What is the core pattern used in solving the 'Queries on a Permutation With Key' problem?

The core pattern involves using an array and a Binary Indexed Tree to track and update the positions of elements in a permutation efficiently.

How does a Binary Indexed Tree help in this problem?

A Binary Indexed Tree allows us to track the position of elements in the permutation in logarithmic time, improving the efficiency of querying and updating positions.

What are the key challenges when implementing a solution for this problem?

The main challenges involve managing the updates to the permutation after each query and ensuring the solution runs efficiently for large inputs.

Can this problem be solved without using a Binary Indexed Tree?

While it's possible to solve this problem without a Binary Indexed Tree, it would result in inefficient time complexity. A BIT provides a significant optimization.

What is the time complexity of the solution for 'Queries on a Permutation With Key'?

The time complexity is O(n log m), where `n` is the number of queries and `m` is the size of the permutation, due to the Binary Indexed Tree operations.

#1409

Medium

auto_awesome数组·结合·二分·indexed·树

LeetCode 题解工作台

查询带键的排列

给定一个正整数数组 queries ，其取值范围在 1 到 m 之间。请你根据以下规则按顺序处理所有 queries[i] （从 i=0 到 i=queries.length-1 ）：首先，你有一个排列 P=[1,2,3,...,m] 。对于当前的 i ，找到 queries[i] 在排列 P…

数组树状数组模拟

题目描述

给定一个正整数数组 queries ，其取值范围在 1 到 m 之间。请你根据以下规则按顺序处理所有 queries[i]（从 i=0 到 i=queries.length-1）：

首先，你有一个排列 P=[1,2,3,...,m]。
对于当前的 i ，找到 queries[i] 在排列 P 中的位置（从 0 开始索引），然后将它移到排列 P 的开头（即下标为 0 处）。注意， queries[i] 的查询结果是 queries[i] 在 P 中移动前的位置。

返回一个数组，包含从给定 queries 中查询到的结果。

示例 1：

输入：queries = [3,1,2,1], m = 5
输出：[2,1,2,1] 
解释：处理 queries 的过程如下：
对于 i=0: queries[i]=3, P=[1,2,3,4,5], 3 在 P 中的位置是 2，然后我们把 3 移动到 P 的开头，得到 P=[3,1,2,4,5] 。
对于 i=1: queries[i]=1, P=[3,1,2,4,5], 1 在 P 中的位置是 1，然后我们把 1 移动到 P 的开头，得到 P=[1,3,2,4,5] 。 
对于 i=2: queries[i]=2, P=[1,3,2,4,5], 2 在 P 中的位置是 2，然后我们把 2 移动到 P 的开头，得到 P=[2,1,3,4,5] 。
对于 i=3: queries[i]=1, P=[2,1,3,4,5], 1 在 P 中的位置是 1，然后我们把 1 移动到 P 的开头，得到 P=[1,2,3,4,5] 。 
因此，包含结果的数组为 [2,1,2,1] 。

示例 2：

输入：queries = [4,1,2,2], m = 4
输出：[3,1,2,0]

示例 3：

输入：queries = [7,5,5,8,3], m = 8
输出：[6,5,0,7,5]

提示：

1 <= m <= 10^3
1 <= queries.length <= m
1 <= queries[i] <= m

lightbulb

解题思路

方法一：模拟

题目数据规模不大，可以直接模拟。

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class Solution:
    def processQueries(self, queries: List[int], m: int) -> List[int]:
        p = list(range(1, m + 1))
        ans = []
        for v in queries:
            j = p.index(v)
            ans.append(j)
            p.pop(j)
            p.insert(0, v)
        return ans

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Check if the candidate understands how to apply a Binary Indexed Tree for array manipulation and position tracking.
question_mark
Assess how well the candidate can manage large inputs efficiently through optimized data structures.
question_mark
Evaluate the candidate's approach to handling queries in constant space or time complexity.

warning

常见陷阱

外企场景

error
Not using a Binary Indexed Tree or another efficient data structure could lead to a time complexity of O(n*m), which is inefficient for larger inputs.
error
Failing to update the Binary Indexed Tree properly after each query will lead to incorrect results.
error
Incorrectly handling edge cases where the queries involve the same element multiple times.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Instead of moving elements to the front, the problem could ask to move elements to the back of the array.
arrow_right_alt
Queries could involve different types of operations such as adding or removing elements from the permutation dynamically.
arrow_right_alt
The problem could be extended to handle range queries where multiple elements need to be processed at once.

help

常见问题

外企场景

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