2336. Smallest Number in Infinite Set

2336. Smallest Number in Infinite Set

Tag: Design Heap

Difficulty: Medium

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.

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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.

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Heap

class SmallestInfiniteSet:

    def __init__(self):
        self.seen = set()
        self.heap = list()
        self.current_min = 1

    def popSmallest(self) -> int:
        if self.heap:
            to_remove = heapq.heappop(self.heap)
            self.seen.remove(to_remove)
        else:
            to_remove = self.current_min
            self.current_min += 1
        return to_remove

    def addBack(self, num: int) -> None:
        # Check if num is already present in or or added back to the infinite set 
        if num in self.seen or self.current_min <= num:
            return
        heapq.heappush(self.heap, num)
        self.seen.add(num)

# Your SmallestInfiniteSet object will be instantiated and called as such:
# obj = SmallestInfiniteSet()
# param_1 = obj.popSmallest()
# obj.addBack(num)

class SmallestInfiniteSet:

    def __init__(self):
        self.heap = list()
        self.min = 1

    def popSmallest(self) -> int:
        if self.heap:
            return heapq.heappop(self.heap)
        self.min += 1
        return self.min - 1

    def addBack(self, num: int) -> None:
        if self.min > num and not num in self.heap:
            heapq.heappush(self.heap, num)


# Your SmallestInfiniteSet object will be instantiated and called as such:
# obj = SmallestInfiniteSet()
# param_1 = obj.popSmallest()
# obj.addBack(num)