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‎README.adoc

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@@ -9469,12 +9469,12 @@ TIP: **公众号的微信号是: `jikerizhi`**。__因为众所周知的原因
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//|Medium
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//|
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//|{counter:codes}
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//|{leetcode_base_url}/maximum-students-taking-exam/[1349. Maximum Students Taking Exam^]
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//|{source_base_url}/_1349_MaximumStudentsTakingExam.java[Java]
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//|{doc_base_url}/1349-maximum-students-taking-exam.adoc[题解]
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//|Hard
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//|
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|{counter:codes}
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|{leetcode_base_url}/maximum-students-taking-exam/[1349. Maximum Students Taking Exam^]
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|{source_base_url}/_1349_MaximumStudentsTakingExam.java[Java]
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|{doc_base_url}/1349-maximum-students-taking-exam.adoc[题解]
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|Hard
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|
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//|{counter:codes}
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//|{leetcode_base_url}/students-with-invalid-departments/[1350. Students With Invalid Departments^]

‎docs/1349-maximum-students-taking-exam.adoc

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[#1349-maximum-students-taking-exam]
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= 1349. Maximum Students Taking Exam
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= 1349. 参加考试的最大学生数
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{leetcode}/problems/maximum-students-taking-exam/[LeetCode - 1349. Maximum Students Taking Exam ^]
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https://leetcode.cn/problems/maximum-students-taking-exam/[LeetCode - 1349. 参加考试的最大学生数 ^]
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Given a `m * n` matrix `seats` that represent seats distributions in a classroom. If a seat is broken, it is denoted by `'#'` character otherwise it is denoted by a `'.'` character.
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给你一个 `m * n` 的矩阵 `seats` 表示教室中的座位分布。如果座位是坏的（不可用），就用 `#` 表示；否则，用 `.` 表示。
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Students can see the answers of those sitting next to the left, right, upper left and upper right, but he cannot see the answers of the student sitting directly in front or behind him. Return the *maximum *number of students that can take the exam together without any cheating being possible.
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学生可以看到左侧、右侧、左上、右上这四个方向上紧邻他的学生的答卷，但是看不到直接坐在他前面或者后面的学生的答卷。请你计算并返回该考场可以容纳的同时参加考试且无法作弊的 **最大** 学生人数。
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Students must be placed in seats in good condition.
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学生必须坐在状况良好的座位上。
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*Example 1:*
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<img height="200" src="https://assets.leetcode.com/uploads/2020/01/29/image.png" width="339" />
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[subs="verbatim,quotes"]
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----
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*Input:* seats = [["#",".","#","#",".","#"],
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[".","#","#","#","#","."],
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["#",".","#","#",".","#"]]
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*Output:* 4
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*Explanation:* Teacher can place 4 students in available seats so they don't cheat on the exam.
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----
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*示例 1：*
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*Example 2:*
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image::images/1349-01.png[{image_attr}]
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[subs="verbatim,quotes"]
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----
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*Input:* seats = [[".","#"],
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["#","#"],
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["#","."],
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["#","#"],
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[".","#"]]
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*Output:* 3
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*Explanation:* Place all students in available seats.
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....
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输入：seats = [["#",".","#","#",".","#"],
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[".","#","#","#","#","."],
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["#",".","#","#",".","#"]]
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输出：4
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解释：教师可以让 4 个学生坐在可用的座位上，这样他们就无法在考试中作弊。
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....
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----
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*示例 2：*
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*Example 3:*
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....
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输入：seats = [[".","#"],
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["#","#"],
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["#","."],
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["#","#"],
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[".","#"]]
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输出：3
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解释：让所有学生坐在可用的座位上。
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....
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[subs="verbatim,quotes"]
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----
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*Input:* seats = [["#",".","*.*",".","#"],
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["*.*","#","*.*","#","*.*"],
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["*.*",".","#",".","*.*"],
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["*.*","#","*.*","#","*.*"],
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["#",".","*.*",".","#"]]
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*Output:* 10
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*Explanation:* Place students in available seats in column 1, 3 and 5.
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----
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*示例 3：*
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....
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输入：seats = [["#",".",".",".","#"],
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[".","#",".","#","."],
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[".",".","#",".","."],
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[".","#",".","#","."],
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["#",".",".",".","#"]]
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输出：10
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解释：让学生坐在第 1、3 和 5 列的可用座位上。
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....
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*Constraints:*
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*提示：*
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* `seats` contains only characters `'.'<font face="sans-serif, Arial, Verdana, Trebuchet MS"> and``'#'.`
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* `seats` 只包含字符 `.` 和 `#`
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* `m == seats.length`
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* `n == seats[i].length`
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* `1 <= m <= 8`
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* `1 <= n <= 8`
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* `+1 <= m <= 8+`
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* `+1 <= n <= 8+`
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== 思路分析
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image::images/1349-10.png[{image_attr}]
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== 思路分析
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image::images/1349-11.png[{image_attr}]
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image::images/1349-12.png[{image_attr}]
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[[src-1349]]
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[tabs]
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====
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一刷::
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一刷（回溯，超时）::
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--
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[{java_src_attr}]
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----
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--
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一刷::
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+
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--
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[{java_src_attr}]
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----
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include::{sourcedir}/_1349_MaximumStudentsTakingExam_1.java[tag=answer]
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----
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--
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// 二刷::
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// +
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// --
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== 参考资料
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. https://leetcode.cn/problems/maximum-students-taking-exam/solutions/101748/can-jia-kao-shi-de-zui-da-xue-sheng-shu-by-leetcod/[1349. 参加考试的最大学生数 - 官方题解^]
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. https://leetcode.cn/problems/maximum-students-taking-exam/solutions/2580043/jiao-ni-yi-bu-bu-si-kao-dong-tai-gui-hua-9y5k/[1349. 参加考试的最大学生数 - 教你一步步思考动态规划：从记忆化搜索到递推^]

