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update: 添加问题“1727.重新排列后的最大子矩阵”的代码和题解 (#1448)
1727: AC.cpp(#1446) - AC,31.11%,44.44% Signed-off-by: LetMeFly666 <Tisfy@qq.com>
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‎.commitmsg‎

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1727: AC.cpp(#1446) - AC,31.11%,44.44%

‎Codes/1727-largest-submatrix-with-rearrangements.cpp‎

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/*
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* @Author: LetMeFly
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* @Date: 2026-03-17 21:54:11
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* @LastEditors: LetMeFly.xyz
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* @LastEditTime: 2026-03-17 22:00:41
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*/
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#ifdef _DEBUG
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#include "_[1,2]toVector.h"
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#endif
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/*
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1 3
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[0,1]
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[0,1]
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[1,1]
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[[0,1],[0,1],[1,1]]
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*/
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class Solution {
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public:
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int largestSubmatrix(vector<vector<int>>& matrix) {
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int n = matrix[0].size();
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vector<int> heights(n);
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int ans = 0;
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for (vector<int>& row : matrix) {
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for (int i = 0; i < n; i++) {
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heights[i] = row[i] ? heights[i] + 1 : 0;
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}
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vector<int> ordered_heights = heights;
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sort(ordered_heights.begin(), ordered_heights.end());
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for (int i = 0; i < n; i++) {
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ans = max(ans, ordered_heights[i] * (n - i));
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}
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}
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return ans;
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}
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};

‎README.md‎

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|1706.球会落何处|中等|<a href="https://leetcode.cn/problems/where-will-the-ball-fall/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2025/02/15/LeetCode%201706.%E7%90%83%E4%BC%9A%E8%90%BD%E4%BD%95%E5%A4%84/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/145648365" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/where-will-the-ball-fall/solutions/3075424/letmefly-1706qiu-hui-luo-he-chu-mo-ni-he-0ohx/" target="_blank">LeetCode题解</a>|
657657
|1710.卡车上的最大单元数|简单|<a href="https://leetcode.cn/problems/maximum-units-on-a-truck/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/11/15/LeetCode%201710.%E5%8D%A1%E8%BD%A6%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%8D%95%E5%85%83%E6%95%B0/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/127859337" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/maximum-units-on-a-truck/solutions/1971195/letmefly-1710qia-che-shang-de-zui-da-dan-v8l8/" target="_blank">LeetCode题解</a>|
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|1726.同积元组|中等|<a href="https://leetcode.cn/problems/tuple-with-same-product/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2023/10/19/LeetCode%201726.%E5%90%8C%E7%A7%AF%E5%85%83%E7%BB%84/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/133921549" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/tuple-with-same-product/solutions/2489115/letmefly-1726tong-ji-yuan-zu-ha-xi-biao-sxuu2/" target="_blank">LeetCode题解</a>|
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|1727.重新排列后的最大子矩阵|中等|<a href="https://leetcode.cn/problems/largest-submatrix-with-rearrangements/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2026/03/17/LeetCode%201727.%E9%87%8D%E6%96%B0%E6%8E%92%E5%88%97%E5%90%8E%E7%9A%84%E6%9C%80%E5%A4%A7%E5%AD%90%E7%9F%A9%E9%98%B5/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/159174953" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/largest-submatrix-with-rearrangements/solutions/3928952/letmefly-1727zhong-xin-pai-lie-hou-de-zu-o8hy/" target="_blank">LeetCode题解</a>|
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|1732.找到最高海拔|简单|<a href="https://leetcode.cn/problems/find-the-highest-altitude/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/11/19/LeetCode%201732.%E6%89%BE%E5%88%B0%E6%9C%80%E9%AB%98%E6%B5%B7%E6%8B%94/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/127932334" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/find-the-highest-altitude/solutions/1979474/letmefly-1732zhao-dao-zui-gao-hai-ba-by-gdbw2/" target="_blank">LeetCode题解</a>|
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|1738.找出第K大的异或坐标值|中等|<a href="https://leetcode.cn/problems/find-kth-largest-xor-coordinate-value/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2024/05/26/LeetCode%201738.%E6%89%BE%E5%87%BA%E7%AC%ACK%E5%A4%A7%E7%9A%84%E5%BC%82%E6%88%96%E5%9D%90%E6%A0%87%E5%80%BC/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/139211887" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/find-kth-largest-xor-coordinate-value/solutions/2790477/letmefly-1738zhao-chu-di-k-da-de-yi-huo-b2qvw/" target="_blank">LeetCode题解</a>|
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|1739.放置盒子|困难|<a href="https://leetcode.cn/problems/building-boxes/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/12/25/LeetCode%201739.%E6%94%BE%E7%BD%AE%E7%9B%92%E5%AD%90/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/128436934" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/building-boxes/solutions/2032356/letmefly-1739fang-zhi-he-zi-by-tisfy-k219/" target="_blank">LeetCode题解</a>|

