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so, I had this exercise where I would receive a list of integers and had to find how many sum pairs were multiple to 60
example:
input: list01 = [10,90,50,40,30]
result = 2
explanation: 10 + 50, 90 + 30
example2:
input: list02 = [60,60,60]
result = 3
explanation: list02[0] + list02[1], list02[0] + list02[2], list02[1] + list02[2]
seems pretty easy, so here is my code:
def getPairCount(numbers):
total = 0
cont = 0
for n in numbers:
cont+=1
for n2 in numbers[cont:]:
if (n + n2) % 60 == 0:
total += 1
return total
it's working, however, for a big input with over 100k+ numbers is taking too long to run, and I need to be able to run in under 8 seconds, any tips on how to solve this issue??
being with another lib that i'm unaware or being able to solve this without a nested loop
Here's a simple solution that should be extremely fast (it runs in O(n) time). It makes use of the following observation: We only care about each value mod 60. E.g. 23 and 143 are effectively the same.
So rather than making an O(n**2) nested pass over the list, we instead count how many of each value we have, mod 60, so each value we count is in the range 0 - 59.
Once we have the counts, we can consider the pairs that sum to 0 or 60. The pairs that work are:
0 + 0
1 + 59
2 + 58
...
29 + 31
30 + 30
After this, the order is reversed, but we only
want to count each pair once.
There are two cases where the values are the same:
0 + 0 and 30 + 30. For each of these, the number
of pairs is (count * (count - 1)) // 2. Note that
this works when count is 0 or 1, since in both cases
we're multiplying by zero.
If the two values are different, then the number of
cases is simply the product of their counts.
Here's the code:
def getPairCount(numbers):
# Count how many of each value we have, mod 60
count_list = [0] * 60
for n in numbers:
n2 = n % 60
count_list[n2] += 1
# Now find the total
total = 0
c0 = count_list[0]
c30 = count_list[30]
total += (c0 * (c0 - 1)) // 2
total += (c30 * (c30 - 1)) // 2
for i in range(1, 30):
j = 60 - i
total += count_list[i] * count_list[j]
return total
This runs in O(n) time, due to the initial one-time pass we make over the list of input values. The loop at the end is just iterating from 1 through 29 and isn't nested, so it should run almost instantly.
Below is a translation of Tom Karzes's answer but using numpy. I benchmarked it and it is only faster if the input is already a numpy array, not a list. I still want to write it here because it nicely shows how loops in python can be one-liners in numpy.
def get_pairs_count(numbers, /):
# Count how many of each value we have, modulo 60.
numbers_mod60 = np.mod(numbers, 60)
_, counts = np.unique(numbers_mod60, return_counts=True)
# Now find the total.
total = 0
c0 = counts[0]
c30 = counts[30]
total += (c0 * (c0 - 1)) // 2
total += (c30 * (c30 - 1)) // 2
total += np.dot(counts[1:30:+1], counts[59:30:-1]) # Notice the slicing indices used.
return total
I have a giant nested for loop....10 in all, but for illustration here, i am including 6. I am doing a summation (over multiple indices; the incides are not independent!). The index in any inner for loop depends on the index of the outer loop (except for one instance). The inner-most loop contains an operation where i slice an array (named 'w') based on 8 different conditions all combined using '&' and '|'. There is also this 'HB' function that takes as an argument this sliced array (named 'wrange'), performs some operations on it and returns an array of the same size.
The timescale for this slicing and the 'HB' function to execute is 300-400 microseconds and 100 microseconds respectively. I need to bring it down drastically. To nanoseconds.!!
Tried using dictionary instead of array (where i am slicing). It is much slower. Tried storing the sliced array for all possible values. That is a very huge computation in its own right since there are many many possible combinations of the conditions (these conditions depend indirectly on the indices of the for loop)
s goes from 1 to 49
t goes from -s to s
and there are 641 combinations of l,n
Here, i have posted one value of s,t and an l,n combination for illustration.
