My Board My Chalk

“You are given two matrices A and B, each with R rows (numbered 1 through R) and C columns (numbered 1 through C). Let’s denote an element of A or B in row i and column j by A(i,j) or B(i,j) respectively….. ” You can read the whole problem here . Problem description in short Given two matrices, A and B. Task is to transform A to B using special some addition-based criteria. The criteria for transformation is as follows we are given a number K 2 ≤ K ≤ min(R, C), where R is row size and C is column size we have to take any submatrix of size Kx1 (i.e. along the column) or 1xK (i.e. along the row), in A, and to all the numbers that fall under that submatrix have, add some integer v, this can be chosen by us. This has to be done in such a way that finally A transforms to B. The actual problem is to check if this kind of transformation is possible, given A and B. Ideation…. Befor e  I begin I wanna say that it is an observation based problem, can have many solutions and my solution is not pe

 There are a few grouping styles that are common in competitive programming to optimise the solution time complexity. Grouping by the powers of 2 Grouping by a fixed bracket size Out of these two, the second one has a special group size, i.e. make the fixed bracket size equal to the Square Root of input size, N. Solving techniques like Square Root decomposition, are actually based upon this grouping style. For example, you want to compute some property for a subarray that can be calculated using N² complexity only. But if you could figure-out some special property that allows you to merge two blocks of the same array, you can compute for √N size block then, merge √N blocks using the merging technique. But this article is actually not about square root and square root decompositions. The problem, I want to address here is related to streaming input, i.e. some query oriented problem that adds a new element to the existing set of input and asks us some result of a query. Something like th

  This article is in continuation of  this one . R ecap In the  previous article , I had tried to emphasize how nᵗʰ Fibonacci Number = Number of ways to climb n step staircase, where you have only two possible options to move, either by climbing 1 step or 2 steps at a time. In the same article, I have mentioned some other  p ossible representations of the Fibonacci Sequence. One of them is the number of ways to tile a N x 1 board with a 1 x 1 square and 2 x 1 domino. By writing the recurrence relation for the same, we can state that NoOfWaysToTile(n) = nᵗʰ Fibonacci Number. Recurrence for the Tiling problem Tiling Problem Relation and Fibonacci Number Reversing the above Equation In this article, I am going to discuss my approach to the Running Sum Identity of the Fibonacci Sequence using the same relation. The Running Sum of Fibonacci Sequence The Left Hand Side (L.H.S.) The L.H.S. of the equation has 2 parts  Fib(n)  and  (- 1) . Fib(n) = nᵗʰ Fibonacci Number = No of ways to tile n x