Python - Intro to Algorithms

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Numbers

• Integers
  • (999).bit_length() gives us the number of bytes held in an integer
  • Cast string to int - int(s, base) => example: d = int(s, 2); If string cannot be represented, this method raises a ValueError exception
• Floats

  • Single Precision: 32 bit float = 1 bit for sign + 23 bits for significant digits or mantissa + 8 buts for exponent.

  • Never compare floats for equality. Use something like this to do it only

      def () a(x, y, places = 7):
          return round(abs(x-y), places) == 0
    

  • Division operator / always returns a float. Floor division can be made using operator //. Modulus can be done using % operator.

  • divmod(x, y) returns both quotient and remainder when we do x/y. For example, divmod(45, 6) returns (7, 3)

  • round(x, n) returns x rounded to n intergral digits if n is negative or n decimal places if n is positive.

  • as_integer_ratio() gives integer fractional representation of a float.

      2.75.as_integer_ratio() returns (11, 4)
    

• Complex Numbers
  • imported from cmath module.
  • Has functions for trigonometric and logarithmic functoins + some complex number functions such as phase(), rect(), etc
• Fraction Module

  • from fractions import Fraction
    

  • Fraction(number.as_integer_ratio()) converts float to fraction
    

  • Fraction(x,y).denominator gives denominator
    

  • Fraction(x,y).numerator gives numerator
    

• Decimal Module

  • sum(0.1 for in range(10)) == 1.0 returns False
    

  • from decimal import Decimal
    sum(Decimal ("0.1") for i in range(10)) == Decimal("1.0")
    

• Other Representations
  • bin(999) returns '0b1111100111
  • hex(999) returns '0x3e7'
  • oct(999) returns '0o1747'
• Random Module
  • example: import random values = [1,2,3,4] print(random.choice(values)) random.shuffle(values) print(values) print(random.randint(0,10))
• Numpy package
  • example: import numpy as np np.array(((11,12,13),(21,22,23),(31,32,33))) - will create an array of array like this [ [11 12 13] [21 22 23] [31 32 33] ]
  x = np.array(...) x.ndim returns number of dimensions of array which will be 2 for previous example