LeetCode-Go/website/content/ChapterTwo/Bit_Manipulation.md

---
title: 2.15 ✅ Bit Manipulation
type: docs
weight: 15
---

# Bit Manipulation

![](https://img.halfrost.com/Leetcode/Bit_Manipulation.png)

- 异或的特性。第 136 题，第 268 题，第 389 题，第 421 题，

```go
x ^ 0 = x
x ^ 11111……1111 = ~x
x ^ (~x) = 11111……1111
x ^ x = 0
a ^ b = c  => a ^ c = b  => b ^ c = a (交换律)
a ^ b ^ c = a ^ (b ^ c) = (a ^ b）^ c (结合律)
```

- 构造特殊 Mask，将特殊位置放 0 或 1。

```go
将 x 最右边的 n 位清零， x & ( ~0 << n )
获取 x 的第 n 位值(0 或者 1)，(x >> n) & 1
获取 x 的第 n 位的幂值，x & (1 << (n - 1))
仅将第 n 位置为 1，x | (1 << n)
仅将第 n 位置为 0，x & (~(1 << n))
将 x 最高位至第 n 位(含)清零，x & ((1 << n) - 1)
将第 n 位至第 0 位(含)清零，x & (~((1 << (n + 1)) - 1)）
```

- 有特殊意义的 & 位操作运算。第 260 题，第 201 题，第 318 题，第 371 题，第 397 题，第 461 题，第 693 题，

```go
X & 1 == 1 判断是否是奇数(偶数)
X & = (X - 1) 将最低位(LSB)的 1 清零
X & -X 得到最低位(LSB)的 1
X & ~X = 0
```



