HackerRank Python Solution - Math Topic - Power - Mod Power

• So far, we have only heard of Python's powers. Now, we will witness them!

• Powers or exponents in Python can be calculated using the built-in power function. Call the power function a^b as shown below:

>>> pow(a,b) 

or

 

>>> a**b

It's also possible to calculate a^b mod m.

 

>>> pow(a,b,m)  

HackerRank Python Solution - Math Topic - Mod Divmod

One of the built-in functions of Python is divmod, which takes two arguments a and b, and returns a tuple containing the quotient of a/b first and then the remainder a.

For example:

 

>>> print divmod(177,10)
(17, 7)

Here, the integer division is 177/10 => 17 and the modulo operator is 177%10 => 7.

HackerRank Python Solution - Math Topic - Triangle Quest 2

• You are given a positive integer N.

• Your task is to print a palindromic triangle of size N.

• For example, a palindromic triangle of size 5 is:

1
121
12321
1234321
123454321

• You can't take more than two lines. The first line (a for-statement) is already written for you.

• You have to complete the code using exactly one print statement. 

HackerRank Python Solution - Math Topic - Find Angle MBC

• ABC is a right triangle, 90˙ at B. Therefore ∡ABC = 90˙

• Point M is the midpoint of hypotenuse AC.

• You are given the lengths AB and BC.

• Your task is to find ∡MBC (angle Ө˙, as shown in the figure) in degrees.

Input Format:

• The first line contains the length of side AB.

• The second line contains the length of side BC.

HackerRank Python Solution - Math Topic - Polar Coordinates

• Polar coordinates are an alternative way of representing Cartesian coordinates or Complex Numbers.

• A complex number z = x + yj,  is completely determined by its real part x and imaginary part y. Here, j is the imaginary unit. 

• A polar coordinate (r,φ) is completely determined by modulus r and phase angle φ.

• If we convert complex number z to its polar coordinate, we find:

• r: Distance from to origin, i.e., √ (x^2 + y^2)

• φ: Counterclockwise angle measured from the positive x-axis to the line segment that joins z to the origin. 

•  Python's cmath module provides access to the mathematical functions for complex numbers.

HackerRank Python Solution - Numpy Topic - Linear Algebra

The NumPy module also comes with a number of built-in routines for linear algebra calculations. These can be found in the sub-module linalg.

linalg.det:

The linalg.det tool computes the determinant of an array.

print numpy.linalg.det([[1 , 2], [2, 1]])       #Output : -3.0

linalg.eig:

The linalg.eig computes the eigenvalues and right eigenvectors of a square array.

HackerRank Python Solution - Numpy Topic - Polynomials

Poly:

The poly tool returns the coefficients of a polynomial with the given sequence of roots.

print numpy.poly([-1, 1, 1, 10])        #Output : [  1 -11   9  11 -10]

Roots:

The roots tool returns the roots of a polynomial with the given coefficients.

HackerRank Python Solution - Numpy Topic - Inner and Outer

Inner:

The inner tool returns the inner product of two arrays.

import numpy

A = numpy.array([0, 1])
B = numpy.array([3, 4])

print numpy.inner(A, B)     #Output : 4

HackerRank Python Solution - Numpy Topic - Dot and Cross

Dot:

The dot tool returns the dot product of two arrays.

import numpy

A = numpy.array([ 1, 2 ])
B = numpy.array([ 3, 4 ])

print numpy.dot(A, B)       #Output : 11

HackerRank Python Solution - Numpy Topic - Mean, Var, and Std

Mean:

The mean tool computes the arithmetic mean along the specified axis.

import numpy

my_array = numpy.array([ [1, 2], [3, 4] ])

print numpy.mean(my_array, axis = 0)        #Output : [ 2.  3.]
print numpy.mean(my_array, axis = 1)        #Output : [ 1.5  3.5]
print numpy.mean(my_array, axis = None)     #Output : 2.5
print numpy.mean(my_array)                  #Output : 2.5

By default, the axis is None. Therefore, it computes the mean of the flattened array.

HackerRank Python Solution - Numpy Topic - Min and Max

Min:

The tool min returns the minimum value along a given axis.

import numpy

my_array = numpy.array([[2, 5], 
                        [3, 7],
                        [1, 3],
                        [4, 0]])

print numpy.min(my_array, axis = 0)         #Output : [1 0]
print numpy.min(my_array, axis = 1)         #Output : [2 3 1 0]
print numpy.min(my_array, axis = None)      #Output : 0
print numpy.min(my_array)                   #Output : 0

By default, the axis value is None. Therefore, it finds the minimum over all the dimensions of the input array.