📄 Description
+Catalan numbers are defined as a mathematical sequence that consists of positive integers, which can be used to find the number of possibilities of various combinations. 
+
+**Examples:**  
+```
+Input  : k = 12
+Output : 1 1 2 5 14 42 132 429 1430 4862 16796 58786 
+
+Input  : k = 10
+Output : 1 1 2 5 14 42 132 429 1430 4862 
+
+Input  : k = 8
+Output : 1 1 2 5 14 42 132 429 
+```
+
+## 📈 Workflow of the script
+- `catalan` - The main function of the script to find out the catalan numbers using Dynamic Approach.
+- `main` - This is the driver code for this code/script.
+- `k` - User given integer which signifies the upper range of the Catalan series.
+
+## 🧮 Algorithm
+Let's see how it works,
+- Create an array `catalan[]` for storing `ith` Catalan number.
+- Initialize, `catalan[0]` and `catalan[1]` = 1
+- Loop through `i = 2` to the given Catalan number `n`.
+- Loop throught `j = 0` to `j < i` and Keep adding value of `catalan[j] * catalan[i – j – 1]` into `catalan[i]`.
+- Finally, `return catalan[n]`.
+
+## 💻 Input and Output 
+- **Test Case 1 :**
+
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Dynamic%20Programming/Nth%20Catalan%20Numbers/Images/catalan-1.png)
+
+- **Test Case 2 :**
+
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Dynamic%20Programming/Nth%20Catalan%20Numbers/Images/catalan-2.png)
+
+- **Test Case 3 :**
+
+![](https://github.com/abhisheks008/PyAlgo-Tree/blob/main/Dynamic%20Programming/Nth%20Catalan%20Numbers/Images/catalan-3.png)
+
+
+## ⏰ Time and Space complexity
+- **Time Complexity:** `O(n^2)`. 
+- **Space Complexity:** `O(n)`.
+
+---------------------------------------------------------------
+## 🖋️ Author
+**Code contributed by, _Abhishek Sharma_, 2022 [@abhisheks008](github.com/abhisheks008)**
+
+[![forthebadge made-with-python](http://ForTheBadge.com/images/badges/made-with-python.svg)](https://www.python.org/)