I was working on this leetcode: https://leetcode.com/problems/remove-boxes/ and my answer is only slightly off for certain test cases. Any advice would be appreciated.
The problem is outlined as the following:
You are given several boxes with different colors represented by different positive numbers.
You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of k boxes, k >= >1), remove them and get k * k points.
Return the maximum points you can get.
Example 1:
Input: boxes = [1]
Output: 1 => (1*1)
Example 2:
Input: boxes = [1,1,1]
Output: 9 => (3*3)
Example 3:
Input: boxes = [1,3,2,2,2,3,4,3,1]
Output: 23
Explanation:
[1, 3, 2, 2, 2, 3, 4, 3, 1]
----> [1, 3, 3, 4, 3, 1] (3*3=9 points)
----> [1, 3, 3, 3, 1] (1*1=1 points)
----> [1, 1] (3*3=9 points)
----> [] (2*2=4 points)
I decided to use recursive backtracking to try and solve this, and my code is the following:
from copy import deepcopy as copy
class Solution:
# Main function
def backtrack(self, boxes, score, seen={}):
# Make list hashable
hashable = tuple(boxes)
if len(boxes) == 0:
return score
if hashable in seen:
return seen[hashable]
pos_scores = []
loop_start = 0
loop_end = len(boxes)
while(loop_start < loop_end):
# keep original boxes for original
box_copy = copy(boxes)
# Returns the continous from starting point
seq_start, seq_end = self.find_seq(box_copy, loop_start)
# Return the box array without the seqence, and the score from removal
new_boxes, new_score = self.remove_sequence(box_copy, seq_start, seq_end)
# Backtrack based off the new box list and new score
pos_scores.append(self.backtrack(box_copy, score+new_score, seen))
# Next iteration will use a fresh copy of the boxes
loop_start = seq_end
seen[hashable] = max(pos_scores)
return seen[hashable]
def remove_sequence(self, boxes, start, end):
rem_counter = 0
for i in range(start, end):
boxes.pop(i - rem_counter)
rem_counter += 1
dist = (end - start)
score = dist * dist
return boxes, score
def find_seq(self, boxes, start):
color = boxes[start]
end = start
for i in range(start, len(boxes)):
if boxes[i] == color:
end += 1
else:
break
return start, end
def removeBoxes(self, boxes) -> int:
return self.backtrack(boxes, 0, {})
My issue is that my code has worked for smaller examples, but is slightly off for the larger ones. I believe my code is almost there, but I think I'm missing an edge case. Any tips would be greatly appreciated. For example, I get the correct answer for [1,1,2,1,2] as well as most test cases. However my answer for the third example is 21, not 23.
Per #Armali's comment, the solution to the code above is to use
hashable = tuple(boxes), score
Related
I would like to get a statistical test statistic to compare two lists. Suppose my Benchmark list is
Benchmark = [a,b,c,d,e,f,g]
and I have two other lists
A = [g,c,b,a,f,e,d]
C = [c,d,e,a,b,f,g]
I want the test to inform me which list is closer to the Benchmark. The test should consider the absolute location, but also the relative location for example it should penalize the fact that in list A 'g' is at the start but in the benchmark it is at the end(how far is something from its true location), but also it should also reward the fact that 'a' and 'b' are close to each other in list C just like in the Benchmark.
A and C are always shuffled Benchmark. I would like a statistical test or some kind of metric that informs me that the orderings of list A , B and C are not statistically different from that of the Benchmark but that of a certain list D is significantly different at a certain threshold or p-value such as 5%. And even among the lists A,B and C, the test should perfectly outline which ordering is closer to the Benchmark.
