《剑指offer》第二十三题：链表中环的入口结点

// 面试题23：链表中环的入口结点
// 题目：一个链表中包含环，如何找出环的入口结点？例如，在图3.8的链表中，
// 环的入口结点是结点3。

#include <cstdio>
#include "list.h"

ListNode* MeetingNode(ListNode* pHead)
{
    if (pHead == nullptr) //空节点
        return nullptr;

    ListNode* pSlow = pHead->m_pNext; //单节点
    if (pSlow == nullptr)
        return nullptr;

    ListNode* pFast = pSlow->m_pNext;
   
    while (pFast != nullptr && pSlow != nullptr)
    {
        if (pFast == pSlow)
            return pFast;

        pSlow = pSlow->m_pNext;
        pFast = pFast->m_pNext;
        if (pFast != nullptr) //快节点走两步
            pFast = pFast->m_pNext;
    }
    return nullptr;
}

ListNode* EntryNodeOfLoop(ListNode* pHead)
{
    //1.首先遍历链表查找是否存在环
    ListNode* meetingNode = MeetingNode(pHead);
    if (meetingNode == nullptr)
        return nullptr;

    //2.然后算出环的长度n
    int length = 1;
    ListNode* pNode = meetingNode;
    while (pNode->m_pNext != meetingNode)
    {
        pNode = pNode->m_pNext;
        ++length;
    }

    //3.接着指针1先走n步
    ListNode* pNodeFast = pHead;
    for (int i = 0; i < length; ++i)
        pNodeFast = pNodeFast->m_pNext;

    //4.最后指针12同时往前遍历, 相等时即入口
    pNode = pHead;
    while (pNode != pNodeFast)
    {
        pNode = pNode->m_pNext;
        pNodeFast = pNodeFast->m_pNext;
    }
    return pNode;
}

// ==================== Test Code ====================
void Test(const char* testName, ListNode* pHead, ListNode* entryNode)
{
    if (testName != nullptr)
        printf("%s begins: ", testName);

    if (EntryNodeOfLoop(pHead) == entryNode)
        printf("Passed.\n");
    else
        printf("FAILED.\n");
}

// A list has a node, without a loop
void Test1()
{
    ListNode* pNode1 = CreateListNode(1);

    Test("Test1", pNode1, nullptr);

    DestroyList(pNode1);
}

// A list has a node, with a loop
void Test2()
{
    ListNode* pNode1 = CreateListNode(1);
    ConnectListNodes(pNode1, pNode1);

    Test("Test2", pNode1, pNode1);

    delete pNode1;
    pNode1 = nullptr;
}

// A list has multiple nodes, with a loop 
void Test3()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode4, pNode5);
    ConnectListNodes(pNode5, pNode3);

    Test("Test3", pNode1, pNode3);

    delete pNode1;
    pNode1 = nullptr;
    delete pNode2;
    pNode2 = nullptr;
    delete pNode3;
    pNode3 = nullptr;
    delete pNode4;
    pNode4 = nullptr;
    delete pNode5;
    pNode5 = nullptr;
}

// A list has multiple nodes, with a loop 
void Test4()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode4, pNode5);
    ConnectListNodes(pNode5, pNode1);

    Test("Test4", pNode1, pNode1);

    delete pNode1;
    pNode1 = nullptr;
    delete pNode2;
    pNode2 = nullptr;
    delete pNode3;
    pNode3 = nullptr;
    delete pNode4;
    pNode4 = nullptr;
    delete pNode5;
    pNode5 = nullptr;
}

// A list has multiple nodes, with a loop 
void Test5()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode4, pNode5);
    ConnectListNodes(pNode5, pNode5);

    Test("Test5", pNode1, pNode5);

    delete pNode1;
    pNode1 = nullptr;
    delete pNode2;
    pNode2 = nullptr;
    delete pNode3;
    pNode3 = nullptr;
    delete pNode4;
    pNode4 = nullptr;
    delete pNode5;
    pNode5 = nullptr;
}

// A list has multiple nodes, without a loop 
void Test6()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode4, pNode5);

    Test("Test6", pNode1, nullptr);

    DestroyList(pNode1);
}

// Empty list
void Test7()
{
    Test("Test7", nullptr, nullptr);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();

    return 0;
}

分析：双指针解决。 

/*
struct ListNode {
    int val;
    struct ListNode *next;
    ListNode(int x) :
        val(x), next(NULL) {
    }
};
*/
class Solution {
public:
    ListNode* EntryNodeOfLoop(ListNode* pHead)
    {
        //1.寻找环
        ListNode* meetingNode = MeetingNode(pHead);
        if (meetingNode == nullptr)
            return nullptr;
        
        //2.确定环长n
        int length = 1;
        ListNode* pNode = meetingNode;
        while (pNode->next != meetingNode)
        {
            pNode = pNode->next;
            ++length;
        }
        
        //3.指针1先走n步
        pNode = pHead;
        for (int i = 0; i < length; ++i)
            pNode = pNode->next;
            
        //4.指针12同时遍历，相遇时即为起点
        ListNode* pNode2 = pHead;
        while (pNode != pNode2)
        {
            pNode = pNode->next;
            pNode2 = pNode2->next;
        }
        return pNode;
    }
    ListNode* MeetingNode(ListNode* pHead)
    {
        if (pHead == nullptr)
            return nullptr;
        
        ListNode* pSlow = pHead->next;
        if (pSlow == nullptr)
            return nullptr;
        
        ListNode* pFast = pSlow->next;
        while (pFast != nullptr && pSlow != nullptr)
        {
            if (pFast == pSlow)
                return pFast;
            
            pSlow = pSlow->next;
            pFast = pFast->next;
            if (pFast != nullptr)
                pFast = pFast->next;
        }
        return nullptr;
    }
};