algorithm - Sum of all subparts of an array of integers -


given array {1,3,5,7}, subparts defined {1357,135,137,157,357,13,15,17,35,37,57,1,3,5,7}. have find sum of these numbers in new array. in case sum comes out 2333. please me find solution in o(n). o(n^2) solution times out.

link problem here or here.

my current attempt( @ finding pattern) is

for(i=0 len) //len length of array {      for(j=0 len-i)      {           sum+= arr[i]*pow(10,j)*((len-i) c i)*pow(2,i)      } }

in words - len-i c = (number of integers right) c weight. (combinations {from permutation , combination}) 2^i = 2 power (number of integers left)

thanks

you can solve problem simple recursive.

def f(arr):     if len(arr) == 1:         return (arr[0], 1)     else:         r = f(arr[:-1])         return (11 * r[0] + (r[1] + 1) * arr[-1], 2 * r[1] + 1)

so, how work? simple. let want compute sum of subpart of {1,3,5,7}. let assume know number of combinatiton of {1,3,5} , sum of subpart of {1,3,5} , can compute {1,3,5,7} using following formula:

sum_subpart({1,3,5,7}) = 11 * sum_subpart({1,3,5}) + number_combination({1,3,5}) * 7 + 7

this formula can derived observing. let have combination of {1,3,5}

a = [135, 13, 15, 35, 1, 3, 5]

we can create list of {1,3,5,7} by

a = [135, 13, 15, 35, 1, 3, 5] +      [135 * 10 + 7,       13  * 10 + 7,       15  * 10 + 7,       35  * 10 + 7,       1   * 10 + 7,       3   * 10 + 7,       5   * 10 + 7] + [7]

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