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Formatted question description: https://leetcode.ca/all/710.html

# 710. Random Pick with Blacklist

Hard

## Description

Given a blacklist B containing unique integers from [0, N), write a function to return a uniform random integer from [0, N) which is NOT in B.

Optimize it such that it minimizes the call to system’s Math.random().

Note:

1. 1 <= N <= 1000000000
2. 0 <= B.length < min(100000, N)
3. [0, N) does NOT include N. See interval notation.

Example 1:

Input:

[“Solution”,”pick”,”pick”,”pick”]

[[1,[]],[],[],[]]

Output: [null,0,0,0]

Example 2:

Input:

[“Solution”,”pick”,”pick”,”pick”]

[[2,[]],[],[],[]]

Output: [null,1,1,1]

Example 3:

Input:

[“Solution”,”pick”,”pick”,”pick”]

[[3,],[],[],[]]

Output: [null,0,0,2]

Example 4:

Input:

[“Solution”,”pick”,”pick”,”pick”]

[[4,],[],[],[]]

Output: [null,1,3,1]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution’s constructor has two arguments, N and the blacklist B. pick has no arguments. Arguments are always wrapped with a list, even if there aren’t any.

## Solution

Given an integer N and a blacklist B, there are N - B.length numbers that can be selected. For example, if N is 100 and B.length is 10, then there are 100 - 10 = 90 numbers that can be selected. Therefore, call Math.random() so that the returned integer is in the range [0, N - B.length).

For each number in the blacklist, it is either less than N - B.length or greater than or equal to N - B.length. If a number in the blacklist is less than N - B.length, then it should be mapped to a number in the range [N - B.length, N) which is not in the blacklist.

In the class, maintain size which is the number of integers that can be selected, maintain a set to store the numbers in the blacklist, and maintain a map.

For the constructor, initialize size = N - B.length, and add all the numbers in the blacklist to the set. Then for each number in the blacklist, map it to num which is in the range [size, N) and is not in the blacklist (num is updated after each mapping), with the map updated.

For the method pick, randomly select an integer in the range [0, size), get the corresponding integer from the map (if the integer is not in the map, then the integer remains unchanged), and return the integer.

• class Solution {
int size;
Set<Integer> blacklistSet;
Map<Integer, Integer> map;

public Solution(int N, int[] blacklist) {
size = N - blacklist.length;
blacklistSet = new HashSet<Integer>();
for (int blacklistNum : blacklist)
map = new HashMap<Integer, Integer>();
int num = size;
for (int blacklistNum : blacklist) {
if (blacklistNum < size) {
while (blacklistSet.contains(num))
num++;
map.put(blacklistNum, num);
num++;
}
}
}

public int pick() {
int num = (int) (Math.random() * size);
num = map.getOrDefault(num, num);
return num;
}
}

/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(N, blacklist);
* int param_1 = obj.pick();
*/

• // OJ: https://leetcode.com/problems/random-pick-with-blacklist/
// Time:
//      Solution: O(BlogB)
//      pick: O(1)
// Space: O(B)
class Solution {
unordered_map<int, int> m;
int len;
public:
Solution(int n, vector<int>& B) {
len = n - B.size();
sort(begin(B), end(B));
int j = lower_bound(begin(B), end(B), len) - begin(B), N = B.size(), next = len;
for (int i = 0; i < N && B[i] < len; ++i) {
while (j < N && B[j] == next) ++j, ++next;
m[B[i]] = next++;
}
}
int pick() {
int r = rand() % len;
return m.count(r) ? m[r] : r;
}
};

• class Solution:
def __init__(self, n: int, blacklist: List[int]):
self.k = n - len(blacklist)
self.d = {}
i = self.k
black = set(blacklist)
for b in blacklist:
if b < self.k:
while i in black:
i += 1
self.d[b] = i
i += 1

def pick(self) -> int:
x = randrange(self.k)
return self.d.get(x, x)

# Your Solution object will be instantiated and called as such:
# obj = Solution(n, blacklist)
# param_1 = obj.pick()


• type Solution struct {
d map[int]int
k int
}

func Constructor(n int, blacklist []int) Solution {
k := n - len(blacklist)
i := k
black := map[int]bool{}
for _, b := range blacklist {
black[b] = true
}
d := map[int]int{}
for _, b := range blacklist {
if b < k {
for black[i] {
i++
}
d[b] = i
i++
}
}
return Solution{d, k}
}

func (this *Solution) Pick() int {
x := rand.Intn(this.k)
if v, ok := this.d[x]; ok {
return v
}
return x
}

/**
* Your Solution object will be instantiated and called as such:
* obj := Constructor(n, blacklist);
* param_1 := obj.Pick();
*/