I'm trying to optimize my code by using dictionaries instead of if-elif statements.
I've read that you can optimize code by using dictionaries instead of if-elif statements, but I don't know how to do that. I'd like to use the logical expressions below somehow in the dictionary. (The code iterates through a and b)
def e_ha(n, t, a, b, E):
if a == b:
return 6
elif (a%n == 0, a != n**2, b == a + 1) == (True, True, True):
return 0
elif ((a-1)%n == 0, (a-1) != n**2, b == a - 1) == (True, True, True):
return 0
elif (a%n == 0, b == a-(n-1)) == (True, True):
return 1
elif (b%n == 0, a == b-(n-1)) == (True, True):
return 1
elif abs(a-b) == 1:
return 1
elif abs(a-b) == n:
return 1
else:
return 0
One naive approach to achieve the best performance is to build a big table storing the results for all possible (a, b) pairs. However, this could consume lots of memory and becomes inpractical for large ns.
Here is how the code can be optimized using a normal approach, as explained in the following step-by-step.
1. Using Explicit and for Logical Expressions
As suggested in the comments, this is much more readable and also more efficient because of the short circuiting behavior of and. This change alone reduces the runtime by 60% in my tests.
2. Remove Redundant Conditions
Since both a and b range from 1 to n**2, if a == n**2, then b == a + 1 can never be fulfilled. Therefore the a != n**2 check in the condition a%n == 0 and a != n**2 and b == a + 1 is redundant. The same applies to the third condition. Eliminating them simplifies these conditions to:
...
elif a % n == 0 and b == a + 1:
elif (a - 1) % n == 0 and b == a - 1:
...
3. Avoid Repeated Computations in Conditions
Note that the above-improved conditions
a % n == 0 and b == a + 1 and (a - 1) % n == 0 and b == a - 1 are special cases of abs(a - b) == 1. Therefore these conditions can be rewritten using nested if-else as follows.
if abs(a - b) == 1:
if a % n == 0 and b > a: return 0
elif b % n == 0 and a > b: return 0 # a - 1 equals to b here so it is replaced to save one computation
else return 1
Also note that the value abs(a - b) is related to all the conditions. Therefore it can be computed before all conditions are checked. With this change, the code becomes
d = abs(a - b)
if d == 0: return 6
elif d == 1:
if a % n == 0 and b > a: return 0
elif b % n == 0 and a > b: return 0
else return 1
elif d == n - 1:
if a % n == 0 and a > b: return 1
elif b % n == 0 and b > a: return 1
else return 0
elif d == n: return 1
else: return 0
4. Simplify Logic
For example, the first nested if-else above can be simplified to
if min(a, b) % n == 0: return 0
else return 1
A more compact syntax is:
return 1 if min(a, b) % n == 0 else 0
5. Apply Python-specific Optimizations
In Python, the number 0 is regarded as having a falsy value. So for numbers if d != 0: and if d == 0: are equivalent to if d: and if not d: respectively. The latter is a bit faster. Applying this change results in the following optimized code (here a more compact syntax is used to shorten the answer).
d = abs(b - a)
if not d: return 6
elif d == 1: return 1 if min(a, b) % n else 0
elif d == n - 1: return 0 if max(a, b) % n else 1
else: return 1 if d == n else 0
Applying steps 2 to 5 above reduces the runtime by another 50%.
6. Adjust Order of Conditions based on Input Distribution
This change relies on the knowledge of the actual input distribution in the application. The target is to make the more frequently seen inputs return faster. In this example, assume the inputs a and b are uniformly distributed within [1, n**2] and n >= 10. In this case, the most frequent scenario is that the value d does not match any of the if conditions and 0 is returned at the end after all conditions are checked. In order to speedup, we can make it fail faster by first checking whether d can possibly lead to a non-zero return value.
