Introduction
This problem is already defined in one of the previous post. You can read that to know the problem in more detail. The definition goes like this, find a pair of numbers to obtain given sum in an array. The task is to find two numbers in an array which when added will produce a desired sum.
Approach to find a Pair of Numbers to obtain given sum
As the theory is already mentioned in the previous post, let us directly jump to all possible solutions. Here I am defining three different solutions to this problem. And the idea is to build a basic understanding and then proposing the b...

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## Solution to find Interleaving of Strings

Introduction
This post is an enhancement over one of the previous posts where the task was to find if a given string C is an interleaving of strings A and B. To know more about the problem description, please visit the previous post
Solution
The previous solution is a iterative solution which requires lot of space. Here we will discuss a recursive solution. Hopefully with small code foot print. Before we jump into the code, let us understand the idea behind the solution.
Here are the example Strings A, B and C
A -> abcd
B -> ade
C -> abadcde
The recursive algorithm...

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## Count Word Frequency in Stream

Introduction
Continuing our discussions on Tries, here is another practical problem which is used in many text processing scenarios. Counting word frequency in stream translates to a scenario where you are given a list of words (dictionary). Now, there is an infinite stream of characters coming in. Your task is to print the frequency of words appearing in the stream.
To know more about the basics of building a Trie, please visit my previous post
Example Problem for counting word frequency in stream
Let us say we have a dictionary which contains the following words
aca
cat
hell...

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## Maximum path sum in a triangle

Problem Statement
Finding the maximum path sum in a triangle is a very common programming problem. You are given a triangle of numbers which can be represented as below. You are allowed to start from the top of the triangle and move to either of the two number below it. As we move down from the top to the bottom in multiple ways, we keep adding the numbers for each node we visit. The goal is to maximize the sum . A more formal problem statement can be found on the Project Euler website.
How to approach the problem
At any point you have two choices you can go to the number below the current ...

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## Solving the N Queen Problem

Introduction
The N Queen Problem is one of the best problem used to teach backtracking and of course recursion. Backtracking is a general algorithm which finds all complete solutions to a problem by building over partial solutions. In this process, the problem might reach to a partial solution which may not result into a complete solution. Such partial solutions are effectively rejected by the backtracking algorithm.
To know more about backtracking please visit the Wikipedia article.
The classic case of N Queen problem
In this problem, you are given an empty chess board of dimensions N *...

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## Building an autocomplete system using Trie

Introduction
Few days back I wrote a post about the Trie data structure. This post is a continuation to it, and intends to introduce some practical problems which Trie solves. An autocomplete system is a perfect use case.
Many of the websites use this feature to help there users with suggestions & autocomplete. Also, in this post we will define a Trie interface and then work through this problem statement.
An autocomplete system using Trie
As we know from the previous text that a Trie is a tree like data structure which stores words such that the search for a word is proportional to ...

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## Paint Fill Implementation – Image Editing

Introduction
Most of the image editing software like Microsoft paint, Paint.NET, Adobe Photoshop offer features like paint fill. This post is an attempt to define a simple version of the algorithm which is used to implement paint fill. The problem definition goes like this:
There is a grid with dimensions N*M such that each cell of the grid is colored. The paint fill technique allows a user to choose a color to be filled, say K and a cell C(i,j).
If the cell C(i,j) has the same color as K, then do nothing.
If the cell C(i,j) has a color L which is different from K then find all the...

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