s = 7
t = -7
l = 72
n = 12
Nl = Dictnorm[n,l]
Gamma_l = Dictfwhm[n,l]
Dictc1 = {}
Dictc2 = {}
Dictwrange = {}
DictH = {}
DictG = {}
product = []
startm = max(-l-t,-l)
endm = min(l-t,l)+1
sum5 = 0
for sp in range(s-2,s+3): #s'
sum4 = 0
for tp in range(-sp,-sp+1): #t'
#print(tp)
sum3 = 0
integral = 1
for lp in range(l-2,l+3): #l'
sum2 = 0
if (n,lp) in Dictknl2.keys():
N1 = Dictnorm[n,lp]
Gamma_1 = Dictfwhm[n,lp]
for lpp in range(l-2,l+3): #l"
sum1 = 0
if ((sp+lpp-lp)%2 == 1 and sp>=abs(lpp-lp) and
lp>=abs(sp-lpp) and lpp>=abs(sp-lp) and
(n,lpp) in Dictknl2.keys()):
F = f(lpp,lp,sp)
N2 = Dictnorm[n,lpp]
Gamma_2 = Dictfwhm[n,lpp]
for m in range(startm, endm): #m
sum0 = 0
L1 = LKD(n,l,m,l,m)
L2 = LKD(n,l,m+t,l,m+t)
for mp in range(max(m+t-tp-5,m-5),
min(m+5,m+t-tp+5)+1): #m'
if (abs(mp)<=lp and abs(mp)<=lpp and
abs(mp+tp)<=lp and abs(mp+tp)<=lpp
and LKD(n,l,m,lp,mp)!=0
and LKD(n,l,m+t,lpp,mp+tp)!=0):
c3 = Dictomega[n,lp,mp+tp]
c4 = Dictomega[n,lpp,mp]
wrange = np.unique(np.concatenate
((Dictwrange[m],
w[((w>=(c3-Gamma_1))&
((c3+Gamma_1)>=w))|
((w>=(c4-Gamma_2))&
((c4+Gamma_2)>=w))])))
factor = (sum(
HB(Dictc1[n,l,m+t],
Dictc2[n,l,m],Nl,
Nl,Gamma_l,
Gamma_l,wrange,
Sigma).conjugate()
*HB(c3,c4,N1,N2,Gamma_1,
Gamma_2,wrange,0)*L1*L2)
*LKD(n,l,m,lp,mp)
*LKD(n,l,m+t,lpp,mp+tp) *DictG[m]
*gamma(lpp,sp,lp,tp,mp)
*F)
sum0 = sum0 + factor #sum over m'
sum1 = sum1 + sum0 #sum over m
sum2 = sum2 + sum1 #sum over l"
sum3 = sum3 + sum2 #sum over l'
sum4 = sum4 + sum3*integral #sum over t'
sum5 = sum5 + sum4 #sum over s'
z = (1/(sum(product)))*sum5
print(z.real,z.imag,l,n)
TL;DR
def HB(a,...f,array1): #########timesucker
perform_some_operations_on_array1_using_a_b_c_d
return operated_on_array1
for i in ():
for j in ():
...
...
for o in ():
array1 = w[w>some_function1(i,j,..k) &
w<some_function2(i,j,..k) |.....] #########timesucker
factor = HB(a,....f,array1) * HB(g,...k,array1) *
alpha*beta*gamma....
It takes about 30 seconds to run this whole section once. I need to bring it down to as low as possible. 1 second is the minimum target
from pylab import *
no_steps = 10000
number = random()
position = zeros(no_steps)
position[0] = 0
time = zeros(no_steps)
time[0] = 0
for i in range(1, no_steps):
time[i] = time[i-1] + 1
if number >= 0.5:
position[i] = position[i-1] + 1
number = random()
else:
position[i] = position[i-1] - 1
number = random()
plot(time, position)
number2 = random()
position2 = zeros(no_steps)
position2[0] = 0
time2 = zeros(no_steps)
time2[0] = 0
for t2 in range(1, no_steps):
time2[t2] = time[t2-1] + 1
if number2 >= 0.5:
position2[t2] = position2[t2-1] + 1
number2 = random()
else:
position2[t2] = position[t2-1] - 1
number2 = random()
plot(time2,position2)
This is supposed to generate random walks by generating a random number each time and checking the conditions. Therefore I assumed that if it works for one walk I can just add more of the same and put them all on the same graph at the end. However, apparently that's not how this works and the graphs that do end up being plotted are extremely similar with the difference in the positions being one of -2 for some reason. The code if I run the blocks separately from their own program will generate two completely different walks, it's just when I put them together that it stops working as intended. What exactly am I missing?
