Types and Operators
/: returns a float |
%: remainder |
int % 10: returns last digit |
//: quotient, rounds down to nearest int |
int // 10: pops off last digit |
int(x): truncates decimals |
bool(x): False for x values that are null or empty x. True for otherwise |
Slicing
s[start: stop(non-inclusive): step] |
s = "12345" |
s[0:5:2] |
"135" |
start and stop must follow the direction as indicated by the step |
s[:1:-1] => "543" s[0:1:-1] => "" |
Slicing of tuples always returns a tuple |
(1, 2, 3)[1: -1] ⇒ (2, ) |
Comparison
b = (8,9) b = (b, b) # b = ((8, 9), (8, 9)) b in b False |
strings are compared lexicographically, if one is not a subset |
'bananb' > 'banana' => True |
if subset: len(s) is compared |
'pqrst' > 'pqrs' => True |
sum of 1 to 2 ** n
20 + 21 + ... + 2k = 2k+1 - 1 |
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Types of Errors
NameError |
Raised when a variable is not found in local or global scope. |
IndexError |
Raised when index of a sequence is out of range (does not occur for slicing) |
ValueError |
Raised when a function receives an argument of the correct type but inappropriate value |
TypeError |
argument passed to a function is incompatible with the type expected / incorrect no. of arguments |
SyntaxError |
ZeroDivisionError |
UnboundLocalError |
Raised when a reference is made to a local variable in a function or method, but no value has been bound to that variable |
RecursionError |
Infinite looping |
RuntimeError |
Raised when an error does not fall under any other category. |
is_fib(n) (T = O(logn), S = O(1))
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Functions on iterables (tuples, strings etc.)
len(), max(), min(), sum() |
tuple(<iterable>) |
<iterable>.count(element) |
<iterable>.index(element, start, end) |
count_digits
def no_of_digits(i):
if abs(i) < 10:
return 1
else:
return 1 + no_of_digits(i // 10)
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factorial
def factorial(n):
if n <= 1: return 1
else:
return n * factorial(n - 1)
#T(n), S(n) = O(n)
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Order of Growth
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def fib(n): if n <= 1: return 1 return fib(n - 1) + fib(n - 2) T = O(2^n)
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Indexing/checking element (in) T(n) = O(n), S(n) = O(1)
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String and Tuple Slicing O(n), where n is length of slice (both time and space)
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String and Tuple Concatenation O(n), where n = len(new seq)
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Printing T(n) = string: O(n), int: O(1)
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T(n) = n * logn
O(n) operations for each level * logn depth
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