Well, if you come to the conclusion that a metric will suffice, here you go:
def dist(a, b):
perm = []
for v in b:
perm.append(a.index(v))
perm_vals = [a[p] for p in perm]
# displacement
ret = 0
for i, v in enumerate(perm):
ret += abs(v - i)
# coherence break
current = perm_vals.index(a[0])
for v in a[1:]:
new = perm_vals.index(v)
ret += abs(new - current) - 1
current = new
return ret
I've created a few samples to test this:
import random
ground_truth = [0, 1, 2, 3, 4, 5, 6]
samples = []
for i in range(7):
samples.append(random.sample(ground_truth, len(ground_truth)))
samples.append([0, 6, 1, 5, 3, 4, 2])
samples.append([6, 5, 4, 3, 2, 1, 0])
samples.append([0, 1, 2, 3, 4, 5, 6])
def dist(a, b):
perm = []
for v in b:
perm.append(a.index(v))
perm_vals = [a[p] for p in perm]
# displacement
ret = 0
for i, v in enumerate(perm):
ret += abs(v - i)
# coherence break
current = perm_vals.index(a[0])
for v in a[1:]:
new = perm_vals.index(v)
ret += abs(new - current) - 1
current = new
return ret
for s in samples:
print(s, dist(ground_truth, s))
The metric is a cost, that is, the lower it is, the better. I designed it to yield 0 iff the permutation is an identity. The job left for you, that which none can do for you, is deciding how strict you want to be when evaluating samples using this metric, which definitely depends on what you're trying to achieve.
The input is an integer that specifies the amount to be ordered.
There are predefined package sizes that have to be used to create that order.
e.g.
Packs
3 for $5
5 for $9
9 for $16
for an input order 13 the output should be:
2x5 + 1x3
So far I've the following approach:
remaining_order = 13
package_numbers = [9,5,3]
required_packages = []
while remaining_order > 0:
found = False
for pack_num in package_numbers:
if pack_num <= remaining_order:
required_packages.append(pack_num)
remaining_order -= pack_num
found = True
break
if not found:
break
But this will lead to the wrong result:
1x9 + 1x3
remaining: 1
So, you need to fill the order with the packages such that the total price is maximal? This is known as Knapsack problem. In that Wikipedia article you'll find several solutions written in Python.
To be more precise, you need a solution for the unbounded knapsack problem, in contrast to popular 0/1 knapsack problem (where each item can be packed only once). Here is working code from Rosetta:
from itertools import product
NAME, SIZE, VALUE = range(3)
items = (
# NAME, SIZE, VALUE
('A', 3, 5),
('B', 5, 9),
('C', 9, 16))
capacity = 13
def knapsack_unbounded_enumeration(items, C):
# find max of any one item
max1 = [int(C / item[SIZE]) for item in items]
itemsizes = [item[SIZE] for item in items]
itemvalues = [item[VALUE] for item in items]
# def totvalue(itemscount, =itemsizes, itemvalues=itemvalues, C=C):
def totvalue(itemscount):
# nonlocal itemsizes, itemvalues, C
totsize = sum(n * size for n, size in zip(itemscount, itemsizes))
totval = sum(n * val for n, val in zip(itemscount, itemvalues))
return (totval, -totsize) if totsize <= C else (-1, 0)
# Try all combinations of bounty items from 0 up to max1
bagged = max(product(*[range(n + 1) for n in max1]), key=totvalue)
numbagged = sum(bagged)
value, size = totvalue(bagged)
size = -size
# convert to (iten, count) pairs) in name order
bagged = ['%dx%d' % (n, items[i][SIZE]) for i, n in enumerate(bagged) if n]
return value, size, numbagged, bagged
if __name__ == '__main__':
value, size, numbagged, bagged = knapsack_unbounded_enumeration(items, capacity)
print(value)
print(bagged)
Output is:
23
['1x3', '2x5']
Keep in mind that this is a NP-hard problem, so it will blow as you enter some large values :)
You can use itertools.product:
import itertools
remaining_order = 13
package_numbers = [9,5,3]
required_packages = []
a=min([x for i in range(1,remaining_order+1//min(package_numbers)) for x in itertools.product(package_numbers,repeat=i)],key=lambda x: abs(sum(x)-remaining_order))
remaining_order-=sum(a)
print(a)
print(remaining_order)
Output:
(5, 5, 3)
0
This simply does the below steps:
Get value closest to 13, in the list with all the product values.
Then simply make it modify the number of remaining_order.
If you want it output with 'x':
import itertools
from collections import Counter
remaining_order = 13
package_numbers = [9,5,3]
required_packages = []
a=min([x for i in range(1,remaining_order+1//min(package_numbers)) for x in itertools.product(package_numbers,repeat=i)],key=lambda x: abs(sum(x)-remaining_order))
remaining_order-=sum(a)
print(' '.join(['{0}x{1}'.format(v,k) for k,v in Counter(a).items()]))
print(remaining_order)
Output:
2x5 + 1x3
0
For you problem, I tried two implementations depending on what you want, in both of the solutions I supposed you absolutely needed your remaining to be at 0. Otherwise the algorithm will return you -1. If you need them, tell me I can adapt my algorithm.
