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Articles by Arnab Chakraborty
Page 354 of 377
Reordered Power of 2 in C++
Suppose we have a positive integer N, we reorder the digits in any order (including the original order) such that the leading digit is non-zero. We have to check whether we can do this in a way such that the resulting number is a power of 2. So if the number is like 46, then the answer will be true.To solve this, we will follow these steps −Define a method called count, this will take x as inputret := 0while x is not 0ret := ret + 10 ^ last digit of xx := x / 10return retFrom the main ...
Read MoreStatic Finger Theorem in Data Structure
STATIC FINGER THEOREM − Let f is treated as a specific element called the finger.Then the below expression is a bound on the cost of splaying a sequenceO(m + n log(n) + Σ Sum log (|f - i[j]| + 1))jNOTE − |f-i| is denoted as the distance in the symmetric ordering of the items between the finger and item i.Where m is denoted as number of update or access operations on a tree having at most n nodes.Observe that, at least in amortized sense, the time taken for first m operations on a tree that never exceeds more than n ...
Read MoreSymmetric Min-Max Heaps
A symmetric min-max heap (SMMH) is defined as a complete binary tree in which each node except the root has exactly one element. The root of an SMMH be empty and the total number of nodes in the SMMH is m + 1, where m is the number of elements.Let y be any node of the SMMH. Let elements(y) be the elements in the sub tree rooted at y but excluding the element (if any) in y. Assume that elements(y) j= ∅. y satisfies the following properties:The left child of y has the minimum element in elements(y).The right child of ...
Read MoreFind the final X and Y when they are Altering under given condition in C++
Consider we have the initial values of two positive integers X and Y. Find the final value of X and Y, such that there will be some alteration as mentioned below −step1 − If X = 0 and Y = 0 then terminate the process, otherwise go to step2step2 − If X >= 2Y, then set X = X – 2Y, and go to step1, otherwise go to step3step3 − If Y >= 2X, then set Y = Y – 2X, and go to step1, otherwise end the process.The number X and Y will be in range [0 and 1018] ...
Read MoreSingle-Source Shortest Paths, Nonnegative Weights
The single source shortest path algorithm (for non-negative weight) is also known Dijkstra algorithm. There is a given graph G(V, E) with its adjacency matrix representation, and a source vertex is also provided. Dijkstra’s algorithm to find the minimum shortest path between source vertex to any other vertex of the graph G.From starting node to any other node, find the smallest distances. In this problem the graph is represented using the adjacency matrix. (Cost matrix and adjacency matrix is similar for this purpose).Input − The adjacency matrix −0 3 6 ∞ ∞ ∞ ∞ 3 0 2 1 ∞ ∞ ...
Read MoreNumber of Paths with Max Score in C++
Suppose we have a square board of characters. We can move on the board starting at the bottom right square marked with the character 'S'. Now we need to reach the top left square marked with the character 'E'. The other squares are labeled either with a numeric character from 1 to 9 or with an obstacle 'X'. In one move we can go up, left or up-left only when there is no obstacle there.We have to find the list of two numbers: the first number is the maximum sum of the numeric characters we can collect, and the second ...
Read MoreBinary Tree Cameras in C++
Suppose we have a binary tree; we place cameras on the nodes of the tree. Now each camera at a node can monitor its parent, itself, and its children. We have to find the minimum number of cameras needed to monitor all nodes of the tree.So, if the input is like −then the output will be 1, because only one camera is enough to track all.To solve this, we will follow these steps −Define one set called covered, of type TreeNode (Tree node has left, right and data field)Define a function solve(), this will take node, parent, if node is ...
Read MoreStream of Characters in C++
Suppose we want to implement the StreamChecker class as follows −StreamChecker(words) − This is the constructor, this initializes the data structure with the given words.query(letter) − This returns true when for some k >= 1, the last k characters queried (in order from oldest to newest, including this letter just queried) spell one of the words in the given list.So, if the input is like word list = ["ce", "g", "lm"], then call query many times for [a, b, c, e, f, g, h, i, j, k, l, m], then the output will be true for e, g, m, and ...
Read MoreBrace Expansion in C++
Suppose we have a string S that represents a list of words. Here each letter in the word has 1 or more options. If there is only one option, the letter is represented as is. If there is more than one option, then curly braces delimit the options. So for example, "{a, b, c}" will represent the options ["a", "b", "c"]. Now for example, if the input is like "{a, b, c}d{e, f}" this will represent the list ["ade", "adf", "bde", "bdf", "cde", "cdf"]. Return all words that can be formed in this manner, in lexicographical order. To ...
Read MoreReveal Cards In Increasing Order in C++
Suppose we have a deck of cards; every card has a one unique number. We can order the deck in any order that we want. So Initially, all the cards start face down (unrevealed) in one deck. Now, we do the following steps multiple times, until all cards are revealed − Take the top card off the deck, reveal it, and answer with it. If there are still cards in the deck, then put the next top card of the deck at the bottom of the deck. If there are still unseen cards, go back to step 1. Otherwise, ...
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