d = abs(a - b)
if 1 < d < n - 1 or d > n: return 0 # Return 0 if d is not in [0, 1, n - 1, n]
elif d == 1: return 1 if min(a, b) % n else 0
elif d == n - 1: return 0 if max(a, b) % n else 1
else: return 1 if d == n else 6 # d == 0 case is moved to the last "else" since it is least frequently seen
7. Using Lookup Tables
Further speedup can be achieved by using lookup tables. Here, the values [0, 1, n - 1, n] for the first conditional check can be stored to speedup the check. In this case, there are two primary options for this: a set or a length-n+1 list of boolean values. The former uses less memory while the latter has better performance. Note that the lookup table should be constructed once outside the function and passed into it. The code using a boolean list as a lookup is as follows:
def func(n, a, b, lookup):
d = abs(a - b)
if not (d <= n and lookup[d]): return 0
...
Applying steps 6 and 7 (with boolean list lookup) reduces the runtime by another 15%.
Note that in this example a 2D lookup table (implemented as nested lists or dictionaries) can also be applied using (min(a, b) % n, d) as indices. However, under the same assumption of input distribution in step 6, this is slightly slower than a 1D lookup because of the overhead of one extra level of indexing.
The runtime above is the total time of applying the function to all possible (a, b) values within [1, n**2] for n=20.
Using a dictionary, where the keys are boolean expressions is not going to work the way you hope it does. There is no such thing as a boolean-expression-object that could take the place of the key, only booleans. In the end, boolean expressions evaluate to either True or False, so at most you could only have two key-value pairs.
I would suggest, however, you make things a bit more readable/pythonic:
if a%n == 0 and a != n**2 and b == a + 1:
or
if all((a%n == 0, a != n**2, b == a + 1)):
You can just use a list of tuples and loop through it:
def e_ha(n, t, a, b, E):
checks = [
(a == b, 6),
(all(a%n == 0, a != n**2, b == a + 1), 0 ),
(all((a-1)%n == 0, (a-1) != n**2, b == a - 1), 0),
(all(a%n == 0, b == a-(n-1)), 1),
(all(b%n == 0, a == b-(n-1)), 1 ),
(abs(a-b) == 1, 1),
(abs(a-b) == n, 1),
(true, 0)
]
for valid, return_value in checks:
if valid:
return return_value
Caveat:
This is most certainly not faster in any way. Timed it multiple times and it was always slower.
It is less readable than the alternative
Related
This is the code about to find out dice gamble's prize amount:
a, b, c = map(int, input().split())
if a == b and b == c: #same all of dice numbers
print(10000 + (a * 1000))
elif a == b or b == c: #same two of dice numbers
print(1000 + (b * 100))
elif a == c: #same two of dice numbers
print(1000 + (a * 100))
else: #no same number
print(max(a, b, c)*100)
This is equivalent:
*_, a, b, c=sorted(input())
print(['1'+b, c][a < b < c]+'000'[a < c:])
But i can't understanding about what does
['1'+b, c][a < b < c]
and
'000'[a < c:]
do.
So, I had tried to find out the meaning of
`['1'+b, c][a < b < c]`
I found this is similar with
`c if a<b<c else '1'+b`
but i can't be sure about that.
anyway, about
`'000'[a < c:]`
I tried input a=c to
`print('000'[a < c:])`
It shows 000.
I tried else that input a<c, it shows 00
Anyone can tell me about this expression?
The original is unnecessarily cryptic. It uses the fact that:
int(False) == 0
int(True) == 1
For instance,
'000'[False:] == '000'[0:] == '000'
'000'[True:] == '000'[1:] == '00'
Similarly,
['1' + b, c][False] == ['1' + b, c][0] == '1' + b
['1' + b, c][True] == ['1' + b, c][1] == c
Here's an equivalent rewrite:
prefix = c if a < b < c else '1' + b
suffix = '00' if a < c else '000'
print(prefix + suffix)
a < c will evaluate to either True or False. So you are effectively getting either print('000'[True:]) or print('000'[False:]).