| No.      | Title | Solution | Difficulty | TimeComplexity | SpaceComplexity |Favorite| Acceptance |
|:--------:|:------- | :--------: | :----------: | :----: | :-----: | :-----: |:-----: |
|0078|Subsets|[Go]({{< relref "/ChapterFour/0001~0099/0078.Subsets.md" >}})|Medium| O(n^2)| O(n)|❤️|65.9%|
|0136|Single Number|[Go]({{< relref "/ChapterFour/0100~0199/0136.Single-Number.md" >}})|Easy| O(n)| O(1)||66.8%|
|0137|Single Number II|[Go]({{< relref "/ChapterFour/0100~0199/0137.Single-Number-II.md" >}})|Medium| O(n)| O(1)|❤️|54.2%|
|0169|Majority Element|[Go]({{< relref "/ChapterFour/0100~0199/0169.Majority-Element.md" >}})|Easy| O(n)| O(1)|❤️|60.3%|
|0187|Repeated DNA Sequences|[Go]({{< relref "/ChapterFour/0100~0199/0187.Repeated-DNA-Sequences.md" >}})|Medium| O(n)| O(1)||41.8%|
|0190|Reverse Bits|[Go]({{< relref "/ChapterFour/0100~0199/0190.Reverse-Bits.md" >}})|Easy| O(n)| O(1)|❤️|42.9%|
|0191|Number of 1 Bits|[Go]({{< relref "/ChapterFour/0100~0199/0191.Number-of-1-Bits.md" >}})|Easy| O(n)| O(1)||54.5%|
|0201|Bitwise AND of Numbers Range|[Go]({{< relref "/ChapterFour/0200~0299/0201.Bitwise-AND-of-Numbers-Range.md" >}})|Medium| O(n)| O(1)|❤️|39.7%|
|0231|Power of Two|[Go]({{< relref "/ChapterFour/0200~0299/0231.Power-of-Two.md" >}})|Easy| O(1)| O(1)||43.8%|
|0260|Single Number III|[Go]({{< relref "/ChapterFour/0200~0299/0260.Single-Number-III.md" >}})|Medium| O(n)| O(1)|❤️|65.5%|
|0268|Missing Number|[Go]({{< relref "/ChapterFour/0200~0299/0268.Missing-Number.md" >}})|Easy| O(n)| O(1)||55.5%|
|0318|Maximum Product of Word Lengths|[Go]({{< relref "/ChapterFour/0300~0399/0318.Maximum-Product-of-Word-Lengths.md" >}})|Medium| O(n)| O(1)||52.6%|
|0338|Counting Bits|[Go]({{< relref "/ChapterFour/0300~0399/0338.Counting-Bits.md" >}})|Medium| O(n)| O(n)||70.7%|
|0342|Power of Four|[Go]({{< relref "/ChapterFour/0300~0399/0342.Power-of-Four.md" >}})|Easy| O(n)| O(1)||41.9%|
|0371|Sum of Two Integers|[Go]({{< relref "/ChapterFour/0300~0399/0371.Sum-of-Two-Integers.md" >}})|Medium| O(n)| O(1)||50.6%|
|0389|Find the Difference|[Go]({{< relref "/ChapterFour/0300~0399/0389.Find-the-Difference.md" >}})|Easy| O(n)| O(1)||58.0%|
|0393|UTF-8 Validation|[Go]({{< relref "/ChapterFour/0300~0399/0393.UTF-8-Validation.md" >}})|Medium| O(n)| O(1)||38.2%|
|0397|Integer Replacement|[Go]({{< relref "/ChapterFour/0300~0399/0397.Integer-Replacement.md" >}})|Medium| O(n)| O(1)||33.6%|
|0401|Binary Watch|[Go]({{< relref "/ChapterFour/0400~0499/0401.Binary-Watch.md" >}})|Easy| O(1)| O(1)||48.7%|
|0405|Convert a Number to Hexadecimal|[Go]({{< relref "/ChapterFour/0400~0499/0405.Convert-a-Number-to-Hexadecimal.md" >}})|Easy| O(n)| O(1)||44.6%|
|0421|Maximum XOR of Two Numbers in an Array|[Go]({{< relref "/ChapterFour/0400~0499/0421.Maximum-XOR-of-Two-Numbers-in-an-Array.md" >}})|Medium| O(n)| O(1)|❤️|54.5%|
|0461|Hamming Distance|[Go]({{< relref "/ChapterFour/0400~0499/0461.Hamming-Distance.md" >}})|Easy| O(n)| O(1)||73.3%|
|0476|Number Complement|[Go]({{< relref "/ChapterFour/0400~0499/0476.Number-Complement.md" >}})|Easy| O(n)| O(1)||65.2%|
|0477|Total Hamming Distance|[Go]({{< relref "/ChapterFour/0400~0499/0477.Total-Hamming-Distance.md" >}})|Medium| O(n)| O(1)||50.7%|
|0693|Binary Number with Alternating Bits|[Go]({{< relref "/ChapterFour/0600~0699/0693.Binary-Number-with-Alternating-Bits.md" >}})|Easy| O(n)| O(1)|❤️|60.0%|
|0756|Pyramid Transition Matrix|[Go]({{< relref "/ChapterFour/0700~0799/0756.Pyramid-Transition-Matrix.md" >}})|Medium| O(n log n)| O(n)||55.7%|
|0762|Prime Number of Set Bits in Binary Representation|[Go]({{< relref "/ChapterFour/0700~0799/0762.Prime-Number-of-Set-Bits-in-Binary-Representation.md" >}})|Easy| O(n)| O(1)||64.7%|
|0784|Letter Case Permutation|[Go]({{< relref "/ChapterFour/0700~0799/0784.Letter-Case-Permutation.md" >}})|Medium| O(n)| O(1)||68.9%|
|0898|Bitwise ORs of Subarrays|[Go]({{< relref "/ChapterFour/0800~0899/0898.Bitwise-ORs-of-Subarrays.md" >}})|Medium| O(n)| O(1)||34.5%|
|1178|Number of Valid Words for Each Puzzle|[Go]({{< relref "/ChapterFour/1100~1199/1178.Number-of-Valid-Words-for-Each-Puzzle.md" >}})|Hard||||39.8%|
|1290|Convert Binary Number in a Linked List to Integer|[Go]({{< relref "/ChapterFour/1200~1299/1290.Convert-Binary-Number-in-a-Linked-List-to-Integer.md" >}})|Easy||||81.7%|
|1461|Check If a String Contains All Binary Codes of Size K|[Go]({{< relref "/ChapterFour/1400~1499/1461.Check-If-a-String-Contains-All-Binary-Codes-of-Size-K.md" >}})|Medium||||54.2%|
|1720|Decode XORed Array|[Go]({{< relref "/ChapterFour/1700~1799/1720.Decode-XORed-Array.md" >}})|Easy||||85.2%|
|------------|-------------------------------------------------------|-------| ----------------| ---------------|-------------|-------------|-------------|


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