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An overlapping area is an area that is shared by two objects. In the case of rectangles, it is the area of the rectangles that belong to both rectangles. In order to find the total areas of two overlapping rectangles, first er need to add the area of both rectangles respectively but in this total, the overlapping area is counted twice. Thus we need to subtract the overlapping area too. Problem Statement Given the bottom left and top right vertices of two rectangles. Find the total area covered by the two rectangles. Sample Example 1 Input bl_x1 = 0 bl_y1 ... Read More
The pairwise product of a set X = {a, b, c} can be defined as the sum of the product of all possible set pairs. The pairs of the set are, Y = {a * a, a * b, a *c, b * b, b * c, c * c}, where the product is commutative. Thus, the pairwise product of set X is the summation of elements of set Y i.e. aa + ab + ac + bb + bc + cc. In mathematical terms, the sum of possible pair products can be depicted as, $$\mathrm{\displaystyle\sum\limits_{i=1, j=i}^{i\leq n, j\leq n}\:(i, ... Read More
Heap Sort − Heap sort is a comparison-based algorithm that used binary tree data structures to sort a list of numbers in increasing or decreasing order. It heap sorts to create a heap data structure where the root is the smallest element and then removes the root and again sorting gives the second smallest number in the list at the root position. Min Heap − Min heap is a data structure where the parent node is always smaller than the child node, thus root node is the smallest element among all. Problem Statement Given an array of integers. Sort them ... Read More
Golomb Sequence − The Golomb Sequence is a non-decreasing sequence of integers where the value of the nth term is the number of times the integer n appeared in the sequence. Some terms of Golomb sequence are, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, … Here as we can see, the 5th term is 3 and 5 also appears 3 times in the sequence. The 6th term is 4 and 6 also appears 4 times in ... Read More
Unsorted Array − An array is a data structure consisting of a collection of elements of the same type. An unsorted array is such a structure where the order of elements is random, i.e. on insertion, the element is added to the last irrespective of the order of previous elements and searching in such an array is not helped by any search algorithm because of lack of a pattern of the positioning of elements. Searching − Searching in an array means finding a particular element in the array which can be either returning the position of a desired element or ... Read More
Fortunate Numbers − It is the smallest integer m > 1 such that, for a given positive integer n, pn# + m is a prime number, where pn# is the product of the first n prime numbers. For example, for calculating the third fortunate number, first calculate the product of the first 3 prime numbers (2, 3, 5) i.e. 30. Upon adding 2 we get 32 which is an even number, adding 3 gives 33 which is a multiple of 3. One would similarly rule out integers up to 6. Adding 7 gives, 37 which is a prime number. Thus, ... Read More
Friendly Numbers − According to number theory, friendly numbers are two or more numbers having the same abundancy index. Abundancy Index − Abundancy index of a natural number can be defined as the ratio between the sum of all the divisors of the natural number and the natural number itself. The abundancy of a number n can be expressed as $\mathrm{\frac{\sigma(n)}{n}}$ where $\mathrm{\sigma(n)}$ denotes the divisor function equal to all the divisors of n. For example, the abundancy index of the natural number 30 is, $$\mathrm{\frac{\sigma(30)}{30}=\frac{1+2+3+5+6+10+15+30}{30}=\frac{72}{30}=\frac{12}{5}}$$ A number n is said to be a ‘friendly number’ if there exists a ... Read More
Hierarchical data is often used to represent multiple levels of nested groups or categories. For example, a company may have a hierarchy of employees, departments, and locations. A product may have a hierarchy of categories and subcategories. One of the challenges of working with hierarchical data is how to represent it in a tabular format which can make it easy to manipulate and analyze. In this article, we are going to present hierarchical data using Pandas' built-in methods like 'set_index()' and 'groupby()'. Python Program to Represent Hierarchical Data using Pandas First, let's briefly discuss Pandas and its ... Read More
A sequence is a collection of objects, and in our case, it is a collection of integers. The task is to find if a sequence with the usage of the addition and subtraction operator within the elements is divisible by M or not. Problem Statement Given an integer M and an array of integers. Using only addition and subtraction between elements check if there is a valid sequence whose solution is divisible by M. Sample Example 1 Input: M = 2, arr = {1, 2, 5} Output: TRUE Explanation − For the given array a valid sequence {1 ... Read More
Finding the percentile rank is a common operation that is used for comparison between data of a single dataset. The end result of this operation shows a certain percentage is greater than or equal to the specified percentile. For instance, suppose a student obtains a score greater than or equal to 80% of all other scores. Then, the percentile rank of that student is 80th. To find the percentile rank of a column in a Pandas DataFrame, we can use the built-in methods named 'rank()' and 'percentile()' provided by Python. Python Program to find Percentile Rank of ... Read More