Nine Chapter
  • Introduction
    • Summary
  • 1.Binary Search
    • Introduction
    • 458.Last position of target
    • 600.Smallest Rectangle Enclosing Black Pixels
    • 585.Maximum Number in Mountain Sequence
    • 183.Wood Cut
    • 62.Search in Rotated Sorted Array
    • 63.Search in Rotated Sorted Array II
    • 159.Find Minimum in Rotated Sorted Array
    • 160.Find Minimum in Rotated Sorted Array II
    • 75.Find Peak Element
    • 60.Search Insert Position
    • 28.Search a 2D Matrix
    • 240. Search a 2D Matrix II
    • 14.First Position of Target
    • 74.First Bad Version
    • 875. Koko Eating Bananas
    • 1011. Capacity To Ship Packages Within D Days (M)
    • 410. Split Array Largest Sum (H)
    • 475. Heaters (M)
    • 1044. Longest Duplicate Substring (H)
  • 2.Binary Tree
    • Summary
      • 二叉树八股文:递归改迭代
      • BST
      • Frame
    • 66.Binary Tree Preorder Traversal
    • 67.🌟Binary Tree Inorder Traversal
    • 145. Binary Tree Postorder Traversal (E)
    • 98.Validate Binary Search Tree(M)
    • 85.Insert Node in a Binary Search Tree
    • 104. Maximum Depth of Binary Tree(E)
    • 235. Lowest Common Ancestor of a Binary Search Tree (E)
    • 236.Lowest Common Ancestor of Binary Tree(M)
    • 578.Lowest Common Ancestor III
    • 1120.Subtree with Maximum Average
    • 596.Minimum Subtree
    • 480.Binary Tree Paths
    • 453.Flatten Binary Tree to Linked List
    • 110.Balanced Binary Tree
    • 376.Binary Tree Path Sum
    • 246.Binary Tree Path Sum II
    • 475.Binary Tree Maximum Path Sum II
    • 124.Binary Tree Maximum Path Sum (H)
    • Path Sum (*)
      • 112. Path Sum
      • 113. Path Sum II
      • 437. Path Sum III
    • 177.Convert Sorted Array to Binary Search Tree With Minimal Height
    • 7.Binary Tree Serialization
    • 72,73.Construct Binary Tree
    • Binary Search Tree Path
    • 245.Subtree
    • 469.Identical Binary Tree
    • 87.Remove Node in Binary Search Tree
    • 116.Populating Next Right Pointers in Each Node (M)
    • 114. Flatten Binary Tree to Linked List(M)
    • 654.Maximum Binary Tree (M)
    • 105. 🌟Construct Binary Tree from Preorder and Inorder Traversal (M)
    • 106. Construct Binary Tree from Inorder and Postorder Traversal (M)
    • 652. Find Duplicate Subtrees(M)
    • 230. Kth Smallest Element in a BST (M)
    • 538&1038. Convert BST to Greater Tree
    • 450. Delete Node in a BST (M)
    • 701. Insert into a Binary Search Tree (M)
    • 96. Unique Binary Search Trees
    • 95. Unique Binary Search Trees II (M)
    • 1373. Maximum Sum BST in Binary Tree (H)
    • 297. Serialize and Deserialize Binary Tree (H)
    • 222. Count Complete Tree Nodes (M)
    • 1120. Maximum Average Subtree
    • 341. Flatten Nested List Iterator
    • 333. Largest BST Subtree (M)
    • 543. Diameter of Binary Tree
    • Binary Tree Longest Consecutive Sequence(*)
      • 298.Binary Tree Longest Consecutive Sequence
      • 549. Binary Tree Longest Consecutive Sequence II (M)
  • 3.Breadth First Search
    • Introduction
      • BFS 算法解题套路框架
      • 双向 BFS 优化
    • 102.Binary Tree Level Order Traversal (M)
    • 103. Binary Tree Zigzag Level Order Traversal (M)
    • 107.Binary Tree Level Order Traversal II(M)
    • 618.Search Graph Nodes
    • 207.Course Schedule (M)
    • 210.Course Schedule II (M)
    • 611.Knight Shortest Path
    • 598.Zombie in Matrix
    • 133.Clone Graph (M)
    • 178.Graph Valid Tree
    • 7.Binary Tree Serialization
    • 574.Build Post Office
    • 573.Build Post Office II