As the algorithm is implemented via dynamic programming, it handles good inputs, at least more than 130 packages !
In the first solution, I admitted we fill with the biggest package each time.
I n the second solution, I try to minimize the price, but the number of packages should always be 0.
remaining_order = 13
package_numbers = sorted([9,5,3], reverse=True) # To make sure the biggest package is the first element
prices = {9: 16, 5: 9, 3: 5}
required_packages = []
# First solution, using the biggest package each time, and making the total order remaining at 0 each time
ans = [[] for _ in range(remaining_order + 1)]
ans[0] = [0, 0, 0]
for i in range(1, remaining_order + 1):
for index, package_number in enumerate(package_numbers):
if i-package_number > -1:
tmp = ans[i-package_number]
if tmp != -1:
ans[i] = [tmp[x] if x != index else tmp[x] + 1 for x in range(len(tmp))]
break
else: # Using for else instead of a boolean value `found`
ans[i] = -1 # -1 is the not found combinations
print(ans[13]) # [0, 2, 1]
print(ans[9]) # [1, 0, 0]
# Second solution, minimizing the price with order at 0
def price(x):
return 16*x[0]+9*x[1]+5*x[2]
ans = [[] for _ in range(remaining_order + 1)]
ans[0] = ([0, 0, 0],0) # combination + price
for i in range(1, remaining_order + 1):
# The not found packages will be (-1, float('inf'))
minimal_price = float('inf')
minimal_combinations = -1
for index, package_number in enumerate(package_numbers):
if i-package_number > -1:
tmp = ans[i-package_number]
if tmp != (-1, float('inf')):
tmp_price = price(tmp[0]) + prices[package_number]
if tmp_price < minimal_price:
minimal_price = tmp_price
minimal_combinations = [tmp[0][x] if x != index else tmp[0][x] + 1 for x in range(len(tmp[0]))]
ans[i] = (minimal_combinations, minimal_price)
print(ans[13]) # ([0, 2, 1], 23)
print(ans[9]) # ([0, 0, 3], 15) Because the price of three packages is lower than the price of a package of 9
In case you need a solution for a small number of possible
package_numbers
but a possibly very big
remaining_order,
in which case all the other solutions would fail, you can use this to reduce remaining_order:
import numpy as np
remaining_order = 13
package_numbers = [9,5,3]
required_packages = []
sub_max=np.sum([(np.product(package_numbers)/i-1)*i for i in package_numbers])
while remaining_order > sub_max:
remaining_order -= np.product(package_numbers)
required_packages.append([max(package_numbers)]*np.product(package_numbers)/max(package_numbers))
Because if any package is in required_packages more often than (np.product(package_numbers)/i-1)*i it's sum is equal to np.product(package_numbers). In case the package max(package_numbers) isn't the one with the samllest price per unit, take the one with the smallest price per unit instead.
Example:
remaining_order = 100
package_numbers = [5,3]
Any part of remaining_order bigger than 5*2 plus 3*4 = 22 can be sorted out by adding 5 three times to the solution and taking remaining_order - 5*3.
So remaining order that actually needs to be calculated is 10. Which can then be solved to beeing 2 times 5. The rest is filled with 6 times 15 which is 18 times 5.
In case the number of possible package_numbers is bigger than just a handful, I recommend building a lookup table (with one of the others answers' code) for all numbers below sub_max which will make this immensely fast for any input.
Since no declaration about the object function is found, I assume your goal is to maximize the package value within the pack's capability.
Explanation: time complexity is fixed. Optimal solution may not be filling the highest valued item as many as possible, you have to search all possible combinations. However, you can reuse the possible optimal solutions you have searched to save space. For example, [5,5,3] is derived from adding 3 to a previous [5,5] try so the intermediate result can be "cached". You may either use an array or you may use a set to store possible solutions. The code below runs the same performance as the rosetta code but I think it's clearer.
