Suppose, we are given an unweighted, undirected graph that contains n vertices and m edges. A bridge edge in a graph is an edge whose removal causes the graph to be disconnected. We have to find out the number of such graphs in a given graph. The graph does not contain parallel edges or self-loops.So, if the input is like n = 5, m = 6, edges = {{1, 2}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {3, 5}}, then the output will be 1.The graph contains only one bridge edge that is {2, 4}.To solve this, we will ... Read More

To return the cumulative product of array elements over a given axis treating NaNs as one, use the nancumprod() method. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones. Ones are returned for slices that are all-NaN or empty.The method returns a new array holding the result is returned unless out is specified, in which case it is returned. Cumulative works like, 5, 5*10, 5*10*15, 5*10*15*20. The 1st parameter is the input array. The 2nd parameter is the Axis along which the cumulative product is computed. By default the input is flattened.The ... Read More

To return the cumulative product of array elements over a given axis treating NaNs as one, use the nancumprod() method. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones. Ones are returned for slices that are all-NaN or empty. The method returns a new array holding the result is returned unless out is specified, in which case it is returned.Cumulative works like, 5, 5*10, 5*10*15, 5*10*15*20. The 1st parameter is the input array. The 2nd parameter is the Axis along which the cumulative product is computed. By default the input is flattened. ... Read More

Suppose, we are given a grid of dimensions h x w. There are two types of cells in the grid, white and black cells. White cells are represented by '.', whereas black cells are represented by '#'. Now the grid has multiple black cells in it that form a polygon. We have to find out the number of sides that the polygon has. It is to be noted, that the outermost cells of the grid are always white.So, if the input is like h = 4, w = 4, grid = {"....", ".##.", ".##.", "...."}, then the output will be ... Read More

Given two tensors, a and b, and an array_like object containing two array_like objects, (a_axes, b_axes), sum the products of a’s and b’s elements (components) over the axes specified by a_axes and b_axes. The third argument can be a single non-negative integer_like scalar, N; if it is such, then the last N dimensions of a and the first N dimensions of b are summed over.To compute the tensor dot product for arrays with different dimensions, use the numpy.tensordot() method. The a, b parameters are Tensors to “dot”. The axes parameter, integer_like If an int N, sum over the last N ... Read More

Suppose, we are given n numbers in array nums. We have to choose a pair of two numbers from the array, and there is a condition that the difference of their positions in the array is equal to the sum of the two numbers. There can be a total of n(n - 1)/2 number of total pairs from the given array of numbers. We have to find out the total number of such pairs from the array.So, if the input is like n = 8, nums = {4, 2, 1, 0, 1, 2, 3, 3}, then the output will be ... Read More

Given two tensors, a and b, and an array_like object containing two array_like objects, (a_axes, b_axes), sum the products of a’s and b’s elements (components) over the axes specified by a_axes and b_axes. The third argument can be a single non-negative integer_like scalar, N; if it is such, then the last N dimensions of a and the first N dimensions of b are summed over.To compute the tensor dot product, use the numpy.tensordot() method in Python. The a, b parameters are Tensors to “dot”. The axes parameter, integer_like If an int N, sum over the last N axes of a ... Read More

To get the Inner product of two arrays, use the numpy.inner() method in Python. Ordinary inner product of vectors for 1-D arrays, in higher dimensions a sum product over the last axes. The parameters are 1 and b, two vectors. If a and b are nonscalar, their last dimensions must match.StepsAt first, import the required libraries −import numpy as npCreating two numpy One-Dimensional array using the array() method −arr1 = np.arange(2).reshape((1, 1, 2)) arr2 = np.arange(6).reshape((3, 2))Display the arrays −print("Array1...", arr1) print("Array2...", arr2)Check the Dimensions of both the arrays −print("Dimensions of Array1...", arr1.ndim) print("Dimensions of Array2...", arr2.ndim)Check the Shape of ... Read More

To get the Outer product of an array and a scalar, use the numpy.outer() method in Python. The 1st parameter a is the first input vector. Input is flattened if not already 1-dimensional. The 2nd parameter b is the second input vector. Input is flattened if not already 1-dimensional. The 3rd parameter out is a location where the result is stored.Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product is −[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]StepsAt first, import the required ... Read More

Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product is −[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]To get the Outer product of an array with vector of letters, use the numpy.outer() method in Python. The 1st parameter a is the first input vector. Input is flattened if not already 1-dimensional. The 2nd parameter b is the second input vector. Input is flattened if not already 1-dimensional. The 3rd parameter out is a location where the result is storedStepsAt first, import ... Read More