    • 127.Topological Sorting
    • 127.Word Ladder
    • 126. Word Ladder II
    • (LeetCode)515.Find Largest Value in Each Tree Row
    • 111. Minimum Depth of Binary Tree (E)
    • 752. Open the Lock
    • 542. 01 Matrix (M)
    • 1306. Jump Game III (M)
  • 4.Depth First Search+BackTracking
    • Summary
      • FloodFill 算法
    • 136.Palindrome Partitioning
    • 39.Combination Sum
    • 40.Combination Sum II
    • 377. Combination Sum IV
    • 77.Combinations (M)
    • 78.Subsets (M)
    • 90.Subsets II (M)
    • 46.🌟Permutations
    • 47.Permutations II
    • 582.Word Break II
    • 490.The Maze (M)
    • 51.N-Queens (H)
    • 52. N-Queens II (H)
    • 698. Partition to K Equal Sum Subsets (M)
    • 22. Generate Parentheses (M)
    • 岛屿问题
      • 200.Number of Islands (M)
      • 1254. Number of Closed Islands (M)
      • 1020. Number of Enclaves (M)
      • 695. Max Area of Island (M)
      • 1905. Count Sub Islands (M)
      • 694. Number of Distinct Islands
    • 131. Palindrome Partitioning (M)
    • 967. Numbers With Same Consecutive Differences (M)
    • 79. Word Search (M)
    • 212. Word Search II (M)
    • 472. Concatenated Words (H)
    • Page 2
    • 291. Word Pattern II
    • 17. Letter Combinations of a Phone Number (M)
  • 5.LinkedList
    • Summary
      • 单链表的倒数第 k 个节点
      • Merge two/k sorted LinkedList
      • Middle of the Linked List
      • 判断链表是否包含环
      • 两个链表是否相交 Intersection of Two Linked Lists
      • 递归反转链表
      • 如何判断回文链表
    • 599.Insert into a Cyclic Sorted List
    • 21.Merge Two Sorted Lists (E)
    • 23.Merge k Sorted Lists (H)
    • 105.Copy List with Random Pointer
    • 141.Linked List Cycle (E)
    • 142.Linked List Cycle II (M)
    • 148.Sort List (M)
    • 86.Partition List (M)
    • 83.Remove Duplicates from Sorted List(E)
    • 82.Remove Duplicates from Sorted List II (M)
    • 206.Reverse Linked List (E)
    • 92.Reverse Linked List II (M)
    • 143.Reorder List (M)
    • 19.Remove Nth Node From End of List (E)
    • 170.Rotate List
    • 🤔25.Reverse Nodes in k-Group (H)
    • 452.Remove Linked List Elements
    • 167.Add Two Numbers
    • 221.Add Two Numbers II
    • 876. Middle of the Linked List (E)
    • 160. Intersection of Two Linked Lists (E)
    • 234. Palindrome Linked List (E)
    • 2130. Maximum Twin Sum of a Linked List (M)
  • 6.Array
    • Summary
      • 前缀和思路PrefixSum
      • 差分数组 Difference Array
      • 双指针Two Pointers
      • 滑动窗口算法算法
      • Sliding windows II
      • 二分搜索Binary Search
      • 排序算法
      • 快速选择算法
    • 604.Window Sum
    • 138.Subarray Sum
    • 41.Maximum Subarray
    • 42.Maximum Subarray II
    • 43.Maximum Subarray III
    • 620.Maximum Subarray IV
    • 621.Maximum Subarray V
    • 6.Merge Two Sorted Arrays
    • 88.Merge Sorted Array
    • 547.Intersection of Two Arrays
    • 548.Intersection of Two Arrays II
    • 139.Subarray Sum Closest
    • 65.Median of two Sorted Arrays
    • 636.132 Pattern
    • 402.Continuous Subarray Sum
    • 303. Range Sum Query - Immutable (E)
    • 304.Range Sum Query 2D - Immutable (M)
    • 560. Subarray Sum Equals K (M)
    • 370. Range Addition(M)
    • 1109. Corporate Flight Bookings(M)
    • 1094. Car Pooling (M)
    • 76. Minimum Window Substring(H)
    • 567. Permutation in String (M)
    • 438. Find All Anagrams in a String(M)
    • 3. Longest Substring Without Repeating Characters (M)
    • 380. Insert Delete GetRandom O(1) (M)
    • 710. Random Pick with Blacklist (H)
    • 528. Random Pick with Weight (M)
    • 26. Remove Duplicates from Sorted Array (E)
