Merge pull request #613 from LetMeFly666/540

添加问题“540.有序数组中的单一元素”的代码和题解

Author: LetMeFly666

Codes/0540-single-element-in-a-sorted-array_20241110.cpp

@@ -0,0 +1,48 @@
+/*
+ * @Author: LetMeFly
+ * @Date: 2024-11-10 16:42:30
+ * @LastEditors: LetMeFly.xyz
+ * @LastEditTime: 2024-11-10 17:28:09
+ */
+#ifdef _WIN32
+#include "_[1,2]toVector.h"
+#endif
+
+#ifdef FirstTry
+class Solution {
+public:
+    int singleNonDuplicate(vector<int>& nums) {
+        int l = 0, r = nums.size();
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (mid == nums.size() - 1 || nums[mid] != nums[mid ^ 1]) {  // 问题出在mid及其之前
+                if ((mid == 0 || nums[mid] != nums[mid - 1]) && (mid == nums.size() - 1 || nums[mid] != nums[mid + 1])) {
+                    return nums[mid];
+                }
+                r = mid;
+            } else {
+                l = mid + 1;
+            }
+        }
+        // printf("l = %d\n", l);  //************
+        return nums[l];
+    }
+};
+#else  // FirstTry
+// SecondTry
+class Solution {
+public:
+    int singleNonDuplicate(vector<int>& nums) {
+        int l = 0, r = nums.size() - 1;
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (nums[mid] == nums[mid ^ 1]) {
+                l = mid + 1;
+            } else {
+                r = mid;
+            }
+        }
+        return nums[l];
+    }
+};
+#endif  // FirstTry

Codes/0540-single-element-in-a-sorted-array_20241110.go

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+/*
+ * @Author: LetMeFly
+ * @Date: 2024-11-10 16:45:15
+ * @LastEditors: LetMeFly.xyz
+ * @LastEditTime: 2024-11-10 17:41:04
+ */
+package main
+
+func singleNonDuplicate(nums []int) int {
+    l, r := 0, len(nums) - 1
+    for l < r {
+        mid := (l + r) >> 1
+        if nums[mid] == nums[mid + 1] {
+            l = mid + 1
+        } else {
+            r = mid
+        }
+    }
+    return nums[l]
+}

Codes/0540-single-element-in-a-sorted-array_20241110.java

@@ -0,0 +1,20 @@
+/*
+ * @Author: LetMeFly
+ * @Date: 2024-11-10 16:45:00
+ * @LastEditors: LetMeFly.xyz
+ * @LastEditTime: 2024-11-10 17:49:31
+ */
+class Solution {
+    public int singleNonDuplicate(int[] nums) {
+        int l = 0, r = nums.length - 1;
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (nums[mid] == nums[mid ^ 1]) {
+                l = mid + 1;
+            } else {
+                r = mid;
+            }
+        }
+        return nums[l];
+    }
+}

Codes/0540-single-element-in-a-sorted-array_20241110.py

@@ -0,0 +1,18 @@
+'''
+Author: LetMeFly
+Date: 2024-11-10 16:44:54
+LastEditors: LetMeFly.xyz
+LastEditTime: 2024-11-10 17:38:12
+'''
+from typing import List
+
+class Solution:
+    def singleNonDuplicate(self, nums: List[int]) -> int:
+        l, r = 0, len(nums) - 1
+        while l < r:
+            mid = (l + r) >> 1
+            if nums[mid] == nums[mid ^ 1]:
+                l = mid + 1
+            else:
+                r = mid
+        return nums[l]

