What is the key strategy to solve the Integer Replacement problem?

The Integer Replacement problem can be solved effectively using state transition dynamic programming, combined with bit manipulation for faster decision-making on odd numbers.

How does memoization help in solving Integer Replacement?

Memoization helps by storing the results of intermediate steps, ensuring that you avoid recalculating the minimum steps for the same number multiple times.

What is the time complexity of the optimal solution for Integer Replacement?

The optimal solution typically has a time complexity of O(log n) due to the nature of halving the number in each step.

How do you handle odd numbers in Integer Replacement?

For odd numbers, you can either subtract 1 or add 1, and bit manipulation can help in making this decision efficiently based on the least significant bit.

Can Integer Replacement be solved with a greedy approach?

Yes, a greedy approach can be used to prioritize operations that reduce the number quickly, although memoization may be necessary for optimal performance.

#397

Medium

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

整数替换

给定一个正整数 n ，你可以做如下操作：如果 n 是偶数，则用 n / 2 替换 n 。如果 n 是奇数，则可以用 n + 1 或 n - 1 替换 n 。返回 n 变为 1 所需的最小替换次数。示例 1：输入： n = 8 输出： 3 解释： 8 -> 4 -> 2 -> 1 示例 …

动态规划贪心位运算记忆化

题目描述

给定一个正整数 n ，你可以做如下操作：

如果 n 是偶数，则用 n / 2替换 n 。
如果 n 是奇数，则可以用 n + 1或n - 1替换 n 。

返回 n 变为 1 所需的 最小替换次数 。

示例 1：

输入：n = 8
输出：3
解释：8 -> 4 -> 2 -> 1

示例 2：

输入：n = 7
输出：4
解释：7 -> 8 -> 4 -> 2 -> 1
或 7 -> 6 -> 3 -> 2 -> 1

示例 3：

输入：n = 4
输出：2

提示：

1 <= n <= 2³¹ - 1

lightbulb

解题思路

方法一

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class Solution:
    def integerReplacement(self, n: int) -> int:
        ans = 0
        while n != 1:
            if (n & 1) == 0:
                n >>= 1
            elif n != 3 and (n & 3) == 3:
                n += 1
            else:
                n -= 1
            ans += 1
        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
Understand dynamic programming and state transitions.
question_mark
Identify efficient ways to optimize the problem using bit manipulation.
question_mark
Evaluate the trade-offs between greedy approaches and memoization.

warning

常见陷阱

外企场景

error
Not considering the optimal approach for odd numbers (subtract or add 1).
error
Failing to memoize results, which can lead to redundant computations and inefficient solutions.
error
Missing edge cases like n = 1 or n being a large number close to 231 - 1.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Extend the problem to handle non-positive integers.
arrow_right_alt
Limit the number of operations or add constraints on the maximum allowed steps.
arrow_right_alt
Explore a version where you must also track the exact sequence of operations taken.

help

常见问题

外企场景

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