title
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 integernumback 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
1000calls will be made in total topopSmallestandaddBack.
solution
One way, we can use the heapq + set. Another way, we can divide it into two parts, maintain the smallest num and a sortedset so that no initial heap in the first.
import heapq
class SmallestInfiniteSet:
def __init__(self):
self.h = list(range(1, 1001, 1))
self.s = set(self.h)
heapq.heapify(self.h)
def popSmallest(self) -> int:
if self.h:
r = heapq.heappop(self.h)
self.s.remove(r)
return r
return -1
def addBack(self, num: int) -> None:
if num in self.s:
return
self.s.add(num)
heapq.heappush(self.h, num)