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Suppose we have a number N. Consider a function gcdSum(x) of a positive integer x which is the gcd of that integer with its sum of digits. We have to find the smallest integer x >= n, such that gcdSum(x) > 1.So, if the input is like N = 31, then the output will be 33, because gcd of 31 and (3+1) is 1. The gcd of 32 and (3+2) is 1, and gcd of 33 and (3+3) is 3.StepsTo solve this, we will follow these steps −for initialize i := n, when i 0, do: ... Read More
Suppose we have two arrays A and B both are with N elements each. Consider Amal and Bimal are playing a game on a board whose cell numbers are numbered from 1 to N. And N-1 roads. Roads are connecting two cells. So ith road is connecting A[i] to B[i]. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. Initially the cell 1 is marked as black color, and cell N is white. Other cells are not colored. Amal plays first, and they are playing alternatively. Amal selects an uncolored cells that is ... Read More
To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More
Suppose we have a numeric string S, and another number M. Let d be the greatest digit in S. We have to find in many different integers not greater than M can be found by choosing an integer n not less than d+1 and seeing S as a base-n number?So, if the input is like S = "999"; M = 1500, then the output will be 3, because S as base 10 number, we get 999, as base 11 number, we get 1197, as base 12 number, we get 1413. These three values are the only ones that we can ... Read More
Suppose we have an array A with n elements, and another value c is there. There is a crazy word processor present in our system where we can type characters but if we do not type for consecutive c seconds, all of the written letters will be removed. A[i] represents the time when we have typed the ith character. We have to find the final number of characters that will remain on the screen after typing all n characters.So, if the input is like A = [1, 3, 8, 14, 19, 20]; c = 5, then the output will be ... Read More
To differentiate a Laguerre series, use the laguerre.lagder() method in Python. The method returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the series 1*L_0 + 2*L_1 + 3*L_2 while [[1, 2], [1, 2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 is y.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond ... Read More
Suppose we have an array A with N elements. Have another number T. Consider Amal is trying to participate in a programming contest. It lasts for T minutes and present N problems. He has A[i] time to solve ith problem. He will choose zero or more problems to solve from the N problems, so that it takes no longer T minutes in total to solve them. We have to find the longest possible time it will take to solve his choice of problems.So, if the input is like T = 17; A = [2, 3, 5, 7, 11], then the ... Read More
To evaluate a 3-D Laguerre series on the Cartesian product of x, y and z, use the polynomial.laguerre.laggrid3d() method in Python. The method returns the values of the three dimensional Laguerre series at points in the Cartesian product of x, y and z.If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape. The 1st parameter, x, y, z are the three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If ... Read More
Suppose we have two numbers r, c and a grid of size n x m. Some cells are in black and remaining are white. In one operation, we can select some black cells and can do exactly one of these two −Color all cells in its row black, orcolor all cells in its column black.We have to find the minimum number of operations needed to make the cells in row r and column c black. If impossible, return -1.So, if the input is likeWBWWWBBBWBWWBBBr = 0 and c = 3then the output will be 1, because we can change the ... Read More
To evaluate a 2-D Laguerre series on the Cartesian product of x and y, use the polynomial.laguerre.laggrid2d() method in Python. The method returns the values of the two dimensional Laguerre series at points in the Cartesian product of x and y.If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape. The 1st parameter, x, y is the two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a list ... Read More