HackerRank Python Solution - Itertools Topic - itertools.permutations()

itertools.permutations(iterable[, r]):

• This tool returns successive length permutations of elements in an iterable.

• If r is not specified or is None, then r defaults to the length of the iterable, and all possible full-length permutations are generated.

• Permutations are printed in a lexicographic sorted order. So, if the input iterable is sorted, the permutation tuples will be produced in sorted order.

Sample Code:

>>> from itertools import permutations
>>> print permutations(['1','2','3'])
<itertools.permutations object at 0x02A45210>
>>> 
>>> print list(permutations(['1','2','3']))
[('1', '2', '3'), ('1', '3', '2'), ('2', '1', '3'), ('2', '3', '1'), ('3', '1', '2'), ('3', '2', '1')]
>>> 
>>> print list(permutations(['1','2','3'],2))
[('1', '2'), ('1', '3'), ('2', '1'), ('2', '3'), ('3', '1'), ('3', '2')]
>>>
>>> print list(permutations('abc',3))
[('a', 'b', 'c'), ('a', 'c', 'b'), ('b', 'a', 'c'), ('b', 'c', 'a'), ('c', 'a', 'b'), ('c', 'b', 'a')]

HackerRank Python Solution - Itertools Topic - itertools.product()

itertools.product():

• This tool computes the cartesian product of input iterables.

• It is equivalent to nested for-loops.

• For example, product(A, B) returns the same as ((x,y) for x in A for y in B).

Sample Code:

>>> from itertools import product
>>>
>>> print list(product([1,2,3],repeat = 2))
[(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]
>>>
>>> print list(product([1,2,3],[3,4]))
[(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)]
>>>
>>> A = [[1,2,3],[3,4,5]]
>>> print list(product(*A))
[(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5)]
>>>
>>> B = [[1,2,3],[3,4,5],[7,8]]
>>> print list(product(*B))
[(1, 3, 7), (1, 3, 8), (1, 4, 7), (1, 4, 8), (1, 5, 7), (1, 5, 8), (2, 3, 7), (2, 3, 8), (2, 4, 7), (2, 4, 8), (2, 5, 7), (2, 5, 8), (3, 3, 7), (3, 3, 8), (3, 4, 7), (3, 4, 8), (3, 5, 7), (3, 5, 8)]

HackerRank Python Solution - Math Topic - Triangle Quest

• You are given a positive integer N. Print a numerical triangle of height N-1 like the one below:

1
22
333
4444
55555
......

• Can you do it using only arithmetic operations, a single for loop, and print statement?

• Use no more than two lines. The first line (the for statement) is already written for you. You have to complete the print statement.

• Note: Using anything related to strings will give a score of 0.

HackerRank Python Solution - Math Topic - Integer Come In All Sizes

• Integers in Python can be as big as the bytes in your machine's memory. There is no limit in size as there is: 2³¹-1 (c++ int) or 2⁶³-1 (C++ long long int).

• As we know, the result of a^b grows really fast with increasing b.

• Let's do some calculations on very large integers.

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.