2349. Design a Number Container System

Problem

Design a number container system that can do the following:

Insert or Replace a number at the given index in the system.
Return the smallest index for the given number in the system.

Implement the NumberContainers class:

NumberContainers() Initializes the number container system.
void change(int index, int number) Fills the container at index with the number. If there is already a number at that index, replace it.
int find(int number) Returns the smallest index for the given number, or -1 if there is no index that is filled by number in the system.

https://leetcode.com/problems/design-a-number-container-system/

Example 1:

Input
["NumberContainers", "find", "change", "change", "change", "change", "find", "change", "find"]
[[], [10], [2, 10], [1, 10], [3, 10], [5, 10], [10], [1, 20], [10]]
Output
[null, -1, null, null, null, null, 1, null, 2]
Explanation

NumberContainers nc = new NumberContainers();
nc.find(10); // There is no index that is filled with number 10. Therefore, we return -1.
nc.change(2, 10); // Your container at index 2 will be filled with number 10.
nc.change(1, 10); // Your container at index 1 will be filled with number 10.
nc.change(3, 10); // Your container at index 3 will be filled with number 10.
nc.change(5, 10); // Your container at index 5 will be filled with number 10.
nc.find(10); // Number 10 is at the indices 1, 2, 3, and 5. Since the smallest index that is filled with 10 is 1, we return 1.
nc.change(1, 20); // Your container at index 1 will be filled with number 20. Note that index 1 was filled with 10 and then replaced with 20.
nc.find(10); // Number 10 is at the indices 2, 3, and 5. The smallest index that is filled with 10 is 2. Therefore, we return 2.

Constraints:

1 <= index, number <= 10⁹
At most 10⁵ calls will be made in total to change and find.

Test Cases

class NumberContainers:

    def __init__(self):


    def change(self, index: int, number: int) -> None:


    def find(self, number: int) -> int:



# Your NumberContainers object will be instantiated and called as such:
# obj = NumberContainers()
# obj.change(index,number)
# param_2 = obj.find(number)

solution_test.py

import pytest

from solution import NumberContainers

null = None


@pytest.mark.parametrize('actions, params, expects', [
    (
        ["NumberContainers", "find", "change", "change", "change", "change", "find", "change", "find"],
        [[], [10], [2, 10], [1, 10], [3, 10], [5, 10], [10], [1, 20], [10]],
        [null, -1, null, null, null, null, 1, null, 2],
    ),
])
@pytest.mark.parametrize('clazz', [NumberContainers])
def test_solution(clazz, actions, params, expects):
    sol = None
    for action, args, expected in zip(actions, params, expects):
        if action == 'NumberContainers':
            sol = clazz(*args)
        else:
            assert getattr(sol, action)(*args) == expected

Thoughts

跟 3160. Find the Number of Distinct Colors Among the Balls 差不多。index 相当于球的编号，number 相当于颜色。主要的区别是本题需要记录每个 number 对应的 index 数组，以便随时可以查询此 number 所在的所有 index 的最小值。

同样用字典记录每个 index 最新的 number。再用字典记录每个 number 的所有 index，用有序数组记录，这里直接用 Python 的 list。需要增加或删除的时候，先用二分法查找再执行插入或删除操作。

构造函数的时间复杂度 O(1)；change 方法的时间复杂度 O(n)；find 方法的时间复杂度 O(n)。空间复杂度 O(n)。其中 n 是 change 的调用次数。

Code

solution.py

from bisect import bisect_left
from collections import defaultdict


class NumberContainers:

    def __init__(self):
        self._numbers: dict[int, int] = {} # index -> number
        self._indices: dict[int, list[int]] = defaultdict(list) # number -> sorted list of indices

    def change(self, index: int, number: int) -> None:
        if index in self._numbers and self._numbers[index] == number:
            return

        if index in self._numbers:
            old_number = self._numbers[index]
            indices = self._indices[old_number]
            del indices[bisect_left(indices, index)]

        self._numbers[index] = number
        indices = self._indices[number]
        indices.insert(bisect_left(indices, index), index)

    def find(self, number: int) -> int:
        if number not in self._indices:
            return -1

        indices = self._indices[number]
        if not indices:
            return -1

        return indices[0]


# Your NumberContainers object will be instantiated and called as such:
# obj = NumberContainers()
# obj.change(index,number)
# param_2 = obj.find(number)