You've accidentally reused variables from the first plot:
for t2 in range(1, no_steps):
time2[t2] = time[t2-1] + 1
^^^^^ ^^^^
if number2 >= 0.5:
position2[t2] = position2[t2-1] + 1
number2 = random()
else:
position2[t2] = position[t2-1] - 1
^^^^^^^^^ ^^^^^^^^
number2 = random()
plot(time2,position2)
I would generate the random walk with a function so you don't have to worry about renaming variables like this:
import numpy
from pylab import *
no_steps = 10000
def random_walk(no_steps):
# 2 * [0, 1] - 1 -> [0, 2] - 1 -> [-1, 1]
directions = 2 * numpy.random.randint(0, 2, size=(1, no_steps)) - 1
positions = numpy.cumsum(directions)
positions -= positions[0] # To make it start from zero
return positions
time1 = numpy.arange(0, no_steps)
plot(time1, random_walk(no_steps))
savefig('1.png')
clf()
time2 = numpy.arange(0, no_steps)
plot(time2, random_walk(no_steps))
savefig('2.png')
I'm getting a list of 5 floats which I would like to use as values to send pwm to an LED. I want to ramp smoothly in a variable amount of milliseconds between the elements in the array.
So if this is my array...
list = [1.222, 3.111, 0.456, 9.222, 22.333]
I want to ramp from 1.222 to 3.111 over say 3000 milliseconds, then from 3.111 to 0.456 over the same amount of time, and when it gets to the end of the list I want the 5th element of the list to ramp to the 1st element of the list and continue indefinitely.
do you think about something like that?
import time
l = [1.222, 3.111, 0.456, 9.222, 22.333]
def play_led(value):
#here should be the led- code
print value
def calc_ramp(given_list, interval_count):
new_list = []
len_list = len(given_list)
for i in range(len_list):
first = given_list[i]
second = given_list[(i+1) % len_list]
delta = (second - first) / interval_count
for j in range(interval_count):
new_list.append(first + j * delta)
return new_list
def endless_play_led(ramp_list,count):
endless = count == 0
count = abs(count)
while endless or count!=0:
for i in range(len(ramp_list)):
play_led(ramp_list[i])
#time.sleep(1)
if not endless:
count -= 1
print '##############',count
endless_play_led(calc_ramp(l, 3),2)
endless_play_led(calc_ramp(l, 3),-2)
endless_play_led(calc_ramp(l, 3),0)
another version, similar to the version of dsgdfg (based on his/her idea), but without timing lag:
import time
list_of_ramp = [1.222, 3.111, 0.456, 9.222, 22.333]
def play_LED(value):
s = ''
for i in range(int(value*4)):
s += '*'
print s, value
def interpol(first, second, fract):
return first + (second - first)*fract
def find_borders(list_of_values, total_time, time_per_step):
len_list = len(list_of_values)
total_steps = total_time // time_per_step
fract = (total_time - total_steps * time_per_step) / float(time_per_step)
index1 = int(total_steps % len_list)
return [list_of_values[index1], list_of_values[(index1 + 1) % len_list], fract]
def start_program(list_of_values, time_per_step, relax_time):
total_start = time.time()
while True:
last_time = time.time()
while time.time() - last_time < relax_time:
pass
x = find_borders(list_of_values,time.time(),time_per_step)
play_LED(interpol(x[0],x[1],x[2]))
start_program(list_of_ramp,time_per_step=5,relax_time=0.5)
(Python) Given two numbers A and B. I need to find all nested "groups" of numbers:
range(2169800, 2171194)
leading numbers: 21698XX, 21699XX, 2170XX, 21710XX, 217110X, 217111X,
217112X, 217113X, 217114X, 217115X, 217116X, 217117X, 217118X, 2171190X,
2171191X, 2171192X, 2171193X, 2171194X
or like this:
range(1000, 1452)
leading numbers: 10XX, 11XX, 12XX, 13XX, 140X, 141X, 142X, 143X,
144X, 1450, 1451, 1452
Harder than it first looked - pretty sure this is solid and will handle most boundary conditions. :) (There are few!!)