    • 27. Remove Element (E)
    • 283. Move Zeroes (E)
    • 659. Split Array into Consecutive Subsequences (M)
    • 4. Median of Two Sorted Arrays (H)
    • 48. Rotate Image (M)
    • 54. Spiral Matrix (M)
    • 59. Spiral Matrix II (M)
    • 918. Maximum Sum Circular Subarray
    • 128. Longest Consecutive Sequence (M)
    • 238. Product of Array Except Self (M)
    • 1438. Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit (M)
    • 1151. Minimum Swaps to Group All 1's Together (M)
    • 2134. Minimum Swaps to Group All 1's Together II
    • 2133. Check if Every Row and Column Contains All Numbers
    • 632. Smallest Range Covering Elements from K Lists (H)
    • 36. Valid Sudoku (M)
    • 383. Ransom Note
    • 228. Summary Ranges
  • 7.Two pointers
    • Summary
      • Two Sum
      • 2Sum 3Sum 4Sum 问题
    • 1.Two Sum I
    • 170.Two Sum III - Data structure design
    • 167.Two Sum II- Input array is sorted
    • 609.Two Sum - Less than or equal to target
    • 610.Two Sum - Difference equals to targe
    • 587.Two Sum - Unique pairs
    • 533.Two Sum - Closest to target
    • 443.Two Sum - Greater than target
    • 653. Two Sum IV - Input is a BST (M)
    • 57.3Sum
    • 59.3Sum Closest
    • 58.4Sum
    • 148.Sort Colors
    • 143.Sort Colors II
    • 31.Partition Array
    • 625.Partition Array II
    • 382.Triangle Count
      • 611. Valid Triangle Number
    • 521.Remove Duplicate Numbers in Array
    • 167. Two Sum II - Input Array Is Sorted (E)
    • 870. Advantage Shuffle (M)
    • 9. Palindrome Number (E)
    • 125. Valid Palindrome(E)
    • 5. Longest Palindromic Substring (M)
    • 42. Trapping Rain Water
    • 11. Container With Most Water (M)
    • 658. Find K Closest Elements (M)
    • 392. Is Subsequence
  • 8.Data Structure
    • Summary
      • 数据结构的存储方式
      • 单调栈
      • 单调队列
      • 二叉堆 Binary Heap
      • TreeMap
      • TreeSet
      • 🌟Trie
      • Trie Application
    • 155. Min Stack (E)
    • 716. Max Stack (E)
    • 1648. Sell Diminishing-Valued Colored Balls
    • 232. Implement Queue using Stacks (E)
    • 225. Implement Stack using Queues(E)
    • 84.Largest Rectangle in Histogram
    • 128.Hash Function
    • Max Tree
    • 544.Top k Largest Numbers
    • 545.Top k Largest Numbers II
    • 613.High Five
    • 606.Kth Largest Element II
    • 5.Kth Largest Element
    • 129.Rehashing
    • 4.Ugly Number II
    • 517.Ugly Number
    • 28. Implement strStr()
    • 594.strStr II
    • 146.LRU Cache
    • 460.LFU Cache
    • 486.Merge k Sorted Arrays
    • 130.Heapify
    • 215. Kth Largest Element in an Array (M)
    • 612.K Closest Points
    • 692. Top K Frequent Words
    • 347.Top K Frequent Elements
    • 601.Flatten 2D Vector
    • 540.Zigzag Iterator
    • 541.Zigzag Iterator II
    • 423.Valid Parentheses
    • 488.Happy Number
    • 547.Intersection of Two Arrays
    • 548.Intersection of Two Arrays II
    • 627.Longest Palindrome
    • 638.Strings Homomorphism
    • 138.Subarray Sum
    • 647.Substring Anagrams
    • 171.Anagrams
    • 739. Daily Temperatures(M)
    • 496. Next Greater Element I (E)
    • 503. Next Greater Element II(M)
    • 316. Remove Duplicate Letters(M) & 1081. Smallest Subsequence of Distinct Characters
    • 239. Sliding Window Maximum (H)
    • 355. Design Twitter (M)
    • 895. Maximum Frequency Stack (H)
    • 20. Valid Parentheses (E)
    • 921. Minimum Add to Make Parentheses Valid (M)
    • 1541. Minimum Insertions to Balance a Parentheses String (M)
    • 32. Longest Valid Parentheses (H)
