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Articles by Arnab Chakraborty
Page 110 of 377
Succinct Encoding of Binary Tree in C++
Suppose we have a binary tree. As we know the succinct encoding of Binary Tree performs close to lowest possible space. The n’th Catalan number is designated by the number of structurally different binary trees with n different nodes. If the n is large, this is about 4n; thus, we require minimum about log2(4) n = 2n bits to encode it. A succinct binary tree therefore would consume 2n + O(n) bits.So, if the input is likethen the output will beencoded −Structure List 1 1 1 0 0 1 0 0 1 0 1 0 0Data List 10 20 40 ...
Read MoreUnique element in an array where all elements occur k times except one in C++
we have an array A. A has all elements occurring m times, but one element occurs only once. We have to find that unique element.So, if the input is like A = [6, 2, 7, 2, 2, 6, 6], m = 3, then the output will be 7.To solve this, we will follow these steps −INT_SIZE := 8 * size of an integer type variableDefine an array count of size: INT_SIZE. and fill with 0for initialize i := 0, when i < INT_SIZE, update (increase i by 1), do −for initialize j := 0, when j < size, update (increase ...
Read MoreMaximum Consecutive Increasing Path Length in Binary Tree in C++
Suppose we have a binary tree; we have to calculate the length of the longest path which consists of nodes with consecutive values in increasing order. Every node will be treated as a path of length 1.So, if the input is likethen the output will be 3 as (11, 12, 13) is maximum consecutive path.To solve this, we will follow these steps −Define a function solve(), this will take root, prev_data, prev_length, if not root is non-zero, then −return prev_lengthcur_data := val of rootif cur_data is same as prev_data + 1, then −return maximum of solve(left of root, cur_data, prev_length+1) ...
Read MoreMinimum Cost Path with Left, Right, Bottom and Up moves allowed in C++
Suppose we have a 2D array. Where each cell of which consists number cost which represents a cost to visit through that cell, we have to find a path from top-left cell to bottom-right cell by which total cost consumed is minimum.So, if the input is like32101661319111448158710111141751234891254221141100331124221then the output will be 340 as (32 + 11 + 14 + 48 + 66 + 13 + 19 + 7 + 34 + 12 + 21 + 42 + 21) = 340To solve this, we will follow these steps −Define cell with x, y coordinate and distance parameter.Define an array matrix of ...
Read MoreMinimum Cost to cut a board into squares in C++
ConceptSuppose a board of length p and width q is given, we require to break this board into p*q squares such that cost of breaking is least. For this board, cutting cost for each edge will be given. In a nutshell, we require selecting such a sequence of cutting such that cost is minimized.Examples With respect of above board optimal way to cut into square is −Total minimum cost in above case is 65. It is computed evaluated implementing following steps.Initial Value : Total_cost = 0 Total_cost = Total_cost + edge_cost * total_pieces Cost 5 Horizontal cut Cost = 0 + ...
Read MoreMinimum Cuts can be made in the Chessboard such that it is not divided into 2 parts in C++
ConceptGiven A x B Chessboard, the task is to calculate the Maximum numbers of cuts that we can build in the Chessboard so that the Chessboard is not divided into 2 parts.Examples The examples are given below −Input A = 2, B = 4Output Number of maximum cuts = 3Input A = 2, B = 2Output Number of maximum cuts = 1MethodFor A = 2, B = 2 ,we can only build 1 cut (mark in red). If we build 1 more cut then the chessboard will divide into 2 piecesFor A = 2, B = 4 ,we can makes 3 cuts (marks in red). ...
Read MoreMinimum edges required to add to make Euler Circuit in C++
ConceptWith respect of a given undirected graph of b nodes and a edges, the job is to determine minimum edges needed to build Euler Circuit in the given graph.Input b = 3, a = 2 Edges[] = {{1, 2}, {2, 3}}Output 1By connecting 1 to 3, we can build a Euler Circuit.MethodWith respect of a Euler Circuit to exist in the graph we need that every node should haveeven degree because then there exists an edge that can be applied to exit the node after entering it.Now, there can be two cases −Existence of one connected component in the graphWith respect of ...
Read MoreMinimum removals from array to make GCD Greater in C++
ConceptWith respect of given N numbers, the target is to determine the minimum removal of numbers such that GCD of the remaining numbers is larger than initial GCD of N numbers. If it is impossible to increase the GCD, print “NO”.Input b[] = {1, 2, 4}Output1After removing the first element, then the new GCD is 2, which is larger than the initialGCD i.e., 1.Input b[] = {6, 9, 15, 30}Output 3The initial gcd is 3, after removing 6 and 9 to obtain a gcd of 15 which is larger than 3. We can also remove 9 and 15 to get a gcd of ...
Read MoreFind a pair from the given array with maximum nCr value in C++
ConceptWith respect of given an array arr[] of n positive integers, the task is to determineelements arr[i] and arr[j] from the array such that arr[i]Carr[j] is at most possible. With respect of more than 1 valid pairs, print any one of them.Input arr[] = {4, 1, 2}Output 4 2 4C1 = 4 4C2 = 4 2C1 = 4 (4, 2) is the only pairs with maximum nCr.MethodnCr is treated as a monotonic increasing function, that is n+1Cr > nCr. We can apply this fact to get close to our answer; we will select the max n among all the given integers. In ...
Read MoreFind the largest Complete Subtree in a given Binary Tree in C++
ConceptWith respect of a given Binary Tree, the task is to determine the size of maximum complete sub-tree in the given Binary Tree.Complete Binary Tree – A Binary tree is treated as Complete Binary Tree if all levels are completely filled without possibly the last level and the last level has all keys as left as possible.It has been noted that all Perfect Binary Trees are Complete Binary tree but reverse in NOT true. It has been seen that if a tree is not complete then it is also not Perfect Binary Tree.Input 2 / \ ...
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