When you have the [] after a string, those will perform a slice on the string. You'd see this in actually practice as something like the following (here's a link for more info:
'abcde'[2] # returns 'c', which, starting from zero, is 2nd item
'abcde'[0] # returns 'a', which is the zero-th item
'abcde'[1:3] # returns 'bc', starting from the 1st item and going to the 3rd, not inclusive of the third
It looks like if you use booleans in such a slice, the False acts as a 0 and True acts as a 1
"abcde"[True] == "abcde"[1] # evaluates to true, these are the same
'abcde'[True] # evaluates to 'b'
"abcde"[False] == "abcde"[2] # evaluates to `False`
"abcde"[True] == "abcde"[2] # evaluates to `False`
"abcde"[False] == "abcde"[0] # evaluates to True, because False is effectively 0 here
So, having a [True:] or [False:] in that string-slice is the same as having [1:] or '[0:]`, which is saying to "give all characters starting with the second (for True/1:) or first (for False/0:) in this string".
The string '000' has length 3. The boolean a < c has value False or True. The operation s[i] for a string s and integer i refers to the i'th element of s, and the operation s[i:] takes the substring of s from index i through the end of s. A boolean value will be converted to an integer in Python as follows: False becomes 0 and True becomes 1.
So, '000'[a < c:] is the same as '000'[0:] if a < c is False, and this is the same as '000'. If a < c is True, then '000'[a < c:] is the same as '000'[1:] which is '00'.
I wrote a function:
# given a n x m grid return how many different ways there are to move from top left to
# bottom right by only being able to move right or down
def grid(n, m, memo = {}):
if f'{n},{m}' in memo:
return memo[f'{n},{m}']
if n == 1 and m == 1:
return 1
if n == 0 or m == 0:
return 0
memo[f'{n},{m}'] = grid(n,m-1,) + grid(n-1,m)
return grid(n,m-1,) + grid(n-1,m)
Recently I read a bit about short-circuiting in Python and I am trying to understand it further.
As I understand it does not provide any boost in runtime, just sort of syntax sugar.
For example:
1 < 2 < 3 # is True
1 < 2 and 2 < 3 # is also True
# hence
(1 < 2 < 3) == 1 < 2 and 2 < 3 # is True
I was wondering can I write my function with this kind of short-circuiting in my if statements?
I came up with this:
def grid(n, m, memo = {}):
if f'{n},{m}' in memo:
return memo[f'{n},{m}']
if (n or m) == 1:
return 1
if (n and m) == 0:
return 0
memo[f'{n},{m}'] = grid(n,m-1,) + grid(n-1,m)
return grid(n,m-1,) + grid(n-1,m)
Is there any smarter way of using the short-circuit here?
(1 < 2 < 3) is not short-circuiting - I think you misunderstood the meaning of the term. You are correct that it is merely syntax sugar - although it can produce some very weird results in obscure cases. (1 < 2 < 3) expands to (1 < 2) and (2 < 3) - the middle operand is copied to both and and is used for the joining operator.
Short circuiting occurs when python already knows the answer to a boolean expression, even before calculating both the inputs. For example
def false():
print("false")
return False
def true():
print("true")
return True
print(false() and true())
The output would be
false
False
Because when python sees False and, it already knows that the result is False (because and requires both operands to be True), so it doesn't bother running the second half of the line.
This real short circuiting does result in a performance boost, but since you can't turn off short circuiting, it doesn't really matter ¯\_(ツ)_/¯
if (n or m) == 1 is definitely not the same thing as if n == 1 or m == 1. The first if statement is equivalent to:
value = n
if not value:
value = m
if value == 1:
# do something:
Or expressed more succinctly:
if (n if n else m) == 1:
# do something
In other words, n or m only evaluates m if n is False (or 0 if n is an integer), otherwise the result of the expression is n.
What you want to avoid redundancy is:
if 1 in (n, m): # equivalent to: if 1 is either n or m:
Update: Demo
n = 4
m = 1
if (n or m) == 1:
print('if branch taken')
else:
print('else branch taken')
Prints:
else branch taken
if (n or m) == 1
evaluates to
if (<bool>) == 1 # e.g. if {True,False} == 1
which is probably not what you want, since it is essentially evaluating the truthiness of n or m.
