Dynamic-Programming | A DP a day keeps the bug | Pub Sub library

Can someone explain what is wrong with my code? I am getting "Abort called" in 7 test cases. Rest are successful.

I have a 2d dp array with of size: n+1 x m+1 were n and m are sizes of a and b respectively. So, the row represent string a and columns represent string b.

First, I set dp[0][0] to 1 since it is possible to turn empty string into empty.

So, initially, i am checking if I can turn any substring of a into the empty string (in the first single for-loop). This is true for all substrings of a without any capital letters. As soon as there is a capital letter, the rest of the substrings cannot be converted.

Then (in the next double for-loop), I am examining all the cases.

Case 1: a[i-1] == b[i-1] -> if both the letter are the exact same, then dp[i][j] = dp[i-1][j-1]

Case 2: a[i-1] is lower case (this has 2 sub cases):

Case 2.1: a[i-1] and b[j-1] are the same letter (but not the same case) -> then we can either change a[i-1] or delete it . So: dp[i][j] = dp[i-1][j-1] || dp[i-1][j].
Case 2.2: a[i-1] and b[j-1] are not the same -> in this case, we can only delete a[i-1] since it is lower case . So: dp[i][j] = dp[i-1][j]

Link to problem: https://www.hackerrank.com/challenges/abbr/problem?h_l=interview&playlist_slugs%5B%5D=interview-preparation-kit&playlist_slugs%5B%5D=dynamic-programming

P.S. The main logic of the program is just inside the abbreviation() function.

Code (EDITTED):

This is the question.

In code world all genders are considered equal ( It means their is nothing like male or female). Now their are N distinct persons living in this hypothetical world. Each person can pair up with any other person or can even remain single. One day Vbhu planned to visit code world. Being a maths guy , he always try to be mathematical. So he started counting the ways in which N persons living in code world can make pairs or remain single. A single person can make pair with at most one other person. Seeing that N can be large , Vibhu ask you for help. Now being a great programmer you need to help Vbhu count the number of ways in which N persons living in code world can make pairs or remain single.

question link = https://www.hackerearth.com/practice/algorithms/dynamic-programming/introduction-to-dynamic-programming-1/practice-problems/algorithm/vibhu-and-his-mathematics/description/

editorial solution :

Let F(X) denote the number of ways for the above problem, meaning we have X number of people. So, Lets tak about Xth person, he might like to remain single or he can pair up with some person from [1,X-1].

So, considering and adding both the cases to the final answer, we get the recurrence:- F(X) = F(X-1) + (X-1)*F(X-2). Lets look at the pseudo code for the implementation of recursive approach.

I understand the case where he remains single(f(x-1)) but for the other case, the total possible way to pick other partner is x-1 but why multiply by f(x-2)

I want to get the longest subarray from a large list. For simplfy, I just show a slice of the array:

I've been attempting the "Egg Drop" Dynamic Programming problem however I'm really confused as to why the answer makes sense.

The problem is usually phrased like the follwoing (longer definitions here, here and here among many other places):

You have a number of floors you can drop an egg from. From some floors the egg will be fine when it hits the ground and from others it will break.

Given a certain number of eggs and a certain number of floors what is the minimum number of drops needed to find the threshold floor (the first floor where the egg will break

Apparently the answer to this a of search of the problem space that enumerates out all possibilites and finds the worst case scenario.

This is definitely a case of me not understanding the question, but why is this the answer? To my mind the answer is one of two things:

• If you have 1 egg then it's however many floors you have as you potentially need to drop it from all of the floors (starting from 1). The first one it breaks at is the 'threshold' and this would confirm an answer for you because you know for a fact that every floor beneath it is 'safe'
• If you have n eggs then isn't the answer 2: you drop it and it breaks, then you drop it on the floor below and it doesn't.

Obviously the n eggs answer requires you to get lucky with both drops, but the question is asking for the minimum number of drops needed to find the threshold i.e. the smallest possible number of drops needed to find the answer and confirm it. If you happened to go down this golden path then isn't that answer 2?

As I said, I'm clearly misunderstanding something about the question here - would someone be able to help?

Thanks!

I'm currently working on the coin change dynamic-programming question on leetcode -- https://leetcode.com/problems/coin-change/.

Here is the question statement:

I am writing to ask the recommendation and suggestion for finding and list the longest path due to I am a newbie for graph structure.

according to my purpose is to find the longest path in the directed acyclic graph. I have found this blog and apply some parts of code to fit with my data. https://www.geeksforgeeks.org/longest-path-in-a-directed-acyclic-graph-dynamic-programming/

Given a list of n-element lists, A, and a target n-element list, t, find a set of lists, S, in A, whose lists sum up to t.

Summing up lists, here, is the addition of elements at the same position. For example, the sum of [1 2] + [2 3] + [7 5] is [10 10].

Here is an example of the problem:

n = 4

A = [[1 2 3 4] [0 0 1 0] [1 0 0 1] [2 0 0 0] [3 0 0 2] [3 0 0 1] [0 0 0 1]]

t = [4 0 1 3]

Then, we must find S.

S = [[3 0 0 1] [0 0 0 1] [0 0 1 0] [1 0 0 1]]

Notice that we don't need all the sets of lists that add up to t -- we only need one.

This problem may seem similar to the dynamic programming coin change that return an array.

Obviously, this problem can be done in brute force with time complexity of O(2^n) by going over the power set of A. Is there a more optimal solution? Is there another problem similar to this?

I am currently passing the sample tests and 2 of the other 10 cases so 4 out of 12. However, I don't make it through all of the data. I am getting a Terminated due to timeout error which means that my solution isn't fast enough.

Why does the order of the iteration loop matter here?