python - straightforward with explanation - O(klogk) where k is number of blacklisted numbers
\nclass Solution:\n   ### since picking a random number may or may not result in ending up picking a blacklist number forever,\n   # we need to first figure out
```\nclass Solution:\n   ### since picking a random number may or may not result in ending up picking a blacklist number forever,\n   # we need to first figure out what numbers we can work with.\n   ### so, therefore idea is to precompute the list of valid ranges a number can be in outside of the blacklist. \n   ### for eg: for n = 3 and blacklist = [0,1] the valid ranges are [[2,2]] or for n = 5 , blacklist = [0,3] valid ranges can be [[1,2],[4,4]]\n   ### note - the valid range i generate are closed intervals (not open intervals).\n   ### once i have the valid ranges, i just pick a random valid range and then pick a random number from that random range\n    def __init__(self, n, blacklist):\n        self.valid_ranges = []\n\t\t## here is where we loose efficiency... there\'s probably a better way to do this than sort the blacklist.\n        blacklist.sort()\n\t\t# if there are no blacklist numbers then my valid range will be [0,n-1] \n\t\t# i.e i should be able to pick any number between 0 and n-1. \n\t\t# lets start there and update the ranges as we examine the blacklist\n        r = [0,n-1]\n\t\t\n\t\t# examine each blacklist number to form the valid ranges of allowed numbers \n        for blacklist_number in blacklist:\n\t\t   # if start position of a valid range is in blacklist, update the start position \n\t\t   # by moving the start position of that interval by one\n            if blacklist_number == r[0]:\n                r[0] = (blacklist_number+1)\n\t\t\t# if the end of the interval has the blacklist number in it, \n\t\t\t# then update the end to before the blacklist number and add it to the valid intervals list\n\t\t\t# and create another interval starting after the interval till the end of original interval\n            elif blacklist_number <= r[1]:\n                r[1] = (blacklist_number-1)\n                self.valid_ranges.append(r)\n                r = [blacklist_number+1,n-1]\n\t\t# once we examined all the blacklist, check if the last interval we were working on might be the last valid interval or not.\n        if r[0] < n and r[1] < n:\n            self.valid_ranges.append(r)\n            \n    def pick(self):\n        from random import randint\n\t\t## pick a random valid range from the list of valid ranges\n        idx1 = randint(0,len(self.valid_ranges)-1)\n\t\t# if the valid range from the list we picked has start and end positions of that interval as same, then simply return that number\n        if self.valid_ranges[idx1][0] == self.valid_ranges[idx1][1]:\n            return self.valid_ranges[idx1][0]\n\t\t# else pick a random integer between the start and end positions of the interval and return it.\n        idx2 = randint(self.valid_ranges[idx1][0],self.valid_ranges[idx1][1])\n        return idx2\n```\n\nEdit - Just realized this solution has the same big picture idea as approach #3...
['Python']