Smallest Number in Infinite Set

Description

You have a set which contains all positive integers [1, 2, 3, 4, 5, ...].

Implement the SmallestInfiniteSet class:

• SmallestInfiniteSet() Initializes the SmallestInfiniteSet object to contain all positive integers.
• int popSmallest() Removes and returns the smallest integer contained in the infinite set.
• void addBack(int num) Adds a positive integer num back into the infinite set, if it is not already in the infinite set.

Example 1:

Input [“SmallestInfiniteSet”, “addBack”, “popSmallest”, “popSmallest”, “popSmallest”, “addBack”, “popSmallest”, “popSmallest”, “popSmallest”] [[], [2], [], [], [], [1], [], [], []] Output [null, null, 1, 2, 3, null, 1, 4, 5]

Explanation SmallestInfiniteSet smallestInfiniteSet = new SmallestInfiniteSet(); smallestInfiniteSet.addBack(2); // 2 is already in the set, so no change is made. smallestInfiniteSet.popSmallest(); // return 1, since 1 is the smallest number, and remove it from the set. smallestInfiniteSet.popSmallest(); // return 2, and remove it from the set. smallestInfiniteSet.popSmallest(); // return 3, and remove it from the set. smallestInfiniteSet.addBack(1); // 1 is added back to the set. smallestInfiniteSet.popSmallest(); // return 1, since 1 was added back to the set and // is the smallest number, and remove it from the set. smallestInfiniteSet.popSmallest(); // return 4, and remove it from the set. smallestInfiniteSet.popSmallest(); // return 5, and remove it from the set.

Constraints:

• 1 <= num <= 1000
• At most 1000 calls will be made in total to popSmallest and addBack.

Code

• std::set 為 red black tree。

Time Complexity: $O(\log n)$, Space Complexity: $O(n)$

注意此解法並不用將所有元素都事先 insert 到 heap 中。

class SmallestInfiniteSet {
    int cur;
    set<int> s;
public:
    SmallestInfiniteSet() {
        cur = 1;
    }
    
    int popSmallest() {
        if(s.size()) {
            int res = *s.begin();
            s.erase(res);
            return res;
        } else {
            cur++;
            return cur - 1;
        }
    }
    
    void addBack(int num) {
        if(cur > num) s.insert(num);
    }
};
 
/**
 * Your SmallestInfiniteSet object will be instantiated and called as such:
 * SmallestInfiniteSet* obj = new SmallestInfiniteSet();
 * int param_1 = obj->popSmallest();
 * obj->addBack(num);
 */

Source

• Smallest Number in Infinite Set - LeetCode