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feat: add solutions to lc problem: No.3125 (doocs#2656)
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‎solution/0400-0499/0422.Valid Word Square/README.md‎

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<p>给你一个单词序列,判断其是否形成了一个有效的单词方块。</p>
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<p>有效的单词方块是指此由单词序列组成的文字方块的&nbsp;第 k 行 和&nbsp;第 k 列 (0 &le; <em>k</em> &lt; max(行数, 列数)) 所显示的字符串完全相同。</p>
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<p>有效的单词方块是指此由单词序列组成的文字方块的&nbsp;第 k 行 和&nbsp;第 k 列 (0 ≤ <em>k</em> &lt; max(行数, 列数)) 所显示的字符串完全相同。</p>
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<p><strong>注意:</strong></p>
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<p><strong>示例 1:</strong></p>
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<pre><strong>输入:</strong>
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<p><strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0400-0499/0422.Valid%20Word%20Square/images/1713840723-rPoAKZ-image.png" style="width: 333px; height: 333px;" /></strong></p>
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<pre>
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<strong>输入:</strong>
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[
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&quot;abcd&quot;,
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&quot;bnrt&quot;,
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&quot;crmy&quot;,
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&quot;dtye&quot;
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"abcd",
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"bnrt",
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"crmy",
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"dtye"
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]
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<strong>输出:</strong>
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true
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<strong>解释:</strong>
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第 1 行和第 1 列都是 &quot;abcd&quot;。
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第 2 行和第 2 列都是 &quot;bnrt&quot;。
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第 3 行和第 3 列都是 &quot;crmy&quot;。
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第 4 行和第 4 列都是 &quot;dtye&quot;。
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第 1 行和第 1 列都是 "abcd"。
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第 2 行和第 2 列都是 "bnrt"。
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第 3 行和第 3 列都是 "crmy"。
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第 4 行和第 4 列都是 "dtye"。
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因此,这是一个有效的单词方块。
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</pre>
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<p><strong>示例 2:</strong></p>
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<pre><strong>输入:</strong>
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<p><strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0400-0499/0422.Valid%20Word%20Square/images/1713840732-EvBDzU-image.png" style="width: 333px; height: 333px;" /></strong></p>
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<pre>
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<strong>输入:</strong>
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[
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&quot;abcd&quot;,
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&quot;bnrt&quot;,
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&quot;crm&quot;,
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&quot;dt&quot;
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"abcd",
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"bnrt",
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"crm",
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"dt"
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]
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<strong>输出:</strong>
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true
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<strong>解释:</strong>
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第 1 行和第 1 列都是 &quot;abcd&quot;。
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第 2 行和第 2 列都是 &quot;bnrt&quot;。
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第 3 行和第 3 列都是 &quot;crm&quot;。
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第 4 行和第 4 列都是 &quot;dt&quot;。
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第 1 行和第 1 列都是 "abcd"。
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第 2 行和第 2 列都是 "bnrt"。
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第 3 行和第 3 列都是 "crm"。
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第 4 行和第 4 列都是 "dt"。
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因此,这是一个有效的单词方块。
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</pre>
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<p><strong>示例 3:</strong></p>
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<pre><strong>输入:</strong>
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<p><strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0400-0499/0422.Valid%20Word%20Square/images/1713840738-tdOYTB-image.png" style="width: 333px; height: 333px;" /></strong></p>
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<pre>
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<strong>输入:</strong>
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[
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&quot;ball&quot;,
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&quot;area&quot;,
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&quot;read&quot;,
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&quot;lady&quot;
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"ball",
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"area",
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"read",
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"lady"
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]
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<strong>输出:</strong>
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false
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<strong>解释:</strong>
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第 3 行是 &quot;read&quot; ,然而第 3 列是 &quot;lead&quot;。
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第 3 行是 "read" ,然而第 3 列是 "lead"。
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因此,这 <strong>不是</strong> 一个有效的单词方块。
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</pre>
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# [3125. Maximum Number That Makes Result of Bitwise AND Zero 🔒](https://leetcode.cn/problems/maximum-number-that-makes-result-of-bitwise-and-zero)
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[English Version](/solution/3100-3199/3125.Maximum%20Number%20That%20Makes%20Result%20of%20Bitwise%20AND%20Zero/README_EN.md)
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<!-- tags: -->
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## 题目描述
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<!-- 这里写题目描述 -->
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Given an integer <code>n</code>, return the <strong>maximum</strong> integer <code>x</code> such that <code>x &lt;= n</code>, and the bitwise <code>AND</code> of all the numbers in the range <code>[x, n]</code> is 0.