‎docs/images/1349-01.png

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‎docs/images/1349-10.png

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‎docs/images/1349-11.png

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‎docs/images/1349-12.png

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‎docs/index.adoc

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// include::1348-tweet-counts-per-frequency.adoc[leveloffset=+1]
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// include::1349-maximum-students-taking-exam.adoc[leveloffset=+1]
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include::1349-maximum-students-taking-exam.adoc[leveloffset=+1]
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// include::1350-students-with-invalid-departments.adoc[leveloffset=+1]
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‎logbook/202503.adoc

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|{doc_base_url}/0918-maximum-sum-circular-subarray.adoc[题解]
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|❌ 理解错题目了。前大，中小，后大，这类子数组也可以产生更多的子数组和。另有“取反”和单调栈解法。
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|{counter:codes2503}
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|{leetcode_base_url}/maximum-students-taking-exam/[1349. 参加考试的最大学生数^]
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|{doc_base_url}/1349-maximum-students-taking-exam.adoc[题解]
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|❌ 回溯解法通过 50 / 57 个测试用例。动态规划解法太难了！
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|===
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‎src/main/java/com/diguage/algo/leetcode/_1349_MaximumStudentsTakingExam.java

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package com.diguage.algo.leetcode;
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public class _1349_MaximumStudentsTakingExam {
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// tag::answer[]
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/**
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* 通过 50 / 57 个测试用例，后超时。
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*
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* @author D瓜哥 · https://www.diguage.com
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* @since 2025-05-15 20:31:46
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*/
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int result = Integer.MIN_VALUE;
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public int maxStudents(char[][] seats) {
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int seatNo = seats.length * seats[0].length - 1;
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backtrack(seats, seatNo, 0);
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return result;
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}
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private void backtrack(char[][] seats, int seatNo, int num) {
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if (seatNo < 0) {
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result = Math.max(result, num);
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return;
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}
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int row = seatNo / seats[0].length;
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int column = seatNo % seats[0].length;
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if (seats[row][column] == '.') {
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for (int i = 1; i >= 0; i--) {
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if (i == 0) {
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seats[row][column] = '0';
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backtrack(seats, seatNo - 1, num);
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seats[row][column] = '.';
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} else {
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seats[row][column] = '1';
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// 左
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boolean left = false;
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if (column > 0 && seats[row][column - 1] == '.') {
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left = true;
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seats[row][column - 1] = '0';
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}
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// 左上
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boolean leftUp = false;
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if (row > 0 && column > 0
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&& seats[row - 1][column - 1] == '.') {
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leftUp = true;
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seats[row - 1][column - 1] = '0';
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}
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// 右
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boolean right = false;
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if (column < seats[0].length - 1 && seats[row][column + 1] == '.') {
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right = true;
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seats[row][column + 1] = '0';
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}
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// 右上
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boolean rightUp = false;
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if (row > 0 && column < seats[row].length - 1
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&& seats[row - 1][column + 1] == '.') {
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rightUp = true;
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seats[row - 1][column + 1] = '0';
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}
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backtrack(seats, seatNo - 1, num + 1);
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// 右上
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if (rightUp) {
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seats[row - 1][column + 1] = '.';
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}
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// 右
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if (right) {
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seats[row][column + 1] = '.';
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}
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// 左上
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if (leftUp) {
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seats[row - 1][column - 1] = '.';
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}
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// 左
