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Articles by Arnab Chakraborty
Page 134 of 377
Find the number of distinct pairs of vertices which have a distance of exactly k in a tree in Python
Finding the number of distinct pairs of vertices with exactly distance k in a tree is a classic dynamic programming problem. We use DFS traversal with memoization to count paths of specific lengths from each node. Problem Understanding Given a tree with n nodes and an integer k, we need to count all distinct pairs of vertices that are exactly k edges apart. For the tree shown below with k = 2: 1 2 3 ...
Read MoreFind the number of distinct islands in a 2D matrix in Python
An island in a 2D binary matrix is a group of connected land cells (represented by 1s) surrounded by water (represented by 0s). Islands are formed by connecting adjacent lands horizontally or vertically. We can solve this problem using Depth-First Search (DFS) to mark visited land cells. Problem Visualization Consider this binary matrix with three distinct islands ? 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 The blue cells form one island, green forms ...
Read MoreFind the number of consecutive zero at the end after multiplying n numbers in Python
When multiplying numbers, trailing zeros are formed by factors of 10, which come from pairs of factors 2 and 5. To find consecutive zeros at the end of a product, we count the factors of 2 and 5 in all numbers and take the minimum count. So, if the input is like [200, 20, 5, 30, 40, 14], then the output will be 6 as 200 × 20 × 5 × 30 × 40 × 14 = 336000000, there are six 0s at the end. Algorithm Approach To solve this problem, we follow these steps: ...
Read MoreFind the missing value from the given equation a + b = c in Python
In Python, we can solve equations of the form a + b = c where one value is missing (represented by ?). This involves parsing the equation string and applying basic arithmetic to find the unknown value. For example, if the input is ? + 4 = 9, the output will be 5. Algorithm To solve this problem, we follow these steps: Remove all spaces from the string and replace + and = with commas Split the string by commas to get individual elements Find the position of the missing value (?) Apply the appropriate ...
Read MoreFind the minimum time after which one can exchange notes in Python
Suppose there are n cashiers exchanging money. At any moment, the i-th cashier has ki people waiting in line. The j-th person in line for the i-th cashier has m[i, j] notes to exchange. We need to find the minimum time required to exchange notes, given that each cashier takes 5 seconds to scan a single note and 15 seconds to complete the exchange process for each customer. Problem Understanding The total time for each cashier consists of ? Scanning time: 5 seconds × total notes for all customers Exchange time: 15 seconds × number of ...
Read MoreFind four factors of N with maximum product and sum equal to N - Set-2 in Python Program
Given a number N, we need to find four factors of N such that their sum equals N and their product is maximized. The factors can be repeated to achieve the maximum product. So, if the input is N = 60, then the output will be: All factors are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] and the maximum product is 50625, where 15 is selected four times (15 + 15 + 15 + 15 = 60 and 15 × 15 × 15 × 15 = 50625). Algorithm Steps To solve this ...
Read MoreFind pairs with given product in a sorted Doubly Linked List in Python
Finding pairs with a given product in a sorted doubly linked list is an efficient algorithm that uses the two-pointer technique. Given a sorted doubly linked list of unique positive numbers, we need to find all pairs whose product equals a target value x, without using extra space. For example, if we have a doubly linked list: 1 ⇄ 2 ⇄ 4 ⇄ 5 ⇄ 6 ⇄ 8 ⇄ 9 and target x = 8, the pairs would be (1, 8) and (2, 4). Algorithm Steps The solution uses two pointers starting from opposite ends of the ...
Read MoreFind original numbers from gcd() every pair in Python
Given an array containing GCD (Greatest Common Divisor) values of every possible pair from an original array, we need to reconstruct the original numbers. This is a reverse engineering problem where we work backwards from the GCD results. Problem Understanding If we have an original array like [13, 6], the GCD array would contain ? gcd(13, 13) = 13 gcd(13, 6) = 1 gcd(6, 13) = 1 gcd(6, 6) = 6 So the GCD array becomes [13, 1, 1, 6]. Our task is to reverse this process. Algorithm Steps The key insight ...
Read MoreFind nth term of a given recurrence relation in Python
A recurrence relation defines a sequence where each term is expressed using previous terms. Given the relation b1=1 and bn+1/bn=2n, we need to find log2(bn) for any given n. Understanding the Mathematical Solution To solve this recurrence relation, we can derive the general formula step by step ? Starting with the given relation: bn+1/bn = 2n bn/bn-1 = 2n-1 ... b2/b1 = 21 Multiplying all these equations together: (bn+1/bn) × (bn/bn-1) × ... × (b2/b1) = 2n + (n-1) + ... + 1 This simplifies to: bn+1/b1 = 2n(n+1)/2 Since b1 = 1, we ...
Read MoreFind n-th lexicographically permutation of a strings in Python
Finding the n-th lexicographically ordered permutation of a string is a classic combinatorial problem. Given a string with lowercase letters, we need to find the specific permutation that would appear at position n when all permutations are sorted alphabetically. For example, if we have string = "pqr" and n = 3, all permutations in lexicographic order are: [pqr, prq, qpr, qrp, rpq, rqp]. The 3rd permutation is "qpr". Algorithm Overview The algorithm uses factorial number system to efficiently find the n-th permutation without generating all permutations ? Precompute factorials for quick ...
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