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Suppose we have a number n, we have to find the number of ways we can fill a (3 x n) block with 2 x 1 dominos. We can rotate the dominos when required. If the answer is very large then return this mod 10^9 + 7. For example, if the input is n = 4, then the output will be 11. Algorithm To solve this problem, we need to use dynamic programming. The key insight is that we can only fill a 3×n grid if n is even, because each domino covers 2 cells. We ... Read More
Given four numbers n, a, b, and c, we need to find the nth (0-indexed) term of the sorted sequence of numbers divisible by a, b, or c. For example, if n = 8, a = 3, b = 7, c = 9, the first 9 terms of the sequence are [3, 6, 7, 9, 12, 14, 15, 18, 21], so the 8th term (0-indexed) is 18. Approach We use binary search with the inclusion-exclusion principle to count numbers divisible by a, b, or c up to a given value ? If minimum of a, ... Read More
Given a list of unique numbers, we need to find the largest subset where every pair of elements satisfies the divisibility condition: either i % j = 0 or j % i = 0. This means one element must divide the other in every pair. For example, if the input is nums = [3, 6, 12, 24, 26, 39], the output will be 4 because the largest valid subset is [3, 6, 12, 24] where 6 is divisible by 3, 12 is divisible by 6, and 24 is divisible by 12. Algorithm We use dynamic programming with ... Read More
Finding sublists that contain exactly k different words is a common problem in data analysis and text processing. We can solve this using the sliding window technique with a helper function approach. Problem Understanding Given a list of words and a value k, we need to count all sublists (contiguous subarrays) that contain exactly k distinct words. For example, with words = ["Kolkata", "Delhi", "Delhi", "Kolkata"] and k = 2, we find 5 sublists with exactly 2 unique words ? ["Kolkata", "Delhi"] ["Delhi", "Kolkata"] ["Kolkata", "Delhi", "Delhi"] ["Delhi", "Delhi", "Kolkata"] ["Kolkata", "Delhi", "Delhi", "Kolkata"] ... Read More
In network communication, messages propagate through nodes with varying transmission times. This problem finds the minimum time needed for a message starting at node 0 to reach all nodes in an undirected network graph. Given n nodes labeled 0 to n, and edges in the form (a, b, t) where t is the transmission time between nodes a and b, we need to find how long it takes for every node to receive the message. Problem Analysis If the input is n = 3 and edges = [[0, 1, 3], [1, 2, 4], [2, 3, 2]], the ... Read More
Suppose we have a list of words called dictionary and we have another two strings start and end. We want to reach from start to end by changing one character at a time and each resulting word should also be in the dictionary. Words are case-sensitive. So we have to find the minimum number of steps it would take to reach at the end. If it is not possible then return -1. So, if the input is like dictionary = ["may", "ray", "rat"] start = "rat" end = "may", then the output will be 3, as we can select ... Read More
In graph theory, an odd-length cycle is a cycle that contains an odd number of vertices. To detect such cycles in an undirected graph, we can use Depth-First Search (DFS) with path tracking to identify back edges that form odd cycles. Problem Understanding Given an undirected graph represented as an adjacency list, we need to determine if there exists any cycle with an odd number of vertices. For example, cycles like [1, 3, 4] (length 3) or [0, 1, 3, 4, 2] (length 5) are odd-length cycles. 0 ... Read More
Suppose we have a list of distinct values and we want to remove each number in non-decreasing order. We have to find the indices of numbers in order of their deletion. So, if the input is like nums = [4, 6, 2, 5, 3, 1], then the output will be [5, 2, 3, 0, 1, 0]. We delete 1 (at index 5), so array becomes [4, 6, 2, 5, 3], then remove 2 (at index 2), array becomes [4, 6, 5, 3], then remove 3 (at index 3) to get [4, 6, 5], then remove 4 (at index 0) ... Read More
Adding tints to grayscale images involves manipulating the RGB channel values to create color effects. In scikit-image (part of the scikit-learn ecosystem), we convert grayscale images to RGB format and apply color multipliers to achieve different tints. Required Libraries First, let's import the necessary modules ? import matplotlib.pyplot as plt from skimage import data, color from skimage import io import numpy as np Loading and Converting Image We'll use a sample image from scikit-image's dataset and convert it to grayscale ? # Load sample image (you can replace with your own ... Read More
Data preprocessing is a crucial step in machine learning that involves cleaning data, removing noise, and transforming raw data into a suitable format. When working with images, preprocessing often includes loading, viewing, and manipulating image data using libraries like scikit-image. The scikit-image library (skimage) provides powerful tools for image processing in Python. It integrates well with NumPy arrays and offers functions to read, display, and process images efficiently. Loading and Displaying an Image Here's how to upload and view an image using scikit-image ? from skimage import io import matplotlib.pyplot as plt # Load ... Read More