‎Solutions/LeetCode 1727.重新排列后的最大子矩阵.md‎

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---
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title: 1727.重新排列后的最大子矩阵：枚举矩形底边是哪一行 + 排序
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date: 2026-03-17 22:03:02
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tags: [题解, LeetCode, 中等, 贪心, 数组, 矩阵, 排序]
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categories: [题解, LeetCode]
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index_img: https://assets.leetcode.cn/aliyun-lc-upload/uploads/2021/01/17/screenshot-2020-12-30-at-40536-pm.png
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---
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# 【LetMeFly】1727.重新排列后的最大子矩阵：枚举矩形底边是哪一行 + 排序
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力扣题目链接：[https://leetcode.cn/problems/largest-submatrix-with-rearrangements/](https://leetcode.cn/problems/largest-submatrix-with-rearrangements/)
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<p>给你一个二进制矩阵 <code>matrix</code> ，它的大小为 <code>m x n</code> ，你可以将 <code>matrix</code> 中的 <strong>列</strong> 按任意顺序重新排列。</p>
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<p>请你返回最优方案下将 <code>matrix</code> 重新排列后，全是 <code>1</code> 的子矩阵面积。</p>
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<p> </p>
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<p><strong>示例 1：</strong></p>
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<p><strong><img alt="" src="https://assets.leetcode.cn/aliyun-lc-upload/uploads/2021/01/17/screenshot-2020-12-30-at-40536-pm.png" style="width: 300px; height: 144px;" /></strong></p>
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<pre>
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<b>输入：</b>matrix = [[0,0,1],[1,1,1],[1,0,1]]
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<b>输出：</b>4
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<b>解释：</b>你可以按照上图方式重新排列矩阵的每一列。
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最大的全 1 子矩阵是上图中加粗的部分，面积为 4 。
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</pre>
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<p><strong>示例 2：</strong></p>
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<p><img alt="" src="https://assets.leetcode.cn/aliyun-lc-upload/uploads/2021/01/17/screenshot-2020-12-30-at-40852-pm.png" style="width: 500px; height: 62px;" /></p>
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<pre>
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<b>输入：</b>matrix = [[1,0,1,0,1]]
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<b>输出：</b>3
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<b>解释：</b>你可以按照上图方式重新排列矩阵的每一列。
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最大的全 1 子矩阵是上图中加粗的部分，面积为 3 。
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</pre>
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<p><strong>示例 3：</strong></p>
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<pre>
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<b>输入：</b>matrix = [[1,1,0],[1,0,1]]
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<b>输出：</b>2
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<b>解释：</b>由于你只能整列整列重新排布，所以没有比面积为 2 更大的全 1 子矩形。</pre>
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<p><strong>示例 4：</strong></p>
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<pre>
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<b>输入：</b>matrix = [[0,0],[0,0]]
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<b>输出：</b>0
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<b>解释：</b>由于矩阵中没有 1 ，没有任何全 1 的子矩阵，所以面积为 0 。</pre>
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<p> </p>
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<p><strong>提示：</strong></p>
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<ul>
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<li><code>m == matrix.length</code></li>
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<li><code>n == matrix[i].length</code></li>
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<li><code>1 <= m * n <= 10<sup>5</sup></code></li>
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<li><code>matrix[i][j]</code> 要么是 <code>0</code> ，要么是 <code>1</code> 。</li>
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</ul>
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## 解题方法：枚举矩形底边是哪一行 + 排序
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对于样例1：
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![sample2](https://assets.leetcode.cn/aliyun-lc-upload/uploads/2021/01/17/screenshot-2020-12-30-at-40536-pm.png)，假设最优的答案矩形的底在第三行，那么怎么计算*以第三行为底的矩形中面积最大的那个*呢？
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> 很简单，看下每一列从第三行开始向上能延伸多少格：`[2, 0, 3]`；排个序：`[0, 2, 3]`。
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>
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> 1. 假设矩形从第一列开始，$0$是矩形的高，则矩形最大面积是$0\times 3=0$
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> 2. 假设矩形从第二列开始，$2$是矩形的高，则矩形最大面积是$2\times 2=4$
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> 3. 假设矩形从第三列开始，$3$是矩形的高，则矩形最大面积是$3\times 1=3$
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>
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> 也就是说矩形从第$i$列开始的话，由于后面列的高都不低于这一列，所以矩形的最大面积是从这一列的高度一直持续到最后一列，为$heights[i]\times (n-i)$，其中$n$是列数。
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>
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> 也就是说，如果固定了矩形底边是哪一行的话，如果我们知道每一列以这个底边向上的连续1个数$height$，就能对$heights$数组从小到大排个序，然后遍历一遍求出最大矩形面积了。
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现在底边有很多行，我们一行一行地枚举并做上述运算，顺便在枚举下一行的时候借助上一行的heights结果计算出新的heights就好了。
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+ 时间复杂度$O(nm\log n)$
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+ 空间复杂度$O(n)$
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### AC代码
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#### C++
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```cpp
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/*
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* @LastEditTime: 2026-03-17 22:00:41
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*/
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class Solution {
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public:
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int largestSubmatrix(vector<vector<int>>& matrix) {
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int n = matrix[0].size();
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vector<int> heights(n);
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int ans = 0;
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for (vector<int>& row : matrix) {
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for (int i = 0; i < n; i++) {
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heights[i] = row[i] ? heights[i] + 1 : 0;
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}
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vector<int> ordered_heights = heights;
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sort(ordered_heights.begin(), ordered_heights.end());
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for (int i = 0; i < n; i++) {
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ans = max(ans, ordered_heights[i] * (n - i));
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}
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}
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return ans;
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}
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};
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```
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> 同步发文于[CSDN](https://letmefly.blog.csdn.net/article/details/159174953)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/2026/03/17/LeetCode%201727.%E9%87%8D%E6%96%B0%E6%8E%92%E5%88%97%E5%90%8E%E7%9A%84%E6%9C%80%E5%A4%A7%E5%AD%90%E7%9F%A9%E9%98%B5/)哦~
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>
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> 千篇源码题解[已开源](https://github.com/LetMeFly666/LeetCode)

‎codestats.plugin.zsh‎

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