# Category: PROGRAMMING

## LeetCode : Maximum Gap

Problem Statement Solution : There were many different approaches that were coming to my mind while beginning to solve the problem, but all of them were non-linear space/time complexities. One thing that I realized was that, if there was some generic O(N) approach that enables us to find difference between any two consecutive numbers in the sorted array, then sorting the numbers itself would be linear. But that is not […]

## LeetCode : Cutoff Trees for Golf

Problem Statement Solution : My solution in Python for this problem is not accepted as of yet due to "Time Limit Exceeded". There is no trick that reduces the worst case time complexity for this problem. The straightforward approach is to first sort the tree heights smallest to largest (ignoring the tree heights with height < 1) and then for each successive pair (A, B) of sorted tree heights, do […]

## LeetCode : Largest Rectangle in Histogram

Problem Statement Solution : At first glance, one can say that a brute force approach would take time complexity. That is correct. Let me begin first with the brute force approach explanation. In order to find the largest rectangle possible, scan each of the unit one rectangle (i.e. the heights given in the input array) and then for each such rectangle i compute the maximum possible width it can be […]

## LeetCode : Smallest Rotation with Highest Score

Problem Statement Solution : As we can see that, we can easily come up with a solution. Rotate the array each time and compute the score. There are N possible rotations for an array of size N, and for each rotated position, computing the score for the array takes O(N) time complexity. Since the approach is very easy, we will not code this approach but will explore whether we can […]

## LeetCode : Dungeon Game

Problem Statement Solution : This problem is probably towards high medium difficulty level but below the hard level of problems. At one glance, one can conclude that we can solve this problem using the dynamic programming technique and it is correct. The only difficulty is in identifying what value to memoize at each step during the King's journey towards the Princess. So this is how it works. The initial health […]

## LeetCode : K Inverse Pairs Array

Problem Statement Solution : One of the strong heuristics that I generally use for solving counting problems in programming is that it is most likely a dynamic programming problem and most of the cases it is true, since most such counting problems can be defined recursively. In this problem, of counting the number of k-inverse pairs in an array of size 'n' (from 1 to n) can be defined recursively. […]

## Dynamic Programming in NLP - Longest Common Subsequence

In this second part of the series on my posts on Dynamic Programming in NLP, I will be showing how to solve the Longest Common Subsequence problem using DP and then use modified versions of the algorithm to find out the similarity between two strings. LCS is a common programming question asked in many technical interviews. Given two strings (sequence of words, characters etc.) S1 and S2, return the number […]

## Dynamic Programming in NLP - Skip Grams

In this series of posts, I will be exploring and showing how dynamic programming technique is used in machine learning and natural language processing. Dynamic programming is very popular in programming interviews. DP technique is used mainly in problems which has optimal substructure and can be defined recursively, which means that a problem of size N can be solved by solving smaller sub-problems of size m < N. Such problems […]

## LeetCode : Cherry Pickup

Problem Statement Solution : This problem is probably one of the most difficult path traversal problem, I have seen on LeetCode and I will let you know the reason why. The most faulty assumption to begin with is that, this can be solved using a greedy approach, i.e. find the maximum possible cherries during the forward traversal (0,0) to (N-1, N-1) and then find the maximum possible cherries during the […]

## LeetCode : Reaching Points

Problem Statement Solution : The obvious way is to go with a DFS or BFS like approach. Starting from the point (sx, sy), we can go in two possible directions (sx + sy, sy) and (sx, sx + sy) and then each of these points can go in two possible directions and so on. Note that the paths will form a tree like structure as we are going in either […]