To save the images in Python with very high quality, you need to follow the steps given below −Create fig and ax variables using subplots method, where default nrows and ncols are 1.Plot the lines using plot() method.We can add axes labels using ylabel() and xlabel().To get a high-quality image, we can use .eps image format.You can increase the dot per inch value, i.e., dpi.Using savefig() method, we can save the image locally.To show the figure, use plt.show().Exampleimport matplotlib.pyplot as plt fig, ax = plt.subplots() plt.plot([0, 5], [0, 5]) plt.ylabel("Y-axis ") plt.xlabel("X-axis ") image_format = 'eps' ... Read More

To shift the Y-axis ticks from left to right, we can perform the following steps −Create a figure using the figure() method.Using the above figure method, create the axis of the plot, using add_subplot(xyz), where x is row, y is column, and z is index.To shift the Y-axis ticks from left to right, use ax.yaxis.tick_right() where ax is axis created using add_subplot(xyz) method.Now plot the line using plot() method, with given x and y points, where x and y points can be created using np.array() method.Set up x and y labels, e.g., X-axis and Y-axis , using xlabel and ylabel ... Read More

In this problem, we are given an integer N. Our task is to create a program to Find Nth term of series 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8…Let’s take an example to understand the problem, InputN = 7Output4Solution ApproachA simple approach to solve the problem is using a loop to find the term at the nth position. The terms will be updated by doubling after each iteration. And adding it to the term counter.Program to illustrate the working of our solution, Example#include using namespace std; int calcNthTerm(int N) {   ... Read More

In this problem, we are given an integer N. Our task is to create a program to Find Nth term of series 0, 2, 4, 8, 12, 18…Let’s take an example to understand the problem, InputN = 5Output12Solution ApproachA simple approach to solve the problem is the formula for the Nth term of the series. For this, we need to observe the series and then generalise the Nth term.The formula of Nth term isT(N) = ( N + (N - 1)*N ) / 2Program to illustrate the working of our solution, Example Live Demo#include using namespace std; int calcNthTerm(int N) ... Read More

In this problem, we are given an integer N. Our task is to create a program to Find Nth term of series 1, 4, 15, 72, 420…Let’s take an example to understand the problem, InputN = 4Output72Solution ApproachA simple approach to solve the problem is the formula for the Nth term of the series. For this, we need to observe the series and then generalise the Nth term.The series can be seen as the product of factorial and a some variables, 1, 4, 15, 72, 420… 1!*(X1), 2!*(X2), 3!*(X3), 4!*(X4), 5!*(X5)... 1*(1), 2*(2), 6*(5/2), 24*(3), 120*(7/2)...Here, the series of product ... Read More

In this problem, we are given an integer N and a recursive function that given Nth term as a function of other terms. Our task is to create a program to Find Nth term (A matrix exponentiation example).The function isT(n) = 2*( T(n-1) ) + 3*( T(n-2) ) Initial values are    T(0) = 1 , T(1) = 1Let’s take an example to understand the problem, InputN = 4Output41ExplanationT(4) = 2* (T(3)) + 3*(T(2)) T(4) = 2* ( 2*(T(2)) + 3*(T(1)) ) + 3*( 2* (T(1)) + 3*(T(0)) ) T(4) = 2*( 2*(2* (T(1)) + 3*(T(0))) + 3*(1) ) + ... Read More

In this problem, we are given two integer values N and X. Our task is to create a program to Find Nth positive number whose digital root is X.Digital Root (X) is a single digit positive number which is found by adding digits of N recursively adding digits, till the sum becomes single digit.Let’s take an example to understand the problem, InputN = 5, X = 4Output40Solution ApproachA simple way to solve the problem is by counting the numbers with a digital root is X. For this, we will start from 1 and then check if the current number’s digital ... Read More

In this problem, we are given an integer value N. Our task is to create a program to Find Nth number of the series 1, 6, 15, 28, 45, …In the series, every element is 2 less than the mean of the previous and next element.Let’s take an example to understand the problem, InputN = 5Output45Solution ApproachThe Nth term of the series 1, 6, 15, 28, 45, … can be found using the formula, TN = 2*N*N - NProgram to illustrate the working of our solution, Example Live Demo#include using namespace std; #define mod 1000000009 int calcNthTerm(long n) {   ... Read More

In this problem, we are given an integer value N. Our task is to create a program to Find nth Hermite number.Hermite Number is a number is the value of hermite number when there are 0 arguments.Nth hermite Number is HN = (-2) * (N - 1) * H(N-2) The base values are H0 = 1 and H0 = 0.The hermite sequence is − 1, 0, -2, 0, 12, 0, -120, 0, 1680, 0….Let’s take an example to understand the problem, InputN = 7Output0InputN = 6Output-120Solution ApproachA simple solution to the problem is using the formula for hermite number. This ... Read More

In this problem, we are given an integer value N. our task is to create a program to find the next spares Number.Sparse Number is a special type of number whose binary conversion does not contain any adjacent 1’s.Example: 5(101) , 16(10000)Problem Description − For the given number N, we need to find the smallest number greater than N which is a sparse number.Let’s take an example to understand the problem, InputN = 7Output8ExplanationThe binary of 8 is 1000 which makes it the smallest sparse number greater than n.Solution ApproachA simple solution to the problem is checking for all numbers ... Read More