To further optimize, use a priority set for opts.
costs = [3,5,9]
value = [5,9,16]
volume = 130
# solutions
opts = set()
opts.add(tuple([0]))
# calc total value
cost_val = dict(zip(costs, value))
def total_value(opt):
return sum([cost_val.get(cost,0) for cost in opt])
def possible_solutions():
solutions = set()
for opt in opts:
for cost in costs:
if cost + sum(opt) > volume:
continue
cnt = (volume - sum(opt)) // cost
for _ in range(1, cnt + 1):
sol = tuple(list(opt) + [cost] * _)
solutions.add(sol)
return solutions
def optimize_max_return(opts):
if not opts:
return tuple([])
cur = list(opts)[0]
for sol in opts:
if total_value(sol) > total_value(cur):
cur = sol
return cur
while sum(optimize_max_return(opts)) <= volume - min(costs):
opts = opts.union(possible_solutions())
print(optimize_max_return(opts))
If your requirement is "just fill the pack" it'll be even simpler using the volume for each item instead.
I'm currently trying to get an array of numbers like this one randomly shuffled:
label_array = np.repeat(np.arange(6), 12)
The only constrain is that no consecutive elements of the shuffle must be the same number. For that I'm currently using this code:
# Check if there are any occurrences of two consecutive
# elements being of the same category (same number)
num_occurrences = np.sum(np.diff(label_array) == 0)
# While there are any occurrences of this...
while num_occurrences != 0:
# ...shuffle the array...
np.random.shuffle(label_array)
# ...create a flag for occurrences...
flag = np.hstack(([False], np.diff(label_array) == 0))
flag_array = label_array[flag]
# ...and shuffle them.
np.random.shuffle(flag_array)
# Then re-assign them to the original array...
label_array[flag] = flag_array
# ...and check the number of occurrences again.
num_occurrences = np.sum(np.diff(label_array) == 0)
Although this works for an array of this size, I don't know if it would work for much bigger arrays. And even so, it may take a lot of time.
So, is there a better way of doing this?
May not be technically the best answer, hopefully it suffices for your requirements.
import numpy as np
def generate_random_array(block_length, block_count):
for blocks in range(0, block_count):
nums = np.arange(block_length)
np.random.shuffle(nums)
try:
if nums[0] == randoms_array [-1]:
nums[0], nums[-1] = nums[-1], nums[0]
except NameError:
randoms_array = []
randoms_array.extend(nums)
return randoms_array
generate_random_array(block_length=1000, block_count=1000)
Here is a way to do it, for Python >= 3.6, using random.choices, which allows to choose from a population with weights.
The idea is to generate the numbers one by one. Each time we generate a new number, we exclude the previous one by temporarily setting its weight to zero. Then, we decrement the weight of the chosen one.
As #roganjosh duly noted, we have a problem at the end when we are left with more than one instance of the last value - and that can be really frequent, especially with a small number of values and a large number of repeats.
The solution I used is to insert these value back into the list where they don't create a conflict, with the short send_back function.
import random
def send_back(value, number, lst):
idx = len(lst)-2
for _ in range(number):
while lst[idx] == value or lst[idx-1] == value:
idx -= 1
lst.insert(idx, value)
def shuffle_without_doubles(nb_values, repeats):
population = list(range(nb_values))
weights = [repeats] * nb_values
out = []
prev = None
for i in range(nb_values * repeats):
if prev is not None:
# remove prev from the list of possible choices
# by turning its weight temporarily to zero
old_weight = weights[prev]
weights[prev] = 0
try:
chosen = random.choices(population, weights)[0]
except IndexError:
# We are here because all of our weights are 0,
# which means that all is left to choose from
# is old_weight times the previous value
send_back(prev, old_weight, out)
break
out.append(chosen)
weights[chosen] -= 1
if prev is not None:
# restore weight
weights[prev] = old_weight
prev = chosen
return out
print(shuffle_without_doubles(6, 12))
[5, 1, 3, 4, 3, 2, 1, 5, 3, 5, 2, 0, 5, 4, 3, 4, 5,
3, 4, 0, 4, 1, 0, 1, 5, 3, 0, 2, 3, 4, 1, 2, 4, 1,
0, 2, 0, 2, 5, 0, 2, 1, 0, 5, 2, 0, 5, 0, 3, 2, 1,
2, 1, 5, 1, 3, 5, 4, 2, 4, 0, 4, 2, 4, 0, 1, 3, 4,
5, 3, 1, 3]
Some crude timing: it takes about 30 seconds to generate (shuffle_without_doubles(600, 1200)), so 720000 values.
