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Suppose, we are given a grid that has 2 rows and n columns. The grid has to be covered by n boards without one board getting over another. Now, the boards have to be colored by any one color between red, blue, and green. Two boards that are adjacent to each other cannot be colored by the same color and if not necessary, all colors do not have to be used. The configuration of the grid is given in the array 'grid', where a particular board in the grid is represented using the same English letter and different boards are ... Read More
Suppose, we are given a graph that has n vertices. The vertices are numbered 1 to n, and they are connected by the edges given in the array 'edges'. Each vertex has an 'x' value within a number from 1 to n that is given in the array 'values'. Now, we have to find out the super vertices from the graph. A vertex i is called a 'super vertex' whenever the shortest path from vertex 1 to i doesn't have a vertex with the same 'x' value as the i-th vertex. We print out all the vertices satisfying this criterion.So, ... Read More
To get the Kronecker product of two arrays, use the numpy.kron() method in Python Numpy. Compute the Kronecker product, a composite array made of blocks of the second array scaled by the first.The function assumes that the number of dimensions of a and b are the same, if necessary, prepending the smallest with ones. If a.shape = (r0, r1, .., rN) and b.shape = (s0, s1, ..., sN), the Kronecker product has shape (r0*s0, r1*s1, ..., rN*SN). The elements are products of elements from a and b, organized explicitly by −kron(a, b)[k0, k1, ..., kN] = a[i0, i1, ..., iN] ... Read More
To raise a square matrix to the power n in Linear Algebra, use the numpy.linalg.matrix_power() in Python For positive integers n, the power is computed by repeated matrix squarings and matrix multiplications. If n == 0, the identity matrix of the same shape as M is returned. If n < 0, the inverse is computed and then raised to the abs(n).The return value is the same shape and type as M; if the exponent is positive or zero then the type of the elements is the same as those of M. If the exponent is negative the elements are floating-point. ... Read More
To get the lowest cost contraction order for an einsum expression, use the numpy.einsum+path() method in Python. The 1st parameter, subscripts specify the subscripts for summation. The 2nd parameter, operands are the arrays for the operation.Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein summation operations, by disabling, or forcing summation over specified subscript labels.The resulting path indicates which terms of the input contraction should ... Read More
Suppose, we are given a grid that contains two types of cells; black cells, and white cells. The black cells are represented as '#' and the white cells are represented as '.'. The grid is given to us in an array of strings. Now, we have to perform the following.We convert each white cell to black that has a side shared with a black cell. We perform this operation until every cell of the grid is black.We count the number of iterations it takes to convert all cells of the grid to black. The grid at the start must contain ... Read More
For Tensor contraction with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein summation ... Read More
To compute outer product of vectors with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered ... Read More
Suppose, there is a building that has center coordinates xc, yc, and height h. We don't know the center coordinates of the building, but we are provided with n pieces of information that contain x and y coordinates and an altitude value a. The altitude of coordinates (x, y) is the maximum of (h - |x - xc| - |y - yc|, 0). We have to find out the center coordinates and the height of the building. The coordinate xi is given in the array x, yi is given in teg array y, and ai is given in array a.So, ... Read More
To perform scalar multiplication with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values. In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical ... Read More