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]

Comments

Post a Comment

Popular posts from this blog

angularjs - ADAL JS Angular- WebAPI add a new role claim to the token -

i have created angular spa webapi backend using adal js authentication.as there no roles in ad, need manually add role claims in order give users access different api controllers. the roles stored in database. expecting inject claim through call webapi after authentication ad. webapi code might this. identity.addclaim(new claim("role", "user")); var ticket = new authenticationticket(identity, props); var accesstoken = startup.oauthbeareroptions.accesstokenformat.protect(ticket); is possible replace adal idtoken new token? is viable solution or there other better way handle this? as initial token generated azuread, possible edit token add new claim? appreciated. graph api supporting group claims. see here: http://justazure.com/azure-active-directory-part-4-group-claims/ if @ examples on page, users assigned groups , app can check group in claims. in current version of portal, need app manifest , modify it.
Read more

php - CakePHP HttpSockets send array of paramms -

i problem when make request (i can request). $link = 'http://uri/path/?param1=1&sid=2&sid=3&sid=4' $http = $httpsocket = new httpsocket(); $res = $httpsocket->get($link); if check request pr($http); i see : [line] => /url/path/?param1=1&sid%5b0%5d=2&sid%5b1%5d=3&sid%5b2%5d=4 http/1.1 and i'm getting empty response because server doesn't know parameters sid%5b0%5d=2 when try send parameters array : $data = array('param1' => '1', 'sid' => array('2','3', '4')); i see same changes %5b0%5d - additional indexes. how fix it? unfortunately , can not change server side, if send request in browser, i'll normal response in json format. when make request, can parameters this: $param1 = $_get['param1']; $sid= $_get['sid']; tip: use diferente names parameters. have multiples sid. use sid1, sid2, sid3... update: can parameters this:
Read more

node.js - Using Node without global install -

i'm working on few node & electron (atom shell) projects , i'm curious how them work without user having install node globally. i've seen few applications including node directory in project contains node.exe binary. how go setting node project use binary? edit: thought should add, i've searched everywhere answer this, unrelated results.
Read more