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if (left) {
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seats[row][column - 1] = '.';
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}
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seats[row][column] = '.';
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}
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}
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} else {
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backtrack(seats, seatNo - 1, num);
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}
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}
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// end::answer[]
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public static void main(String[] args) {
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new _1349_MaximumStudentsTakingExam().maxStudents(new char[][]{
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{'.', '.', '.', '.', '#', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '#', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '#', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '#', '.', '.', '#', '.'}
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// {'.', '#', '.', '#'},
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// {'.', '.', '.', '#'},
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// {'#', '#', '.', '.'},
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// {'.', '#', '#', '#'}
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// {'.', '#', '.', '#'},
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// {'.', '.', '.', '#'},
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// {'#', '#', '.', '.'},
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// {'.', '#', '#', '#'}
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// {'#', '.', '#', '#', '.', '#'},
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// {'.', '#', '#', '#', '#', '.'},
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// {'#', '.', '#', '#', '.', '#'}
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});
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}
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}

‎src/main/java/com/diguage/algo/leetcode/_1349_MaximumStudentsTakingExam_1.java

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package com.diguage.algo.leetcode;
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public class _1349_MaximumStudentsTakingExam_1 {
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// tag::answer[]
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/**
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* @author D瓜哥 · https://www.diguage.com
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* @since 2025-05-15 20:31:46
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*/
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public int maxStudents(char[][] seats) {
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int m = seats.length;
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int n = seats[0].length;
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int[] a = new int[m]; // a[i] 是第 i 排可用椅子的下标集合
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for (int i = 0; i < m; i++) {
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for (int j = 0; j < n; j++) {
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if (seats[i][j] == '.') {
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a[i] |= 1 << j;
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}
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}
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}
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int[][] f = new int[m][1 << n];
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for (int j = 1; j < (1 << n); j++) {
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int lb = j & -j;
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f[0][j] = f[0][j & ~(lb * 3)] + 1;
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}
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for (int i = 1; i < m; i++) {
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for (int j = a[i]; j > 0; j = (j - 1) & a[i]) { // 枚举 a[i] 的子集 j
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f[i][j] = f[i - 1][a[i - 1]]; // 第 i 排空着
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for (int s = j; s > 0; s = (s - 1) & j) { // 枚举 j 的子集 s
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if ((s & (s >> 1)) == 0) {// s 没有连续的 1
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int t = a[i - 1] & ~(s << 1 | s >> 1); // 去掉不能坐人的位置
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f[i][j] = Math.max(f[i][j], f[i - 1][t] + f[0][s]);
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}
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}
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}
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f[i][0] = f[i - 1][a[i - 1]];
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}
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return f[m - 1][a[m - 1]];
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}
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// end::answer[]
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public static void main(String[] args) {
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new _1349_MaximumStudentsTakingExam_1().maxStudents(new char[][]{
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{'.', '.', '.', '.', '#', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '#', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '#', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '.', '.', '.', '.', '.'},
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{'.', '.', '.', '#', '.', '.', '#', '.'}
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// {'.', '#', '.', '#'},
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// {'.', '.', '.', '#'},
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// {'#', '#', '.', '.'},
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// {'.', '#', '#', '#'}
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// {'.', '#', '.', '#'},
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// {'.', '.', '.', '#'},
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// {'#', '#', '.', '.'},
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// {'.', '#', '#', '#'}
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// {'#', '.', '#', '#', '.', '#'},
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// {'.', '#', '#', '#', '#', '.'},
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// {'#', '.', '#', '#', '.', '#'}
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});
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}
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}

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