剑指offer

// 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。

ListNode* FindFirstNode(ListNode* HeadNode)
{
    if(!HeadNode)
        return nullptr;
    ListNode* FastNode = HeadNode;
    ListNode* SlowNode = HeadNode;
    while(FastNode&(FastNode->NextPoint))
    {
        SlowNode = SlowNode->NextPoint;
        FastNode = SlowNode->NextPoint;
        if(FastNode == SlowNode)
        {
            SlowNode = HeadNode;
            while(FastNode != SlowNode)
            {
                FastNode = FastNode->NextPoint;
                SlowNode = SlowNode->NextPoint;
            }
            return SlowNode;
        }
    }
    return nullptr;
}

//找到链表中环形链表的入口点
ListNode* FindTheFirstNode(ListNode* Node)
{
    if(Node ==nullptr)
        return nullptr;
    ListNode* Fastp = Node;
    ListNode  Slowp = Node;
    while((Fastp!= Slowp)&(Fastp!=nullptr))
    {
        Fastp = Fastp->NextPoint->NextPoint;
        Slowp = Slowp->NextPoint;
    }
    Slowp =Node;
    while(SLowp != Fastp)
    {
        Slowp = Slowp->NextPoint;
        Fastp = Fastp->NextPoint;
    }
    return slowp;
}

　　// 面试题22：链表中倒数第k个结点
// 题目：输入一个链表，输出该链表中倒数第k个结点。为了符合大多数人的习惯，
// 本题从1开始计数，即链表的尾结点是倒数第1个结点。例如一个链表有6个结点，
// 从头结点开始它们的值依次是1、2、3、4、5、6。这个链表的倒数第3个结点是
// 值为4的结点。

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

ListNode* FindKthToTail(ListNode* pListHead, unsigned int k)
{
    if(pListHead == nullptr || k == 0)
        return nullptr;

    ListNode *pAhead = pListHead;
    ListNode *pBehind = nullptr;

    for(unsigned int i = 0; i < k - 1; ++ i)
    {
        if(pAhead->m_pNext != nullptr)
            pAhead = pAhead->m_pNext;
        else
        {
            return nullptr;
        }
    }

    pBehind = pListHead;
    while(pAhead->m_pNext != nullptr)
    {
        pAhead = pAhead->m_pNext;
        pBehind = pBehind->m_pNext;
    }

    return pBehind;
}

// ====================测试代码====================
// 测试要找的结点在链表中间
void Test1()
{
    printf("=====Test1 starts:=====
");
    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);

    printf("expected result: 4.
");
    ListNode* pNode = FindKthToTail(pNode1, 2);
    PrintListNode(pNode);

    DestroyList(pNode1);
}

// 测试要找的结点是链表的尾结点
void Test2()
{
    printf("=====Test2 starts:=====
");
    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);

    printf("expected result: 5.
");
    ListNode* pNode = FindKthToTail(pNode1, 1);
    PrintListNode(pNode);

    DestroyList(pNode1);
}

// 测试要找的结点是链表的头结点
void Test3()
{
    printf("=====Test3 starts:=====
");
    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);

    printf("expected result: 1.
");
    ListNode* pNode = FindKthToTail(pNode1, 5);
    PrintListNode(pNode);

    DestroyList(pNode1);
}

// 测试空链表
void Test4()
{
    printf("=====Test4 starts:=====
");
    printf("expected result: nullptr.
");
    ListNode* pNode = FindKthToTail(nullptr, 100);
    PrintListNode(pNode);
}

// 测试输入的第二个参数大于链表的结点总数
void Test5()
{
    printf("=====Test5 starts:=====
");
    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);

    printf("expected result: nullptr.
");
    ListNode* pNode = FindKthToTail(pNode1, 6);
    PrintListNode(pNode);

    DestroyList(pNode1);
}

// 测试输入的第二个参数为0
void Test6()
{
    printf("=====Test6 starts:=====
");
    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);

    printf("expected result: nullptr.
");
    ListNode* pNode = FindKthToTail(pNode1, 0);
    PrintListNode(pNode);

    DestroyList(pNode1);
}

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

    return 0;
}

 // 面试题52：两个链表的第一个公共结点
// 题目：输入两个链表，找出它们的第一个公共结点。

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

unsigned int GetListLength(ListNode* pHead);