README.md

@@ -205,6 +205,7 @@
 |0529.扫雷游戏|中等|<a href="https://leetcode.cn/problems/minesweeper/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/11/23/LeetCode%200529.%E6%89%AB%E9%9B%B7%E6%B8%B8%E6%88%8F/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/127997191" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/minesweeper/solutions/1986830/letmefly-529sao-lei-you-xi-by-tisfy-cffc/" target="_blank">LeetCode题解</a>|
 |0530.二叉搜索树的最小绝对差|简单|<a href="https://leetcode.cn/problems/minimum-absolute-difference-in-bst/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/11/23/LeetCode%200530.%E4%BA%8C%E5%8F%89%E6%90%9C%E7%B4%A2%E6%A0%91%E7%9A%84%E6%9C%80%E5%B0%8F%E7%BB%9D%E5%AF%B9%E5%B7%AE/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/127997530" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/minimum-absolute-difference-in-bst/solutions/1986865/letmefly-530er-cha-sou-suo-shu-de-zui-xi-716i/" target="_blank">LeetCode题解</a>|
 |0538.把二叉搜索树转换为累加树|中等|<a href="https://leetcode.cn/problems/convert-bst-to-greater-tree/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/12/04/LeetCode%200538.%E6%8A%8A%E4%BA%8C%E5%8F%89%E6%90%9C%E7%B4%A2%E6%A0%91%E8%BD%AC%E6%8D%A2%E4%B8%BA%E7%B4%AF%E5%8A%A0%E6%A0%91/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/128174296" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/convert-bst-to-greater-tree/solutions/2005661/letmefly-538ba-er-cha-sou-suo-shu-zhuan-vivvg/" target="_blank">LeetCode题解</a>|
+|0540.有序数组中的单一元素|中等|<a href="https://leetcode.cn/problems/single-element-in-a-sorted-array/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2024/11/10/LeetCode%200540.%E6%9C%89%E5%BA%8F%E6%95%B0%E7%BB%84%E4%B8%AD%E7%9A%84%E5%8D%95%E4%B8%80%E5%85%83%E7%B4%A0/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/143663976" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/single-element-in-a-sorted-array/solutions/2983931/letmefly-540you-xu-shu-zu-zhong-de-dan-y-uhdj/" target="_blank">LeetCode题解</a>|
 |0542.01矩阵|中等|<a href="https://leetcode.cn/problems/01-matrix/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/12/04/LeetCode%200542.01%E7%9F%A9%E9%98%B5/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/128175163" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/01-matrix/solutions/2005765/letmefly-54201-ju-zhen-by-tisfy-cycy/" target="_blank">LeetCode题解</a>|
 |0543.二叉树的直径|简单|<a href="https://leetcode.cn/problems/diameter-of-binary-tree/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/12/05/LeetCode%200543.%E4%BA%8C%E5%8F%89%E6%A0%91%E7%9A%84%E7%9B%B4%E5%BE%84/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/128194953" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/diameter-of-binary-tree/solutions/2007705/letmefly-543er-cha-shu-de-zhi-jing-by-ti-k7o9/" target="_blank">LeetCode题解</a>|
 |0547.省份数量|中等|<a href="https://leetcode.cn/problems/number-of-provinces/solutions/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/12/13/LeetCode%200547.%E7%9C%81%E4%BB%BD%E6%95%B0%E9%87%8F/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/128304781" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/number-of-provinces/solutions/2018995/letmefly-547sheng-fen-shu-liang-by-tisfy-nykg/" target="_blank">LeetCode题解</a>|