Your existing code already captures the nature of short-circuiting;
if n == 1 and m == 1
will only evaluate the second argument m == 1 iff n == 1, or will otherwise short-circuit.
To your comment
As I understand it does not provide any boost in runtime, just sort of syntax suggar.
Well, actually it does provide a runtime boost if Python is able to skip evaluating what would otherwise be "expensive" conditions to evaluate because it is able to short-circuit early.
I am pretty sure that this must be some glaringly stupid mistake by me. But can anyone explain what is wrong in this division code using recursion. I know there are a lot of alternatives, but I need to know what is wrong with this
def division(a, b):
x = 0
if a < b:
return x
else:
x += 1
return division(a - b, b)
return x
When I do division(10, 2), it gives me 0 as output
You always set your local variable x to 0.
Then if the dividend is smaller than the divisor you return that x which is of course 0.
On the other hand when the dividend is greater or equal to the divisor you increment x by 1 and do a recursive call with a decremented dividend which will of course lead to the first case at the end and still you return an x which holds the value of 0.
Note: Nonetheless your final return is not reachable since both your if and else branch contains a return.
So please try considering this solution:
def division(a, b):
if a < b:
return 0
else:
return 1 + division(a-b, b)
Update:
A possible solution for working with negative integers following python's round towards negative infinity division:
def division_with_negatives(a, b):
a_abs, b_abs = abs(a), abs(b)
if (a >= 0 and b >= 0) or (a < 0 and b < 0):
# branch for positive results
if a_abs < b_abs:
return 0
else:
return 1 + division_with_negatives(a_abs - b_abs, b_abs)
else:
# branch for negative results
if b_abs > a_abs or a_abs == b_abs:
return -1
else:
return -1 + division_with_negatives(a_abs - b_abs, -b_abs)
assert division_with_negatives(-4, 1) == -4 // 1
assert division_with_negatives(10, 2) == 10 // 2
assert division_with_negatives(1, -5) == 1 // -5
assert division_with_negatives(-3, -2) == -3 // -2
This might save you from RecursionError:
def div(x, y):
if y == 0:
return 0
elif x == y:
return 1
elif x < y:
if y * -1 == x:
return -1
elif x % y == 0:
return 1 + div(x - y, y)
else:
return 0
else:
if y < 0:
return 1 - div(x - y, -y)
else:
return 1 + div(x - y, y)
#Application
A = div(1, 2)
B = div(-9, 9)
C = div(3, 2)
D = div(-9, -3)
E = div(100, -2)
print(A) # 0
print(B) # -1
print(C) # 1
print(D) # 3
print(E) # -50
Your escape condition is if a < b. That means that for this function to terminate, this must be fulfilled to leave the recursion. However, because x is declared at the top of the function, only redefined inside the body of the else statement but never returned, the function will always terminate with a value of x = 0.
You should either set x = 1 + division(a-b,b) or return division(a-b,b) + 1 and remove the unreachable returnat the end.
def div(a, b, x):
if a < b:
return x
else:
x +=1
return div(a - b, b, x)
print(div(130, 10, 0))
# 13
This might work a little better for you:
def division(a,b,x=0):
if a < b:
return x
else:
x += 1
return division(a-b,b,x)
return x
Every time your function ran through a new recusion, you were setting x to 0. This way, it defaults to 0 if x is not specified, and should work like I think you want.
Also note that this will not work for negative numbers, but you probably knew that :)
With global you get:
def division(a,b):
global x
if a < b: return x
else:
x += 1
return division(a-b,b)
x=0
print (division(10,2))
But you have to set x to zero every time before call the division
i think this is best way, this way u can get floating answer also
def division(a,b):
if a == 0 or a == 1 or a == 2:
return b
else:
return a / division(a % b,b)
print(division(9,2))
I am trying to find the great common divisor by using a function and solving it iteratively. Though, for some reason, I am not sure why I am not getting the right output.
The greatest common divisor between 30 & 15 should be 15, however, my output is always giving me the wrong number. I have a strong feeling that my "if" statement is strongly incorrect. Please help!
def square(a,b):
'''
x: int or float.
