What is the best approach for solving the Final Array State After K Multiplication Operations I problem?

Using a priority queue to maintain the order of elements is the most efficient approach. It ensures that the array is updated correctly after each operation, while maintaining a time complexity of O(N + k * log N).

How does the priority queue help in solving the Final Array State After K Multiplication Operations I problem?

The priority queue allows efficient access and modification of the element that needs to be multiplied, while maintaining the array's order in logarithmic time, which is crucial for handling multiple operations efficiently.

Can I solve this problem without using a priority queue?

While it's possible to solve the problem without a priority queue, doing so would likely increase the time complexity due to the need for sorting or searching through the array after each operation.

What is the time complexity of the Final Array State After K Multiplication Operations I problem?

The time complexity is O(N + k * log N), where N is the length of the array and k is the number of operations. The priority queue ensures that each operation is handled in logarithmic time.

What should I focus on when solving the Final Array State After K Multiplication Operations I problem?

Focus on efficiently managing the array's order after each multiplication by using a priority queue. Ensure that the time complexity remains optimal by maintaining the array's sorted state during the operations.

#3264

Easy

auto_awesome数组·数学

LeetCode 题解工作台

K 次乘运算后的最终数组 I

给你一个整数数组 nums ，一个整数 k 和一个整数 multiplier 。你需要对 nums 执行 k 次操作，每次操作中：找到 nums 中的最小值 x ，如果存在多个最小值，选择最前面的一个。将 x 替换为 x * multiplier 。请你返回执行完 k 次乘运算之后，…

数组数学堆（优先队列）模拟

题目描述

给你一个整数数组 nums ，一个整数 k 和一个整数 multiplier 。

你需要对 nums 执行 k 次操作，每次操作中：

找到 nums 中的最小值 x ，如果存在多个最小值，选择最前面的一个。
将 x 替换为 x * multiplier 。

请你返回执行完 k 次乘运算之后，最终的 nums 数组。

示例 1：

输入：nums = [2,1,3,5,6], k = 5, multiplier = 2

输出：[8,4,6,5,6]

解释：

操作	结果
1 次操作后	[2, 2, 3, 5, 6]
2 次操作后	[4, 2, 3, 5, 6]
3 次操作后	[4, 4, 3, 5, 6]
4 次操作后	[4, 4, 6, 5, 6]
5 次操作后	[8, 4, 6, 5, 6]

示例 2：

输入：nums = [1,2], k = 3, multiplier = 4

输出：[16,8]

解释：

操作	结果
1 次操作后	[4, 2]
2 次操作后	[4, 8]
3 次操作后	[16, 8]

提示：

1 <= nums.length <= 100
1 <= nums[i] <= 100
1 <= k <= 10
1 <= multiplier <= 5

lightbulb

解题思路

方法一：优先队列（小根堆）+ 模拟

我们可以用一个小根堆来维护数组 $\textit{nums}$ 中的元素，每次从小根堆中取出最小值，将其乘以 $\textit{multiplier}$ 后再放回小根堆中。在实现过程中，我们往小根堆插入的是元素的下标，然后自定义比较函数，使得小根堆按照 $\textit{nums}$ 中元素的大小作为第一关键字，下标作为第二关键字进行排序。

最后，我们返回数组 $\textit{nums}$ 即可。

时间复杂度 $O((n + k) \times \log n)$ ，空间复杂度 $O(n)$ 。其中 $n$ 是数组 $\textit{nums}$ 的长度。

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class Solution:
    def getFinalState(self, nums: List[int], k: int, multiplier: int) -> List[int]:
        pq = [(x, i) for i, x in enumerate(nums)]
        heapify(pq)
        for _ in range(k):
            _, i = heappop(pq)
            nums[i] *= multiplier
            heappush(pq, (nums[i], i))
        return nums

speed

复杂度分析

指标	值
时间	O(N + k \cdot \log N)
空间	O(N)

psychology

面试官常问的追问

外企场景

question_mark
Look for the candidate's ability to handle the array transformations efficiently with a priority queue.
question_mark
Check if the candidate understands the trade-offs of using a priority queue and its logarithmic time complexity.
question_mark
Evaluate the candidate's approach to maintaining the array's sorted order throughout multiple operations.

warning

常见陷阱

外企场景

error
Overcomplicating the solution by trying to manually sort the array after each operation, which increases time complexity.
error
Failing to account for the fact that the array size can vary up to 100 elements, making inefficient solutions impractical.
error
Not correctly updating the priority queue after each operation, leading to incorrect final results.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Increasing the number of operations k beyond the usual limits and testing if the approach still handles it efficiently.
arrow_right_alt
Changing the multiplier value dynamically during the operations instead of keeping it constant.
arrow_right_alt
Testing with different initial array sizes and ensuring the priority queue implementation scales well.

help

常见问题

外企场景

继续练习

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