Solutions/LeetCode 0540.有序数组中的单一元素.md

@@ -0,0 +1,143 @@
+---
+title: 540.有序数组中的单一元素
+date: 2024-11-10 17:53:24
+tags: [题解, LeetCode, 中等, 数组, 二分查找, 位运算]
+---
+
+# 【LetMeFly】540.有序数组中的单一元素：二分查找（位运算优化）
+
+力扣题目链接：[https://leetcode.cn/problems/single-element-in-a-sorted-array/](https://leetcode.cn/problems/single-element-in-a-sorted-array/)
+
+<p>给你一个仅由整数组成的有序数组，其中每个元素都会出现两次，唯有一个数只会出现一次。</p>
+
+<p>请你找出并返回只出现一次的那个数。</p>
+
+<p>你设计的解决方案必须满足 <code>O(log n)</code> 时间复杂度和 <code>O(1)</code> 空间复杂度。</p>
+
+<p>&nbsp;</p>
+
+<p><strong>示例 1:</strong></p>
+
+<pre>
+<strong>输入:</strong> nums = [1,1,2,3,3,4,4,8,8]
+<strong>输出:</strong> 2
+</pre>
+
+<p><strong>示例 2:</strong></p>
+
+<pre>
+<strong>输入:</strong> nums =  [3,3,7,7,10,11,11]
+<strong>输出:</strong> 10
+</pre>
+
+<p>&nbsp;</p>
+
+<p><meta charset="UTF-8" /></p>
+
+<p><strong>提示:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= nums[i]&nbsp;&lt;= 10<sup>5</sup></code></li>
+</ul>
+
+
+    
+## 解题方法：二分查找
+
+数组元素有序说明，我们可以直接随机选择一个下标，如果“当前下标为偶数且当前元素和下一个元素相同”或者“当前下标为奇数并且当前元素和上一个元素相同”，则说明从头开始到这个元素为止每个元素都是成对出现的。
+
+因此我们可以直接进行二分操作：每次枚举mid并在$O(1)$的时间内得到$[0, mid]$中的每个元素是否都成对出现。若成对出现则说明答案在$mid + 1$及之后；否则说明答案在$mid$及之前。
+
+位运算优化：
+
+1. $\frac{l+r}2=(l+r)>>1$
+2. 如果$mid$是奇数，那么应该判断$nums[mid]$是否和$nums[mid - 1]$相等；如果$mid$是偶数，那么应该判断$nums[mid]$是否和$nums[mid + 1]$相等。总之，我们只需要判断$nums[mid]$和$nums[mid \hat\ 1]$是否相等（其中$\hat\ $是异或符）
+
+(・∀・(・∀・(・∀・*)
+
++ 时间复杂度$O(\log len(nums))$
++ 空间复杂度$O(1)$
+
+### AC代码
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    int singleNonDuplicate(vector<int>& nums) {
+        int l = 0, r = nums.size() - 1;
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (nums[mid] == nums[mid ^ 1]) {
+                l = mid + 1;
+            } else {
+                r = mid;
+            }
+        }
+        return nums[l];
+    }
+};
+```
+
+#### Python
+
+```python
+from typing import List
+
+class Solution:
+    def singleNonDuplicate(self, nums: List[int]) -> int:
+        l, r = 0, len(nums) - 1
+        while l < r:
+            mid = (l + r) >> 1
+            if nums[mid] == nums[mid ^ 1]:
+                l = mid + 1
+            else:
+                r = mid
+        return nums[l]
+```
+
+#### Java
+
+```java
+class Solution {
+    public int singleNonDuplicate(int[] nums) {
+        int l = 0, r = nums.length - 1;
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (nums[mid] == nums[mid ^ 1]) {
+                l = mid + 1;
+            } else {
+                r = mid;
+            }
+        }
+        return nums[l];
+    }
+}
+```
+
+#### Go
+
+```go
+package main
+
+func singleNonDuplicate(nums []int) int {
+    l, r := 0, len(nums) - 1
+    for l < r {
+        mid := (l + r) >> 1
+        if nums[mid] == nums[mid + 1] {
+            l = mid + 1
+        } else {
+            r = mid
+        }
+    }
+    return nums[l]
+}
+```
+
+> 同步发文于CSDN和我的[个人博客](https://blog.letmefly.xyz/)，原创不易，转载经作者同意后请附上[原文链接](https://blog.letmefly.xyz/2024/11/10/LeetCode%200540.%E6%9C%89%E5%BA%8F%E6%95%B0%E7%BB%84%E4%B8%AD%E7%9A%84%E5%8D%95%E4%B8%80%E5%85%83%E7%B4%A0/)哦~
+>
+> Tisfy：[https://letmefly.blog.csdn.net/article/details/143663976](https://letmefly.blog.csdn.net/article/details/143663976)
+
+emm，某事还是很累，这篇题解写地晕哩糊涂的。