'''
c = a + b
while c > 0:
c -= 1
if a % c == 0 and b % c == 0:
return c
else:
return 1
obj = square(30,15)
print (obj)
You should return a value only if you finished iterating all numbers and found none of them a divisor to both numbers:
def square(a, b):
c = a + b
while c > 0:
if a % c == 0 and b % c == 0:
return c
c -= 1
return 1
However, the last return will be unneeded in this case, as c would go from a + b to 1, and mod 1 will always bring a common divisor, so the loop will always terminate with 1, for the worst case.
Also, a number greater than a and b can not be a common divisor of them. (x mod y for y > x yields x), and gcd is the formal name for the task, so I would go with
def gcd(a, b):
for c in range(min(a, b), 0, -1):
if a % c == b % c == 0:
return c
for iterational solution.
You might be interested to know that there is a common recursive solution to the GCD problem based on the Euclidian algorighm.
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)
print(gcd(30, 15))
# 15
You can add any operator(including parentheses and + - * / ** ) between 9 8 7 6 5 4 3 2 1.
For example,
98*76-5432*1=2016
9*8*7*(6+5-4-3)*(2-1)=2016
I wrote a programme like this
from __future__ import division
s = ['+','-','*','/','','(',')']
def calc(s):
a=s.split()
return eval(''.join(a))
a=['','9','','8','','7','','6','','5','','4','','3','','2','','1.','']
def test(tmp):
if tmp == 20:
try:
z = eval(''.join(a))
if z == 2016:
print ''.join(a)
except:
pass
return
for i in s:
#print a
a[tmp] = i
test(tmp+2)
for j in s:
a[0] = j
test(2)
But it is not right, because there can be multiple operators exist between numbers.
There's a well known trick to questions that involve constructing arithmetic expressions with brackets: often it's easier to use reverse polish notation instead.
Here's code that does this.
# Compute "a op b", returning None if the result
# is no good (eg: 9/0 or too big).
def do_op(a, op, b):
if op == '+':
return a + b
if op == '-':
return a - b
if op == '*':
return a * b
if op == '/':
if b == 0 or a % b != 0:
return None
return a // b
if op == '**':
# Disallow arguments that would result
# in fractions or huge numbers, being careful
# to allow valid results.
if a == 1:
return a
if a == -1:
return -1 if b % 2 else 1
if a == 0 and b == 0:
return None
if b < 0 or b > 20 or a > 10000 or a < -10000:
return None
return a ** b
assert False
# Generates expressions that result in the given target.
# ops is the a record of the operations applied so far,
# stack is the evaluation stack, and num is the first
# digit that we've not pushed yet.
def sums(ops, stack, num, target):
if not num and len(stack) == 1:
if stack[0] == target:
yield ops
return
# If num is 7, say, try pushing 7, 76, 765, 7654, ..., 7654321.
k = num
for i in xrange(num, 0, -1):
for s in sums(ops + [k], stack + [k], i-1, target):
yield s
k = 10 * k + (i - 1)
# If we've less that 2 things on the stack, we can't apply
# any operations.
if len(stack) < 2:
return
# Try each of the possible ops in turn.
for op in ['+', '-', '*', '/', '**']:
result = do_op(stack[-2], op, stack[-1])
if result is None:
continue
for s in sums(ops + [op], stack[:-2] + [result], num, target):
yield s
# Convert a list of operations that represent an expression in RPN
# into infix notation. Every operation is bracketed, even when
# that's redundant.
def to_infix(ops):
stack = []
for p in ops:
if isinstance(p, int):
stack = stack + [p]
else:
stack = stack[:-2] + ['(%s%s%s)' % (stack[-2], p, stack[-1])]
assert len(stack) == 1
return stack[0]
# Starting with an empty stack (and no operations), with 9 as the first
# unused digit, generate all expressions that evaluate to 2016.
for s in sums([], [], 9, 2016):
print to_infix(s)
It takes a few minutes to run, but there's a lot (more than 25000) of valid expressions that evaluate to 2016.
My favorite is (((98*76)-5432)*1).