This blog post is primarily focused on strengthening the concept of Dynamic Programming by using Minimum Edit Distance problem. Although you won't require any knowledge of Dynamic Programming to understand this post. However, if you are also looking for an elaborate explanation of Dynamic Programming, then please visit this post .
What is Minimum Edit Distance ?
Given two strings P and Q, it is possible to transform P into Q or vice-versa by performing the following operations on one of the strings. For e.g let us assume that we need to transform the string P into the string Q. Then, the fol...

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# dynamic programming

## Solving 0/1 Knapsack problem using Dynamic Programming

Introduction
A knapsack is a bag with straps, usually carried by soldiers to help them take their valuables or things which they might need during their journey. The 0/1 knapsack problem is a very famous interview problem. The problem statement is as follows:
Given a set of items, each of which is associated with some weight and value. Find the subset of items which can be carried into the knapsack with weight limit W. It is required that the cumulative value of the items in the knapsack is maximum value possible.
In simple words, it asks you to pick certain items from the set of items ...

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## Find Interleaving Strings using Dynamic Programming

Introduction
This problem is already discussed in the post here. This post attempts to solve the same using the dynamic programming approach. Here is a brief description of the problem. Given three strings A, B and C such that A is "ab", B is "ade" and C is "adabe" find if C is an interleaving of A and B or not.
Interleaving means constructing the third string C using the characters of A and B such that the characters in A and B preserve their relative ordering in C. In the above example C is an interleaving of A and B.
Approach to Find Interleaving Strings using Dynamic Programming
How ...

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## Dynamic Programming – CrazyNumbers

Problem Statement
We are interested in finding the count of all N digit crazy numbers. Let us define a crazy number. A crazy number is a number where the magnitude of its consecutive digits differ by 1.
For e.g.: Here is a list of all 2 digit crazy numbers:
The total number of 2 digit crazy numbers is 17. You can notice that in all the numbers the digits differ only by 1.
Similarly for three digit numbers the count reaches 32. For four digit numbers it becomes 61 and very soon it increases exponentially to 924903595810 for a 40 digit number.
It might look like the a problem wh...

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## Dynamic Programming – Longest Palindromic Sequence

[nextpage title="Introduction"]
Palindromes are fascinating character sequences in a string. A palindrome is a string which reads the same when read from either of the ends. This post in particular talks about palindromic sub sequences.
To know more about a sub sequence, please check my post on Longest Common Sub sequence.
A palindromic sequence means a sequence of characters which is a palindrome. Now, we must understand it clearly that we are talking about a sub sequence and not a substring.
Understanding the Longest Palindromic Subsequence problem better
It is really easy to say if...

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