Programming Articles - Page 843 of 3363

In this article, we will describe the important information on solving the number of sinks nodes in a graph. We have a Directed Acyclic Graph with N nodes (1 to N) and M edges in this problem. The goal is to find how many sink nodes are there in the given graph. A sink node is a node that does not produce any outgoing edges. So here is a simple example −Input : n = 4, m = 2 Edges[] = {{2, 3}, {4, 3}} Output : 2Simple Approach to Find the SolutionIn this approach, we will go through ... Read More

In this article, we will provide complete information to determine the number of siblings of a given node in the n-ary tree. We need to find the node's siblings with the value of key as given by the user; if it is non, then output as -1. There is only one approach that we can use −Simple ApproachIn this approach, we will go through all the nodes and check if a child has the same value as the user. If it exists, we answer a number of children - 1(the given value).Example #include using namespace std; class Node { ... Read More

The linear function named scipy.linalg.solveh_triangular is used to solve the banded matrix equation. In the below given example we will be solving the triangular system ax = b where −$$\mathrm{a} = \begin{bmatrix} 3 & 0 & 0 & 0\ 2 & 1 & 0 & 0\ 1 &0 &1 &0 \ 1& 1& 1& 1 \end{bmatrix};\; \mathrm{b} =\begin{bmatrix} 1\ 2\ 1\ 2 \end{bmatrix}$$Examplefrom scipy.linalg import solve_triangular import numpy as np a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]]) b = np.array([1, 2, 1, 2]) x = solve_triangular(a, b, lower=True) print (x)Outputarray([ 0.33333333, 1.33333333, 0.66666667, -0.33333333])

The linear function named scipy.linalg.solve_triangular is used to solve the triangular matrix e8quation. The form of this function is as follows −scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, debug=None, check_finite=True)This linear function will solve the equation ax = b for x where a is a triangular matrix.P ParametersBelow are given the parameters of the function scipy.linalg.solve_triangular() −a− (M, M) array_likeThis parameter represents the triangular matrix.b− (M, ) or (M, N)array_likeThis parameter represents the right-hand side matrix in the equation ax = b.lower− bool, optionalBy using this parameter, we will be able to use only the data that is contained in the ... Read More

The linear function named scipy.linalg.solveh_banded is used to solve the banded matrix equation. In the below given example we will be solving the circulant system Cx = b −Examplefrom scipy.linalg import solve_circulant, solve, circulant, lstsq import numpy as np c = np.array([2, 2, 4]) b = np.array([1, 2, 3]) solve_circulant(c, b)Output array([ 0.75, -0.25, 0.25])ExampleLet’s see a singular example, it will raise an LinAlgError −from scipy.linalg import solve_circulant, solve, circulant, lstsq import numpy as np c = np.array([1, 1, 0, 0]) b = np.array([1, 2, 3, 4]) solve_circulant(c, b)Output -------------------------------------------------------------------------- LinAlgError Traceback (most recent call last) in ... Read More

The linear function named scipy.linalg.solve_circulant is used to solve the circulant matrix equation. The form of this function is as follows −scipy.linalg.solve_circulant(c, b, singular=’raise’, tol=None, caxis=-1, baxis=0, outaxis=0)This linear function will solve the equation Cx = b for x where C is a Circulant matrix associated with the vector c.The circulant matrix equation is solved by doing division in Fourier space as follows −x = ifft(fft(b) / fft(c))Here fft is the fast Fourier transform and ifft is the inverse fast Fourier transform.ParametersBelow are given the parameters of the function scipy.linalg.solve_circulant() −c− array_likeThis parameter represents the coefficient of the circulant matrix.b− ... Read More

The linear function named scipy.linalg.solveh_banded is used to solve the banded matrix equation. In the below given example we will be solving the banded system Hx = b where −$$\mathrm{H} = \begin{bmatrix} 8 & 2-1j&0 &0 \ 2+1j & 5& 1j & -2-1j0\ 0 & -1j& 9& \ 0 & 0& -2+1j& 6 \end{bmatrix} \mathrm{b}=\begin{bmatrix} 1\ 1+1j\ 1-2j\ 0 \end{bmatrix}$$For our example below, we will be putting the upper diagonal in the array hb −Examplefrom scipy.linalg import solveh_banded hb = np.array([[0, 2-1j, 1j, -2-1j],  [8, 5, 9, 6 ]]) b = np.array([1, 1+1j, 1-2j, 0]) x = solveh_banded(hb, b) ... Read More

In this article, we have to find the number of segments or subarrays in a given sequence where elements greater than the given number X.We can count overlapping segments only once, and two contiguous elements or segments should not count separately. So here is the basic example of the given problem −Input : arr[ ] = { 9, 6, 7, 11, 5, 7, 8, 10, 3}, X = 7 Output : 3 Explanation : { 9 }, { 11 } and { 8, 10 } are the segments greater than 7 Input : arr[ ] = { 9, 6, ... Read More

In this article, we will explain the approaches to find the number of reflexive relations on a set. In this problem, we are given with number n, and on a set of n natural numbers, we must determine the number of reflexive relations.Reflexive Relation − A relation in a set A is called reflexive if ( a, a ) belongs to R for every 'a' belongs to set A. For example −Input : x = 1 Output : 1 Explanation : set = { 1 }, reflexive relations on A * A : { { 1 } } Input ... Read More

The linear function named scipy.linalg.solveh_banded is used to solve Hermitian positive-definite banded matrix equations. The form of this function is as follows −scipy.linalg.solveh_banded(ab, b, overwrite_ab=False, overwrite_b=False, lower=False, check_finite=True)This linear function will solve the equation ax = b for x where a is Hermitian positivedefinite banded matrix.The banded matrix a is stored in ab in lower or upper diagonal ordered form as follows −ab[u + i - j, j] == a[i, j] (if upper form; i= j)The example of ab in the upper form is given as follows − *    *   a02   a13   a24  a35 * ... Read More