How Many Numbers? II
Problem Description:
We want to find the numbers higher or equal than 1000 that the sum of every four consecutives digits cannot be higher than a certain given value. If the number is num = d1d2d3d4d5d6, and the maximum sum of 4 contiguous digits is maxSum, then:
d1 + d2 + d3 + d4 <= maxSum
d2 + d3 + d4 + d5 <= maxSum
d3 + d4 + d5 + d6 <= maxSum
For that purpose, we need to create a function, max_sumDig(), that receives nMax, as the max value of the interval to study (the range (1000, nMax) ), and a certain value, maxSum, the maximum sum that every four consecutive digits should be less or equal to. The function should output the following list with the data detailed bellow:
[(1), (2), (3)]
(1) - the amount of numbers that satisfy the constraint presented above
(2) - the closest number to the mean of the results, if there are more than one, the smallest number should be chosen.
(3) - the total sum of all the found numbers
Let’s see a case with all the details:
max_sumDig(2000, 3) -------> [11, 1110, 12555]
(1) -There are 11 found numbers: 1000, 1001, 1002, 1010, 1011, 1020, 1100, 1101, 1110, 1200 and 2000
(2) - The mean of all the found numbers is:
(1000 + 1001 + 1002 + 1010 + 1011 + 1020 + 1100 + 1101 + 1110 + 1200 + 2000) /11 = 1141.36363,
so 1110 is the number that is closest to that mean value.
(3) - 12555 is the sum of all the found numbers
1000 + 1001 + 1002 + 1010 + 1011 + 1020 + 1100 + 1101 + 1110 + 1200 + 2000 = 12555
Finally, let’s see another cases
max_sumDig(2000, 4) -----> [21, 1120, 23665]
max_sumDig(2000, 7) -----> [85, 1200, 99986]
max_sumDig(3000, 7) -----> [141, 1600, 220756]
Happy coding!!
Sample Tests:
test.describe("Example tests")
test.it("nMax = " + str(2000))
test.it("maxSum = " + str(3))
test.assert_equals(max_sumDig(2000, 3), [11, 1110, 12555])
test.it("nMax = " + str(2000))
test.it("maxSum = " + str(4))
test.assert_equals(max_sumDig(2000, 4), [21, 1120, 23665])
test.it("nMax = " + str(2000))
test.it("maxSum = " + str(7))
test.assert_equals(max_sumDig(2000, 7), [85, 1200, 99986])
test.it("nMax = " + str(3000))
test.it("maxSum = " + str(7))
test.assert_equals(max_sumDig(3000, 7), [141, 1600, 220756])
test.it("nMax = " + str(4000))
test.it("maxSum = " + str(4))
test.assert_equals(max_sumDig(4000, 4), [35, 2000, 58331])
Version of Python:
During my codes(method1,it’s python3.7,the codewars system make me only use 2.7.6)
Solutions:
Method1:
import numpy as np
def max_sumDig(nMax, maxSum):
lists=[]
for i in range(1000,nMax+1):
list1=list(str(i))
list1=list(map(int,list1))
list2=[np.sum(list1[i:i+4]) for i in range(len(list1)-3)]
if max(list2)<=maxSum:
lists.append(i)
means=np.sum(lists)/len(lists)
closest=min(lists, key=lambda x:abs(x-means))
return [len(lists),closest,np.sum(lists)]
Unfortunately, method1 runs time out.Also,when I run it in jupyter notebook, everything is ok.But when I run it in codewars, sample Test occurs unbelievable error.If you know why, thanks a lot for you to contact with me.
Method2:
def check(num,max_sum):
l = [int(i) for i in str(num)]
for i in range(0,len(l) - 3):
if sum(l[i:i+4]) > max_sum:return False
return True
def max_sumDig(nMax, maxSum):
found = [i for i in range(1000,nMax + 1) if check(i,maxSum)]
mean = sum(found) / float(len(found))
for i in range(len(found) - 1):
if abs(mean - found[i]) < abs(mean - found[i + 1]):
mean = found[i]
break
return [len(found), mean, sum(found)]
Method3:
def max_sumDig(nMax, maxSum, digits=4):
values = [int(n) for n in map(str, xrange(10 ** (digits - 1), nMax + 1))
if all(sum(map(int, n[i:i+digits])) <= maxSum for i in range(len(n) - digits + 1))]
return [len(values), min(values, key=lambda n:abs(n - 1. * sum(values) / len(values))), sum(values)]
Method4:
def max_sumDig(nMax, maxSum):
def isGood(s): return all(sum(map(int, str(s[i:i+4]))) <= maxSum for i in range(len(s)-3) )
lst = [n for n in range(1000, nMax+1) if isGood(str(n))]
s, l = sum(lst), len(lst)
avg = 1.0*s/l
iAvg = next( i for i,n in enumerate(lst) if n > avg )
nearest = sorted(lst[iAvg-1:iAvg+1], key=lambda n: abs(n-avg))[0]
return [l, nearest, s]
Method5:
def max_sumDig(nMax, maxSum):
answers = []
for i in range(1000, nMax + 1):
good = True
n = [int(x) for x in str(i)]
for j in range(0, len(n)-3):
if sum([n[j],n[j+1],n[j+2],n[j+3]]) > maxSum:
good = False
if good == True:
answers.append(i)
num, tot = len(answers), sum(answers)
return [num, min(answers, key=lambda x: abs(x-(tot/float(num)))), tot]