I came from Creating a list without back-to-back repetitions from multiple repeating elements (referred as "problem A") as I organise my notes and there was no correct answer under "problem A" nor in the current one. Also these two problems seems different because problem A requires same elements.
Basically what you asked is same as an algorithm problem (link) where the randomness is not required. But when you have like almost half of all numbers same, the result can only be like "ABACADAEA...", where "ABCDE" are numbers. In the most voted answer to this problem, a priority queue is used so the time complexity is O(n log m), where n is the length of the output and m is the count of option.
As for this problem A easier way is to use itertools.permutations and randomly select some of them with different beginning and ending so it looks like "random"
I write draft code here and it works.
from itertools import permutations
from random import choice
def no_dup_shuffle(ele_count: int, repeat: int):
"""
Return a shuffle of `ele_count` elements repeating `repeat` times.
"""
p = permutations(range(ele_count))
res = []
curr = last = [-1] # -1 is a dummy value for the first `extend`
for _ in range(repeat):
while curr[0] == last[-1]:
curr = choice(list(p))
res.extend(curr)
last = curr
return res
def test_no_dup_shuffle(count, rep):
r = no_dup_shuffle(count, rep)
assert len(r) == count * rep # check result length
assert len(set(r)) == count # check all elements are used and in `range(count)`
for i, n in enumerate(r): # check no duplicate
assert n != r[i - 1]
print(r)
if __name__ == "__main__":
test_no_dup_shuffle(5, 3)
test_no_dup_shuffle(3, 17)
I'm trying to apply genetic algorithm for 8 queens puzzle. I've coded whole algorithm but it keeps getting stuck when it finds solution with 6 unhit queens and can't get over it. I feel like there's some diversity problem but I can't figure out what to do with it. My question is what is wrong with this realisation and why it keeps getting stuck on 6 unhit queens and can't make a final move? I've already examined every bit of code and I think there's some misinterpretation of algorithm itself evolved. That's why I attached whole code. So I hope that someone would tell me where I did wrong. Thanks in advance.
def mutate(self, children):
rnd.seed()
count = 0
for child in children:
count += 1
if rnd.random() < self.mut_prob:
i = rnd.randrange(0, 7)
ind = child[i].index(1)
child[i][ind] = 0
j = rnd.randrange(0, 7)
child[i][j] = 1
def solve(self, min_fitness= 7, max_epochs=100):
prev_pop = self.initial_population()
epochs = 0
max_fitness = 0
while (max_fitness <= min_fitness) and (epochs < max_epochs):
fitness = self.fitness_function(prev_pop)
fitness.sort(key=lambda tup: tup[1])
best_sol = fitness[len(fitness) - 1][0]
max_fitness = fitness[len(fitness) - 1][1]
mating = self.roulette(fitness)
mating_chromes = []
pop = copy.deepcopy(prev_pop)
for chrom in mating:
mating_chromes.append(pop[chrom])
pop.clear()
children = self.crossover(mating_chromes)
self.mutate(children)
fit = self.fitness_function(prev_pop)
to_destroy = self.reduction(fitness)
for el in to_destroy:
prev_pop[el] = children.pop(0)
epochs += 1
print(max_fitness)
print(epochs)
for el in prev_pop[best_sol]:
print(el)
print("\n")
print("im fine")
return 0
s = Solver_8_queens()
arr = s.solve()
One problem with your code is the way you use Python function random.randrange(). The documentation says that randrange(a, b) will return a random number x such that a <= x < b (note that b is not included).
When you write something like i = random.randrange(0, 7) you will get a random number from the semi-open interval [0, 7), while what you (most likely) want is the number from closed interval [0, 7], because board size is 8x8. So check all calls to randrange(), fix them if they are incorrect and see whether it solves the problem.