    • Basic Calculator (*)
      • 224. Basic Calculator
      • 227. Basic Calculator II (M)
    • 844. Backspace String Compare
    • 295. Find Median from Data Stream
    • 208. Implement Trie (Prefix Tree)
    • 461.Kth Smallest Numbers in Unsorted Array
    • 1152.Analyze user website visit pattern
    • 811. Subdomain Visit Count (M)
    • 71. Simplify Path (M)
    • 362. Design Hit Counter
  • 9.Dynamic Programming
    • Summary
      • 最优子结构 Optimal Sustructure
      • 子序列解题模板
      • 空间压缩
      • 背包问题
        • Untitled
      • 股票买卖问题
      • KMP
    • 109.Triangle
    • 110.Minimum Path Sum
    • 114.Unique Paths
    • 115.Unique Paths II
    • 70.Climbing Stairs
    • 272.Climbing StairsII
    • 116.Jump Game
    • 117.Jump Game II
    • 322.Coin Change
    • 518. Coin Change 2 ()
    • Backpack I~VI
      • LintCode 563.Backpack V (M)
    • Best Time to Buy and Sell Stock(*)
      • 121. Best Time to Buy and Sell Stock
      • 122. Best Time to Buy and Sell Stock II (M)
      • 123. Best Time to Buy and Sell Stock III (H)
      • 188. Best Time to Buy and Sell Stock IV (H)
      • 309. Best Time to Buy and Sell Stock with Cooldown (M)
      • 714. Best Time to Buy and Sell Stock with Transaction Fee (M)
    • 394.Coins in a line
    • 395.Coins in a Line II
    • 509. Fibonacci Number (E)
    • 931. Minimum Falling Path Sum (M)
    • 494. Target Sum (M)
    • 72. Edit Distance (H)
    • 300.Longest Increasing Subsequence
    • 1143. Longest Common Subsequence (M)
    • 718. Maximum Length of Repeated Subarray
    • 583. Delete Operation for Two Strings (M)
    • 712. Minimum ASCII Delete Sum for Two Strings(M)
    • 53. Maximum Subarray (E)
    • 516. Longest Palindromic Subsequence (M)
    • 1312. Minimum Insertion Steps to Make a String Palindrome (H)
    • 416. Partition Equal Subset Sum (M)
    • 64. Minimum Path Sum(M)
    • 651. 4 Keys Keyboards (M)
    • House Robber (*)
      • 198. House Robber (M)
      • 213. House Robbber II
      • 337. House Robber III (M)
    • Word Break (*)
      • 139.Word Break (M)
    • 140. Word Break II (H)
    • 828. Count Unique Characters of All Substrings of a Given String (H)
    • 174. Dungeon Game (H)
    • 1567. Maximum Length of Subarray With Positive Product (M)
  • 10. Graph
    • Introduction
      • 有向图的环检测
      • 拓扑排序
      • 二分图判定
      • Union-Find
      • 最小生成树(Minimum Spanning Tree)算法
        • KRUSKAL 最小生成树算法
        • Prim 最小生成树算法
      • Dijkstra 最短路径算法
      • BFS vs DFS
    • 797. All Paths From Source to Target (M)
    • 785. Is Graph Bipartite? (M)
    • 886. Possible Bipartition (M)
    • 130. Surrounded Regions (M)
    • 990. Satisfiability of Equality Equations (M)
    • 721. Accounts Merge (M)
    • 323. Number of Connected Components in an Undirected Graph (M)
    • 261. Graph Valid Tree
    • 1135. Connecting Cities With Minimum Cost
    • 1584. Min Cost to Connect All Points (M)
    • 277. Find the Celebrity (M)
    • 743. Network Delay Time (M)
    • 1631. Path With Minimum Effort (M)
    • 1514. Path with Maximum Probability (M)
    • 589.Connecting Graph
    • 🌟787. Cheapest Flights Within K Stops (M)
    • 2050. Parallel Courses III (H)
    • 1293. Shortest Path in a Grid with Obstacles Elimination (H)
    • 864. Shortest Path to Get All Keys (H)
    • 269. Alien Dictionary (H)
    • 1192. Critical Connections in a Network (H)
    • 529. Minesweeper (M)
  • 11.Math
    • Page 1
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  1. 3.Breadth First Search