ListNode* FindFirstCommonNode(ListNode *pHead1, ListNode *pHead2)
{
    // 得到两个链表的长度
    unsigned int nLength1 = GetListLength(pHead1);
    unsigned int nLength2 = GetListLength(pHead2);
    int nLengthDif = nLength1 - nLength2;

    ListNode* pListHeadLong = pHead1;
    ListNode* pListHeadShort = pHead2;
    if(nLength2 > nLength1)
    {
        pListHeadLong = pHead2;
        pListHeadShort = pHead1;
        nLengthDif = nLength2 - nLength1;
    }

    // 先在长链表上走几步，再同时在两个链表上遍历
    for(int i = 0; i < nLengthDif; ++i)
        pListHeadLong = pListHeadLong->m_pNext;

    while((pListHeadLong != nullptr) &&
        (pListHeadShort != nullptr) &&
        (pListHeadLong != pListHeadShort))
    {
        pListHeadLong = pListHeadLong->m_pNext;
        pListHeadShort = pListHeadShort->m_pNext;
    }

    // 得到第一个公共结点
    ListNode* pFisrtCommonNode = pListHeadLong;

    return pFisrtCommonNode;
}

unsigned int GetListLength(ListNode* pHead)
{
    unsigned int nLength = 0;
    ListNode* pNode = pHead;
    while(pNode != nullptr)
    {
        ++nLength;
        pNode = pNode->m_pNext;
    }

    return nLength;
}

// ====================测试代码====================
void DestroyNode(ListNode* pNode);

void Test(char* testName, ListNode* pHead1, ListNode* pHead2, ListNode* pExpected)
{
    if(testName != nullptr)
        printf("%s begins: ", testName);

    ListNode* pResult = FindFirstCommonNode(pHead1, pHead2);
    if(pResult == pExpected)
        printf("Passed.
");
    else
        printf("Failed.
");
}

// 第一个公共结点在链表中间
// 1 - 2 - 3 
//            6 - 7
//     4 - 5 /
void Test1()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);
    ListNode* pNode6 = CreateListNode(6);
    ListNode* pNode7 = CreateListNode(7);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode6);
    ConnectListNodes(pNode4, pNode5);
    ConnectListNodes(pNode5, pNode6);
    ConnectListNodes(pNode6, pNode7);

    Test("Test1", pNode1, pNode4, pNode6);

    DestroyNode(pNode1);
    DestroyNode(pNode2);
    DestroyNode(pNode3);
    DestroyNode(pNode4);
    DestroyNode(pNode5);
    DestroyNode(pNode6);
    DestroyNode(pNode7);
}

// 没有公共结点
// 1 - 2 - 3 - 4
//            
// 5 - 6 - 7
void Test2()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);
    ListNode* pNode6 = CreateListNode(6);
    ListNode* pNode7 = CreateListNode(7);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode5, pNode6);
    ConnectListNodes(pNode6, pNode7);

    Test("Test2", pNode1, pNode5, nullptr);

    DestroyList(pNode1);
    DestroyList(pNode5);
}

// 公共结点是最后一个结点
// 1 - 2 - 3 - 4 
//                7
//         5 - 6 /
void Test3()
{
    ListNode* pNode1 = CreateListNode(1);
    ListNode* pNode2 = CreateListNode(2);
    ListNode* pNode3 = CreateListNode(3);
    ListNode* pNode4 = CreateListNode(4);
    ListNode* pNode5 = CreateListNode(5);
    ListNode* pNode6 = CreateListNode(6);
    ListNode* pNode7 = CreateListNode(7);

    ConnectListNodes(pNode1, pNode2);
    ConnectListNodes(pNode2, pNode3);
    ConnectListNodes(pNode3, pNode4);
    ConnectListNodes(pNode4, pNode7);
    ConnectListNodes(pNode5, pNode6);
    ConnectListNodes(pNode6, pNode7);

    Test("Test3", pNode1, pNode5, pNode7);

    DestroyNode(pNode1);
    DestroyNode(pNode2);
    DestroyNode(pNode3);
    DestroyNode(pNode4);
    DestroyNode(pNode5);
    DestroyNode(pNode6);
    DestroyNode(pNode7);
}