I have a list that contains sublists with 3 values and I need to print out a list that looks like:
I also need to compare the third column values with eachother to tell if they are increasing or decreasing as you go down.
bb = 3.9
lowest = 0.4
#appending all the information to a list
allinfo= []
while bb>=lowest:
everything = angleWithPost(bb,cc,dd,ee)
allinfo.append(everything)
bb-=0.1
I think the general idea for finding out whether or not the third column values are increasing or decreasing is:
#Checking whether or not Fnet are increasing or decreasing
ii=0
while ii<=(10*(bb-lowest)):
if allinfo[ii][2]>allinfo[ii+1][2]:
abc = "decreasing"
elif allinfo[ii][2]<allinfo[ii+1][2]:
abc = "increasing"
ii+=1
Then when i want to print out my table similar to the one above.
jj=0
while jj<=(10*(bb-lowest))
print "%8.2f %12.2f %12.2f %s" %(allinfo[jj][0], allinfo[jj][1], allinfo[jj][2], abc)
jj+=1
here is the angle with part
def chainPoints(aa,DIS,SEG,H):
#xtuple x chain points
n=0
xterms = []
xterm = -DIS
while n<=SEG:
xterms.append(xterm)
n+=1
xterm = -DIS + n*2*DIS/(SEG)
#
#ytuple y chain points
k=0
yterms = []
while k<=SEG:
yterm = H + aa*m.cosh(xterms[k]/aa) - aa*m.cosh(DIS/aa)
yterms.append(yterm)
k+=1
return(xterms,yterms)
#
#
def chainLength(aa,DIS,SEG,H):
xterms, yterms = chainPoints(aa,DIS,SEG,H)# using x points and y points from the chainpoints function
#length of chain
ff=1
Lterm=0.
totallength=0.
while ff<=SEG:
Lterm = m.sqrt((xterms[ff]-xterms[ff-1])**2 + (yterms[ff]-yterms[ff-1])**2)
totallength += Lterm
ff+=1
return(totallength)
#
def angleWithPost(aa,DIS,SEG,H):
xterms, yterms = chainPoints(aa,DIS,SEG,H)
totallength = chainLength(aa,DIS,SEG,H)
#Find the angle
thetaradians = (m.pi)/2. + m.atan(((yterms[1]-yterms[0])/(xterms[1]-xterms[0])))
#Need to print out the degrees
thetadegrees = (180/m.pi)*thetaradians
#finding the net force
Fnet = abs((rho*grav*totallength))/(2.*m.cos(thetaradians))
return(totallength, thetadegrees, Fnet)
Review this Python2 implementation which uses map and an iterator trick.
from itertools import izip_longest, islice
from pprint import pprint
data = [
[1, 2, 3],
[1, 2, 4],
[1, 2, 3],
[1, 2, 5],
]
class AddDirection(object):
def __init__(self):
# This default is used if the series begins with equal values or has a
# single element.
self.increasing = True
def __call__(self, pair):
crow, nrow = pair
if nrow is None or crow[-1] == nrow[-1]:
# This is the last row or the direction didn't change. Just return
# the direction we previouly had.
inc = self.increasing
elif crow[-1] > nrow[-1]:
inc = False
else:
# Here crow[-1] < nrow[-1].
inc = True
self.increasing = inc
return crow + ["Increasing" if inc else "Decreasing"]
result = map(AddDirection(), izip_longest(data, islice(data, 1, None)))
pprint(result)
The output:
pts/1$ python2 a.py
[[1, 2, 3, 'Increasing'],
[1, 2, 4, 'Decreasing'],
[1, 2, 3, 'Increasing'],
[1, 2, 5, 'Increasing']]
Whenever you want to transform the contents of a list (in this case the list of rows), map is a good place where to begin thinking.
When the algorithm requires data from several places of a list, offsetting the list and zipping the needed values is also a powerful technique. Using generators so that the list doesn't have to be copied, makes this viable in real code.
Finally, when you need to keep state between calls (in this case the direction), using an object is the best choice.
Sorry if the code is too terse!
Basically you want to add a 4th column to the inner list and print the results?
#print headers of table here, use .format for consistent padding
previous = 0
for l in outer_list:
if l[2] > previous:
l.append('increasing')
elif l[2] < previous:
l.append('decreasing')
previous = l[2]
#print row here use .format for consistent padding
Update for list of tuples, add value to tuple:
import random
outer_list = [ (i, i, random.randint(0,10),)for i in range(0,10)]
previous = 0
allinfo = []
for l in outer_list:
if l[2] > previous:
allinfo.append(l +('increasing',))
elif l[2] < previous:
allinfo.append(l +('decreasing',))
previous = l[2]
#print row here use .format for consistent padding
print(allinfo)
This most definitely can be optimized and you could reduce the number of times you are iterating over the data.