752. Open the Lock

https://leetcode.com/problems/open-the-lock/

You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'. The wheels can rotate freely and wrap around: for example we can turn '9' to be '0', or '0' to be '9'. Each move consists of turning one wheel one slot.

The lock initially starts at '0000', a string representing the state of the 4 wheels.

You are given a list of deadends dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.

Given a target representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.

Example 1:

Input: deadends = ["0201","0101","0102","1212","2002"], target = "0202"
Output: 6
Explanation:
A sequence of valid moves would be "0000" -> "1000" -> "1100" -> "1200" -> "1201" -> "1202" -> "0202".
Note that a sequence like "0000" -> "0001" -> "0002" -> "0102" -> "0202" would be invalid,
because the wheels of the lock become stuck after the display becomes the dead end "0102".

Example 2:

Input: deadends = ["8888"], target = "0009"
Output: 1
Explanation:
We can turn the last wheel in reverse to move from "0000" -> "0009".

Example 3:

Input: deadends = ["8887","8889","8878","8898","8788","8988","7888","9888"], target = "8888"
Output: -1
Explanation:
We can't reach the target without getting stuck.

Example 4:

Input: deadends = ["0000"], target = "8888"
Output: -1

Constraints:

  • 1 <= deadends.length <= 500

  • deadends[i].length == 4

  • target.length == 4

  • target will not be in the list deadends.

  • target and deadends[i] consist of digits only

Solution:

题目中描述的就是我们生活中常见的那种密码锁,若果没有任何约束,最少的拨动次数很好算,就像我们平时开密码锁那样直奔密码拨就行了。

但现在的难点就在于,不能出现 deadends,应该如何计算出最少的转动次数呢?

第一步,我们不管所有的限制条件,不管 deadends 和 target 的限制,就思考一个问题:如果让你设计一个算法,穷举所有可能的密码组合,你怎么做?

穷举呗,再简单一点,如果你只转一下锁,有几种可能?总共有 4 个位置,每个位置可以向上转,也可以向下转,也就是有 8 种可能对吧。

比如说从 "0000" 开始,转一次,可以穷举出 "1000", "9000", "0100", "0900"... 共 8 种密码。然后,再以这 8 种密码作为基础,对每个密码再转一下,穷举出所有可能…

仔细想想,这就可以抽象成一幅图,每个节点有 8 个相邻的节点,又让你求最短距离,这不就是典型的 BFS 嘛,框架就可以派上用场了,先写出一个「简陋」的 BFS 框架代码再说别的:

// 将 s[j] 向上拨动一次
String plusOne(String s, int j) {
    char[] ch = s.toCharArray();
    if (ch[j] == '9')
        ch[j] = '0';
    else
        ch[j] += 1;
    return new String(ch);
}
// 将 s[i] 向下拨动一次
String minusOne(String s, int j) {
    char[] ch = s.toCharArray();
    if (ch[j] == '0')
        ch[j] = '9';
    else
        ch[j] -= 1;
    return new String(ch);
}

// BFS 框架,打印出所有可能的密码
void BFS(String target) {
    Queue<String> q = new LinkedList<>();
    q.offer("0000");
    
    while (!q.isEmpty()) {
        int sz = q.size();
        /* 将当前队列中的所有节点向周围扩散 */
        for (int i = 0; i < sz; i++) {
            String cur = q.poll();
            /* 判断是否到达终点 */
            System.out.println(cur);

            /* 将一个节点的相邻节点加入队列 */
            for (int j = 0; j < 4; j++) {
                String up = plusOne(cur, j);
                String down = minusOne(cur, j);
                q.offer(up);
                q.offer(down);
            }
        }
        /* 在这里增加步数 */
    }
    return;
}

