[Leedcode] Necessary interview questions and proof questions for circular linked lists (with pictures)

Necessary interview questions and proof questions for circular linked lists (with diagrams)

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foreword

This article introduces two interview questions related to the circular linked list and the extended proof questions (with source code + diagram)

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1. The first question

1. Topic

141. Ring linked list: as follows (example):

给你一个链表的头节点 head ，判断链表中是否有环。

如果链表中有某个节点，可以通过连续跟踪next指针再次到达，则链表中存在环。
为了表示给定链表中的环，评测系统内部使用整数pos来表示链表尾连接到链表中的位置(索引从0开始).
注意：pos 不作为参数进行传递。仅仅是为了标识链表的实际情况。

如果链表中存在环 ，则返回 true  否则，返回 false 

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2. Ideas

slow and fast point to the beginning of the linked list, slow takes one step at a time, fast takes two steps at a time, fast without a ring will go to the empty, fast with a ring will catch up with slow, as shown in the figure below !

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3. Code

The code is as follows (example):

struct ListNode 
{
    
    
     int val;
     struct ListNode *next;
};
bool hasCycle(struct ListNode *head) 
{
    
    
    struct ListNode* slow = head , *fast = head;
    while(fast && fast -> next)
    {
    
    
        slow = slow -> next;
        fast = fast -> next -> next;
        if(slow == fast)
        {
    
    
            return true;
        }
    }
    return false;
}

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4. Extended Questions

(1) Proof Question 1:

Topic: As follows (example):
Why do slow and fast meet in the ring? Will you miss it in the ring and never meet it?

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Conclusion: As follows (example):
They will definitely meet, but proof is needed!

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Proof of analysis: as follows (example):

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(2) Proof Question 2:

Topic: As follows (example):
Why do slow take one step and fast take two steps? Can fast take n steps at a time (n>2)?

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Conclusion: As follows (example):
When n>2, they may not meet each other and need to be proved!

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Proof of analysis: as follows (example):

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2. The second question

1. Topic

142. Ring linked list 2: as follows (example):

给定一个链表的头节点head，返回链表开始入环的第一个节点。如果链表无环，则返回null。

如果链表中有某个节点，可以通过连续跟踪next指针再次到达，则链表中存在环。
为了表示给定链表中的环，评测系统内部使用整数pos来表示链表尾连接到链表中的位置（索引从0开始）。
如果pos是-1，则在该链表中没有环。注意：pos不作为参数进行传递，仅仅是为了标识链表的实际情况。

不允许修改链表。

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2. Ideas + extended proof questions

Idea/Conclusion: As follows (example):

A pointer starts from the meeting point, and a pointer starts from the head of the linked list, and they will meet at the entry point of the ring!

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The proof method (1) is shown in the figure below

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The proof method (2) is shown in the figure below

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Summarize

The above is what I want to talk about today. This article introduces the necessary interview questions and proof questions for circular linked lists (solutions with attached pictures).
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