def leading(a, b):
# generate digit pairs a=123, b=456 -> [(1, 4), (2, 5), (3, 6)]
zip_digits = zip(str(a), str(b))
zip_digits = map(lambda (x,y):(int(x), int(y)), zip_digits)
# this ignores problems where the last matching digits are 0 and 9
# leading (12000, 12999) is same as leading(12, 12)
while(zip_digits[-1] == (0,9)):
zip_digits.pop()
# start recursion
return compute_leading(zip_digits)
def compute_leading(zip_digits):
if(len(zip_digits) == 1): # 1 digit case is simple!! :)
(a,b) = zip_digits.pop()
return range(a, b+1)
#now we partition the problem
# given leading(123,456) we decompose this into 3 problems
# lows -> leading(123,129)
# middle -> leading(130,449) which we can recurse to leading(13,44)
# highs -> leading(450,456)
last_digits = zip_digits.pop()
low_prefix = reduce(lambda x, y : 10 * x + y, [tup[0] for tup in zip_digits]) * 10 # base for lows e.g. 120
high_prefix = reduce(lambda x, y : 10 * x + y, [tup[1] for tup in zip_digits]) * 10 # base for highs e.g. 450
lows = range(low_prefix + last_digits[0], low_prefix + 10)
highs = range(high_prefix + 0, high_prefix + last_digits[1] + 1)
#check for boundary cases where lows or highs have all ten digits
(a,b) = zip_digits.pop() # pop last digits of middle so they can be adjusted
if len(lows) == 10:
lows = []
else:
a = a + 1
if len(highs) == 10:
highs = []
else:
b = b - 1
zip_digits.append((a,b)) # push back last digits of middle after adjustments
return lows + compute_leading(zip_digits) + highs # and recurse - woohoo!!
print leading(199,411)
print leading(2169800, 2171194)
print leading(1000, 1452)
def foo(start, end):
index = 0
is_lower = False
while index < len(start):
if is_lower and start[index] == '0':
break
if not is_lower and start[index] < end[index]:
first_lower = index
is_lower = True
index += 1
return index-1, first_lower
start = '2169800'
end = '2171194'
result = []
while int(start) < int(end):
index, first_lower = foo(start, end)
range_end = index > first_lower and 10 or int(end[first_lower])
for x in range(int(start[index]), range_end):
result.append(start[:index] + str(x) + 'X'*(len(start)-index-1))
if range_end == 10:
start = str(int(start[:index])+1)+'0'+start[index+1:]
else:
start = start[:index] + str(range_end) + start[index+1:]
result.append(end)
print "Leading numbers:"
print result
I test the examples you've given, it is right. Hope this will help you
This should give you a good starting point :
def leading(start, end):
leading = []
hundreds = start // 100
while (end - hundreds * 100) > 100:
i = hundreds * 100
leading.append(range(i,i+100))
hundreds += 1
c = hundreds * 100
tens = 1
while (end - c - tens * 10) > 10:
i = c + tens * 10
leading.append(range(i, i + 10))
tens += 1
c += tens * 10
ones = 1
while (end - c - ones) > 0:
i = c + ones
leading.append(i)
ones += 1
leading.append(end)
return leading
Ok, the whole could be one loop-level deeper. But I thought it might be clearer this way. Hope, this helps you...
Update :
Now I see what you want. Furthermore, maria's code doesn't seem to be working for me. (Sorry...)
So please consider the following code :
def leading(start, end):
depth = 2
while 10 ** depth > end : depth -=1
leading = []
const = 0
coeff = start // 10 ** depth
while depth >= 0:
while (end - const - coeff * 10 ** depth) >= 10 ** depth:
leading.append(str(const / 10 ** depth + coeff) + "X" * depth)
coeff += 1
const += coeff * 10 ** depth
coeff = 0
depth -= 1
leading.append(end)
return leading
print leading(199,411)
print leading(2169800, 2171194)
print leading(1000, 1453)
print leading(1,12)
Now, let me try to explain the approach here.
The algorithm will try to find "end" starting from value "start" and check whether "end" is in the next 10^2 (which is 100 in this case). If it fails, it will make a leap of 10^2 until it succeeds. When it succeeds it will go one depth level lower. That is, it will make leaps one order of magnitude smaller. And loop that way until the depth is equal to zero (= leaps of 10^0 = 1). The algorithm stops when it reaches the "end" value.
You may also notice that I have the implemented the wrapping loop I mentioned so it is now possible to define the starting depth (or leap size) in a variable.
The first while loop makes sure the first leap does not overshoot the "end" value.
If you have any questions, just feel free to ask.