// 公共结点是第一个结点
// 1 - 2 - 3 - 4 - 5
// 两个链表完全重合   
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);

    Test("Test4", pNode1, pNode1, pNode1);

    DestroyList(pNode1);
}

// 输入的两个链表有一个空链表
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);

    Test("Test5", nullptr, pNode1, nullptr);

    DestroyList(pNode1);
}

// 输入的两个链表有一个空链表
void Test6()
{
    Test("Test6", nullptr, nullptr, nullptr);
}

void DestroyNode(ListNode* pNode)
{
    delete pNode;
    pNode = nullptr;
}

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

    return 0;
}

　// 面试题51：数组中的逆序对
// 题目：在数组中的两个数字如果前面一个数字大于后面的数字，则这两个数字组
// 成一个逆序对。输入一个数组，求出这个数组中的逆序对的总数。

　

#include <cstdio>

int InversePairsCore(int* data, int* copy, int start, int end);

int InversePairs(int* data, int length)
{
    if(data == nullptr || length < 0)
        return 0;

    int* copy = new int[length];
    for(int i = 0; i < length; ++i)
        copy[i] = data[i];

    int count = InversePairsCore(data, copy, 0, length - 1);
    delete[] copy;

    return count;
}

int InversePairsCore(int* data, int* copy, int start, int end)
{
    if(start == end)
    {
        copy[start] = data[start];
        return 0;
    }

    int length = (end - start) / 2;

    int left = InversePairsCore(copy, data, start, start + length);
    int right = InversePairsCore(copy, data, start + length + 1, end);

    // i初始化为前半段最后一个数字的下标
    int i = start + length;
    // j初始化为后半段最后一个数字的下标
    int j = end;
    int indexCopy = end;
    int count = 0;
    while(i >= start && j >= start + length + 1)
    {
        if(data[i] > data[j])
        {
            copy[indexCopy--] = data[i--];
            count += j - start - length;
        }
        else
        {
            copy[indexCopy--] = data[j--];
        }
    }

    for(; i >= start; --i)
        copy[indexCopy--] = data[i];

    for(; j >= start + length + 1; --j)
        copy[indexCopy--] = data[j];

    return left + right + count;
}

// ====================测试代码====================
void Test(char* testName, int* data, int length, int expected)
{
    if(testName != nullptr)
        printf("%s begins: ", testName);

    if(InversePairs(data, length) == expected)
        printf("Passed.
");
    else
        printf("Failed.
");
}

void Test1()
{
    int data[] = { 1, 2, 3, 4, 7, 6, 5 };
    int expected = 3;

    Test("Test1", data, sizeof(data) / sizeof(int), expected);
}

// 递减排序数组
void Test2()
{
    int data[] = { 6, 5, 4, 3, 2, 1 };
    int expected = 15;

    Test("Test2", data, sizeof(data) / sizeof(int), expected);
}

// 递增排序数组
void Test3()
{
    int data[] = { 1, 2, 3, 4, 5, 6 };
    int expected = 0;

    Test("Test3", data, sizeof(data) / sizeof(int), expected);
}

// 数组中只有一个数字
void Test4()
{
    int data[] = { 1 };
    int expected = 0;

    Test("Test4", data, sizeof(data) / sizeof(int), expected);
}


// 数组中只有两个数字，递增排序
void Test5()
{
    int data[] = { 1, 2 };
    int expected = 0;

    Test("Test5", data, sizeof(data) / sizeof(int), expected);
}

// 数组中只有两个数字，递减排序
void Test6()
{
    int data[] = { 2, 1 };
    int expected = 1;

    Test("Test6", data, sizeof(data) / sizeof(int), expected);
}

// 数组中有相等的数字
void Test7()
{
    int data[] = { 1, 2, 1, 2, 1 };
    int expected = 3;

    Test("Test7", data, sizeof(data) / sizeof(int), expected);
}

void Test8()
{
    int expected = 0;

    Test("Test8", nullptr, 0, expected);
}

int main(int argc, char* argv[])
{
    Test1();
    Test2();
    Test3();
    Test4();
    Test5();
    Test6();
    Test7();
    Test8();

    return 0;
}