PS:这段代码当然有很多问题,但是我们做算法题肯定不是一蹴而就的,而是从简陋到完美的。不要完美主义,咱要慢慢来,好不。

这段 BFS 代码已经能够穷举所有可能的密码组合了,但是显然不能完成题目,有如下问题需要解决:

1、会走回头路。比如说我们从 "0000" 拨到 "1000",但是等从队列拿出 "1000" 时,还会拨出一个 "0000",这样的话会产生死循环。

2、没有终止条件,按照题目要求,我们找到 target 就应该结束并返回拨动的次数。

3、没有对 deadends 的处理,按道理这些「死亡密码」是不能出现的,也就是说你遇到这些密码的时候需要跳过。

如果你能够看懂上面那段代码,真得给你鼓掌,只要按照 BFS 框架在对应的位置稍作修改即可修复这些问题:

int openLock(String[] deadends, String target) {
    // 记录需要跳过的死亡密码
    Set<String> deads = new HashSet<>();
    for (String s : deadends) deads.add(s);
    // 记录已经穷举过的密码,防止走回头路
    Set<String> visited = new HashSet<>();
    Queue<String> q = new LinkedList<>();
    // 从起点开始启动广度优先搜索
    int step = 0;
    q.offer("0000");
    visited.add("0000");
    
    while (!q.isEmpty()) {
        int sz = q.size();
        /* 将当前队列中的所有节点向周围扩散 */
        for (int i = 0; i < sz; i++) {
            String cur = q.poll();
            
            /* 判断是否到达终点 */
            if (deads.contains(cur))
                continue;
            if (cur.equals(target))
                return step;
            
            /* 将一个节点的未遍历相邻节点加入队列 */
            for (int j = 0; j < 4; j++) {
                String up = plusOne(cur, j);
                if (!visited.contains(up)) {
                    q.offer(up);
                    visited.add(up);
                }
                String down = minusOne(cur, j);
                if (!visited.contains(down)) {
                    q.offer(down);
                    visited.add(down);
                }
            }
        }
        /* 在这里增加步数 */
        step++;
    }
    // 如果穷举完都没找到目标密码,那就是找不到了
    return -1;
}

至此,我们就解决这道题目了。有一个比较小的优化:可以不需要 dead 这个哈希集合,可以直接将这些元素初始化到 visited 集合中,效果是一样的,可能更加优雅一些。

Followup:

可以使用双向 BFS 算法来提高效率的,代码稍加修改即可:

int openLock(String[] deadends, String target) {
    Set<String> deads = new HashSet<>();
    for (String s : deadends) deads.add(s);
    // 用集合不用队列,可以快速判断元素是否存在
    Set<String> q1 = new HashSet<>();
    Set<String> q2 = new HashSet<>();
    Set<String> visited = new HashSet<>();
    
    int step = 0;
    q1.add("0000");
    q2.add(target);
    
    while (!q1.isEmpty() && !q2.isEmpty()) {
        // 哈希集合在遍历的过程中不能修改,用 temp 存储扩散结果
        Set<String> temp = new HashSet<>();

        /* 将 q1 中的所有节点向周围扩散 */
        for (String cur : q1) {
            /* 判断是否到达终点 */
            if (deads.contains(cur))
                continue;
            if (q2.contains(cur))
                return step;
            visited.add(cur);

            /* 将一个节点的未遍历相邻节点加入集合 */
            for (int j = 0; j < 4; j++) {
                String up = plusOne(cur, j);
                if (!visited.contains(up))
                    temp.add(up);
                String down = minusOne(cur, j);
                if (!visited.contains(down))
                    temp.add(down);
            }
        }
        /* 在这里增加步数 */
        step++;
        // temp 相当于 q1
        // 这里交换 q1 q2,下一轮 while 就是扩散 q2
        q1 = q2;
        q2 = temp;
    }
    return -1;
}

双向 BFS 还是遵循 BFS 算法框架的,只是不再使用队列,而是使用 HashSet 方便快速判断两个集合是否有交集。

另外的一个技巧点就是 while 循环的最后交换 q1 和 q2 的内容,所以只要默认扩散 q1 就相当于轮流扩散 q1 和 q2。

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