2336. Smallest Number in Infinite Set

Description of Problem

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.

Solution

Tags: BTree,Divide and Conquer

Explanation

Divide the data strcture into two parts: finite set (using BTree) and infinite set (using current smallest integer).

Code (Rust)

use std::collections::{BTreeSet,HashSet};
use std::cmp::Reverse;

struct SmallestInfiniteSet {
    tree_in_finite : BTreeSet<i32>,
    smallest_in_infinite : i32,
}

/** 
 * `&self` means the method takes an immutable reference.
 * If you need a mutable reference, change it to `&mut self` instead.
 */
impl SmallestInfiniteSet {

    fn new() -> Self {
        SmallestInfiniteSet {
            tree_in_finite : BTreeSet::new(),
            smallest_in_infinite : 1,
        }
    }
    
    fn pop_smallest(&mut self) -> i32 {
        if let Some(smallest) = self.tree_in_finite.pop_first() {
            return smallest;
        }
        else{
            let smallest = self.smallest_in_infinite;
            self.smallest_in_infinite += 1;
            return smallest;
        }
    }
    
    fn add_back(&mut self, num: i32) {
        if num >= self.smallest_in_infinite {
            // ignore the number
        }else {
            // put the number into finite_part
            self.tree_in_finite.insert(num);
        }
    }

}

/**
 * Your SmallestInfiniteSet object will be instantiated and called as such:
 * let obj = SmallestInfiniteSet::new();
 * let ret_1: i32 = obj.pop_smallest();
 * obj.add_back(num);
 */