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<p>&nbsp;</p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 7</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[6, 7]</code> is 6.<br />
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The bitwise <code>AND</code> of <code>[5, 6, 7]</code> is 4.<br />
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The bitwise <code>AND</code> of <code>[4, 5, 6, 7]</code> is 4.<br />
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The bitwise <code>AND</code> of <code>[3, 4, 5, 6, 7]</code> is 0.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 9</span></p>
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<p><strong>Output:</strong> <span class="example-io">7</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[7, 8, 9]</code> is 0.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 17</span></p>
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<p><strong>Output:</strong> <span class="example-io">15</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[15, 16, 17]</code> is 0.</p>
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</div>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= n &lt;= 10<sup>15</sup></code></li>
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</ul>
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## 解法
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### 方法一:位运算
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我们可以找到 $n$ 的二进制表示中最高位的 1ドル,ドル那么最大的 $x$ 一定小于 $n$ 且该位为 0ドル,ドル其他低位均为 1ドル$。即 $x = 2^{\text{最高位的位数} - 1} - 1$。
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````python
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<!-- tabs:start -->
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```python
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class Solution:
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def maxNumber(self, n: int) -> int:
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return (1 << (n.bit_length() - 1)) - 1
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````
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```java
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class Solution {
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public long maxNumber(long n) {
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return (1L << (63 - Long.numberOfLeadingZeros(n))) - 1;
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}
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}
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```
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```cpp
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class Solution {
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public:
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long long maxNumber(long long n) {
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return (1LL << (63 - __builtin_clzll(n))) - 1;
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}
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};
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```
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```go
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func maxNumber(n int64) int64 {
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return int64(1<<(bits.Len64(uint64(n))-1)) - 1
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}
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```
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<!-- tabs:end -->
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<!-- end -->
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# [3125. Maximum Number That Makes Result of Bitwise AND Zero 🔒](https://leetcode.com/problems/maximum-number-that-makes-result-of-bitwise-and-zero)
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[中文文档](/solution/3100-3199/3125.Maximum%20Number%20That%20Makes%20Result%20of%20Bitwise%20AND%20Zero/README.md)
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<!-- tags: -->
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## Description
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Given an integer <code>n</code>, return the <strong>maximum</strong> integer <code>x</code> such that <code>x &lt;= n</code>, and the bitwise <code>AND</code> of all the numbers in the range <code>[x, n]</code> is 0.
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<p>&nbsp;</p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 7</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[6, 7]</code> is 6.<br />
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The bitwise <code>AND</code> of <code>[5, 6, 7]</code> is 4.<br />
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The bitwise <code>AND</code> of <code>[4, 5, 6, 7]</code> is 4.<br />
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The bitwise <code>AND</code> of <code>[3, 4, 5, 6, 7]</code> is 0.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 9</span></p>
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<p><strong>Output:</strong> <span class="example-io">7</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[7, 8, 9]</code> is 0.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 17</span></p>
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<p><strong>Output:</strong> <span class="example-io">15</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The bitwise <code>AND</code> of <code>[15, 16, 17]</code> is 0.</p>
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</div>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= n &lt;= 10<sup>15</sup></code></li>
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</ul>
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## Solutions
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### Solution 1: Bit Manipulation
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We can find the highest bit of 1ドル$ in the binary representation of $n$. The maximum $x$ must be less than $n$ and this bit is 0ドル,ドル and all other lower bits are 1ドル,ドル i.e., $x = 2^{\text{number of the highest bit}} - 1$. This is because $x \text{ and } (x + 1) = 0$ must hold.
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The time complexity is $O(\log n),ドル and the space complexity is $O(1)$.
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<!-- tabs:start -->
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```python
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class Solution:
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def maxNumber(self, n: int) -> int:
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return (1 << (n.bit_length() - 1)) - 1
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```
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```java
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class Solution {
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public long maxNumber(long n) {
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return (1L << (63 - Long.numberOfLeadingZeros(n))) - 1;
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}
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}
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```
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```cpp
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class Solution {
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public:
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long long maxNumber(long long n) {
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return (1LL << (63 - __builtin_clzll(n))) - 1;
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}
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};
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```
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```go
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func maxNumber(n int64) int64 {
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return int64(1<<(bits.Len64(uint64(n))-1)) - 1
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}
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```
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<!-- tabs:end -->
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<!-- end -->
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class Solution {
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public:
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long long maxNumber(long long n) {
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return (1LL << (63 - __builtin_clzll(n))) - 1;
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}
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};
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func maxNumber(n int64) int64 {
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return int64(1<<(bits.Len64(uint64(n))-1)) - 1
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}
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class Solution {
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public long maxNumber(long n) {
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return (1L << (63 - Long.numberOfLeadingZeros(n))) - 1;
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}
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}
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class Solution:
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def maxNumber(self, n: int) -> int:
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return (1 << (n.bit_length() - 1)) - 1

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